Recent zbMATH articles in MSC 74Jhttps://www.zbmath.org/atom/cc/74J2021-04-16T16:22:00+00:00WerkzeugWave propagation in structures. 3rd revised, updated and augmented edition.https://www.zbmath.org/1456.740762021-04-16T16:22:00+00:00"Doyle, James F."https://www.zbmath.org/authors/?q=ai:doyle.james-fPublisher's description: This third edition builds on the introduction of spectral analysis as a means of investigating wave propagation and transient oscillations in structures. Each chapter of the textbook has been revised, updated and augmented with new material, such as a modified treatment of the curved plate and cylinder problem that yields a relatively simple but accurate spectral analysis. Finite element methods are now integrated into the spectral analyses to gain further insights into the high-frequency problems. In addition, a completely new chapter has been added that deals with waves in periodic and discretized structures. Examples for phononic materials meta-materials as well as genuine atomic systems are given.
See the reviews of the first and second editions in [Zbl 0715.73022; Zbl 0876.73018].Lamb wave scattering by a symmetric pair of surface-breaking cracks in a plate.https://www.zbmath.org/1456.740882021-04-16T16:22:00+00:00"Golato, Andrew"https://www.zbmath.org/authors/?q=ai:golato.andrew"Demirli, Ramazan"https://www.zbmath.org/authors/?q=ai:demirli.ramazan"Santhanam, Sridhar"https://www.zbmath.org/authors/?q=ai:santhanam.sridharSummary: The scattering problem of a Lamb wave incident on a symmetric pair of surface-breaking transverse cracks in a plate is considered. The Lamb wave is assumed to be obliquely incident on the crack plane. Since the cracks are part-through, the scattered field will contain reflected as well as transmitted waves. The energy of the incoming wave is partitioned into reflected and transmitted wave modes. Energy coefficients of the reflected and transmitted waves are calculated as a function of incident frequency and crack depth. The incidence angle of the incoming wave is also treated as a parameter. Both the reflected and transmitted wave fields are considered as linear superpositions of all real and complex wave modes in the plate. Decomposition of modes is achieved with the help of an orthogonality condition based on the principle of reciprocal work. Continuity of displacement and stress fields is imposed at the crack plane. Energy coefficients for reflection and transmission are obtained from the mode amplitudes. Energy coefficients are shown to be a strong function of incident frequency and crack depth. Experiments are conducted with a PZT transducer network interacting with a symmetric pair of machined cracks in an aluminum plate. Trends predicted by the analysis are reflected in the experimental results.Time-domain computation of the response of composite layered anisotropic plates to a localized source.https://www.zbmath.org/1456.740102021-04-16T16:22:00+00:00"Ducasse, Eric"https://www.zbmath.org/authors/?q=ai:ducasse.eric"Deschamps, Marc"https://www.zbmath.org/authors/?q=ai:deschamps.marcSummary: This paper describes how a modal approach in the time-domain can be suitable for calculating the elastodynamic field in a layered plate. This elastodynamic field is generated by impulsive sources located in a small region of a composite plate consisting of anisotropic layers stuck together. The aim is to calculate the transient response of the elastic plate around the location of the sources, generally emitting \(n\)-cycle pulses. First, we apply a 2D Fourier transform to the wave equation with respect to the coordinates in the plate plane, and then, in the 2D spectrum domain, for any given wave-vector in the plate plane, solving a vibration problem with respect to time and position in the direction perpendicular to the plate. The solution is expressed as the sum of mode responses, each mode having a resonance frequency and a shape which depend on the wave-vector in the plate plane. These calculations are different from those obtained by the usual method in the harmonic domain, where the modes are searched for a fixed frequency, such as Lamb waves, i.e. guided waves that propagate along the plate. In our case, the solution is given as a summation of plate resonances, i.e. a decomposition on the real eigenfrequencies, associated to Lamb waves with the same fixed wave-vector. This difference is of importance since only Lamb modes with real frequencies and real-valued wavenumbers in the plate plane are involved here, contrary to the usual harmonic methods, where these modes can be evanescent. This is of great interest as it can simplify the calculation of the generated field near the source. Finally, we obtain a solution in the physical domain by performing an inverse 2D Fourier transform. After a detailed description of the method, results are shown for two typical plates. It is emphasized that the method is accurate for observation points located both above or below the source and reasonably far from it along the plate.High energy density in the collision of \(N\) kinks in the \(\phi^4\) model.https://www.zbmath.org/1456.740962021-04-16T16:22:00+00:00"Marjaneh, Aliakbar Moradi"https://www.zbmath.org/authors/?q=ai:moradi-marjaneh.aliakbar"Saadatmand, Danial"https://www.zbmath.org/authors/?q=ai:saadatmand.danial"Zhou, Kun"https://www.zbmath.org/authors/?q=ai:zhou.kun"Dmitriev, Sergey V."https://www.zbmath.org/authors/?q=ai:dmitriev.sergey-v"Zomorrodian, Mohammad Ebrahim"https://www.zbmath.org/authors/?q=ai:zomorrodian.mohammad-ebrahimSummary: Recently for the sine-Gordon equation it has been established that during collisions of \(N\) slow kinks maximal energy density increases as \(N^2\). In this numerical study, the same scaling rule is established for the non-integrable \(\phi^4\) model for \(N\leq 5\). For odd (even) \(N\) the maximal energy density is in the form of potential (kinetic) energy density. Maximal elastic strain is also calculated. In addition, the effect of the kink's internal modes on the maximal energy density is analysed for \(N=1\), 2, and 3. Our results suggest that in multi-soliton collisions very high energy density can be achieved in a controllable manner.Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media.https://www.zbmath.org/1456.740862021-04-16T16:22:00+00:00"Baydoun, I."https://www.zbmath.org/authors/?q=ai:baydoun.ibrahim"Savin, É."https://www.zbmath.org/authors/?q=ai:savin.eric"Cottereau, R."https://www.zbmath.org/authors/?q=ai:cottereau.regis"Clouteau, D."https://www.zbmath.org/authors/?q=ai:clouteau.didier"Guilleminot, J."https://www.zbmath.org/authors/?q=ai:guilleminot.johannSummary: In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneities -- the so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position \(\times\) wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as [\textit{G. Bal}, ibid. 43, No. 2, 132--157 (2005; Zbl 1231.76257)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.Effective resonant model and simulations in the time-domain of wave scattering from a periodic row of highly-contrasted inclusions.https://www.zbmath.org/1456.740932021-04-16T16:22:00+00:00"Touboul, Marie"https://www.zbmath.org/authors/?q=ai:touboul.marie"Pham, Kim"https://www.zbmath.org/authors/?q=ai:pham.kim-son"Maurel, Agnès"https://www.zbmath.org/authors/?q=ai:maurel.agnes"Marigo, Jean-Jacques"https://www.zbmath.org/authors/?q=ai:marigo.jean-jacques"Lombard, Bruno"https://www.zbmath.org/authors/?q=ai:lombard.bruno"Bellis, Cédric"https://www.zbmath.org/authors/?q=ai:bellis.cedricSummary: The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In [the second author et al., ``Two scale homogenization of a row of locally resonant inclusions -- the case of anti-plane shear waves'', J. Mech. Phys. Solids 106, 80--94 (2017; \url{doi:10.1016/j.jmps.2017.05.001})], two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.Space-time focusing of acoustic waves on unknown scatterers.https://www.zbmath.org/1456.740872021-04-16T16:22:00+00:00"Cassier, Maxence"https://www.zbmath.org/authors/?q=ai:cassier.maxence"Hazard, Christophe"https://www.zbmath.org/authors/?q=ai:hazard.christopheSummary: Consider a propagative medium, possibly inhomogeneous, containing some scatterers whose positions are unknown. Using an array of transmit-receive transducers, how can one generate a wave that would focus in space and time near one of the scatterers, that is, a wave whose energy would confine near the scatterer during a short time? The answer proposed in the present paper is based on the so-called DORT method (French acronym for: decomposition of the time reversal operator) which has led to numerous applications owing to the related space-focusing properties in the frequency domain, i.e., for time-harmonic waves. This method essentially consists in a singular value decomposition (SVD) of the scattering operator, that is, the operator which maps the input signals sent to the transducers to the measure of the scattered wave. By introducing a particular SVD related to the symmetry of the scattering operator, we show how to synchronize the time-harmonic signals derived from the DORT method to achieve space-time focusing. We consider the case of the scalar wave equation and we make use of an asymptotic model for small sound-soft scatterers, usually called the Foldy-Lax model. In this context, several mathematical and numerical arguments that support our idea are explored.Continuous dependence on the coefficients for a class of non-autonomous evolutionary equations.https://www.zbmath.org/1456.351942021-04-16T16:22:00+00:00"Waurick, Marcus"https://www.zbmath.org/authors/?q=ai:waurick.marcusSummary: The continuous dependence of solutions to certain equations on the coefficients is addressed. The class of equations under consideration has only recently be shown to be well posed. We give criteria that guarantee that convergence of the coefficients in the weak operator topology implies weak convergence of the respective solutions. We discuss three examples: A homogenization problem for a Kelvin-Voigt model for elasticity, the discussion of continuous dependence of the coefficients for acoustic waves with impedance type boundary conditions and a singular perturbation problem for a mixed type equation. By means of counterexamples, we show optimality of the results obtained.
For the entire collection see [Zbl 1420.78002].One-dimensional linear elastic waves at moving property interface.https://www.zbmath.org/1456.740742021-04-16T16:22:00+00:00"Shui, Lang-Quan"https://www.zbmath.org/authors/?q=ai:shui.langquan"Yue, Zhu-Feng"https://www.zbmath.org/authors/?q=ai:yue.zhufeng"Liu, Yong-Shou"https://www.zbmath.org/authors/?q=ai:liu.yongshou"Liu, Qing-Chang"https://www.zbmath.org/authors/?q=ai:liu.qingchang"Guo, Jiao-Jiao"https://www.zbmath.org/authors/?q=ai:guo.jiao-jiaoSummary: Smart materials exhibit time-varying properties while time-varying external field is applied. To investigate the one-dimensional (1-D) homogeneous time-varying properties, a moving property interface (MPI) model is proposed, and the propagation of linear elastic waves at 1-D MPI is studied in this paper. Based on the idea of weak solutions and an infinity approximation, a novel method to deal with the difficulties in using the continuities to study the waves at MPI is also proposed. Some interesting phenomena are revealed: (i) besides wave impedance, the property interface motion and wave velocity are also very important factors that influence the wave propagation; (ii) at MPI, there may exist shock waves; (iii) the property interface motion has a significant impact on the wave frequency and energy. This research provides a theoretical viewpoint in the study of smart materials with a time-dependent mechanical properties at different loading conditions.A facile method to realize perfectly matched layers for elastic waves.https://www.zbmath.org/1456.740692021-04-16T16:22:00+00:00"Chang, Zheng"https://www.zbmath.org/authors/?q=ai:chang.zheng"Guo, Dengke"https://www.zbmath.org/authors/?q=ai:guo.dengke"Feng, Xi-Qiao"https://www.zbmath.org/authors/?q=ai:feng.xiqiao"Hu, Gengkai"https://www.zbmath.org/authors/?q=ai:hu.gengkaiSummary: In perfectly matched layer (PML) technique, an artificial layer is introduced in the simulation of wave propagation as a boundary condition which absorbs all incident waves without any reflection. Such a layer is generally thought to be unrealizable due to its complicated material formulation. In this paper, on the basis of transformation elastodynamics and complex coordinate transformation, a novel method is proposed to design PMLs for elastic waves. By applying the conformal transformation technique, the proposed PML is formulated in terms of conventional constitutive parameters and then can be easily realized by functionally graded viscoelastic materials. We perform numerical simulations to validate the material realization and performance of this PML.The effect of rotation and initial stress on the propagation of waves in a transversely isotropic elastic solid.https://www.zbmath.org/1456.740812021-04-16T16:22:00+00:00"Ogden, Ray W."https://www.zbmath.org/authors/?q=ai:ogden.raymond-w"Singh, Baljeet"https://www.zbmath.org/authors/?q=ai:singh.baljeetSummary: In this paper the equations governing small amplitude motions in a rotating transversely isotropic initially stressed elastic solid are derived, both for compressible and incompressible linearly elastic materials. The equations are first applied to study the effects of initial stress and rotation on the speed of homogeneous plane waves propagating in a configuration with uniform initial stress. The general forms of the constitutive law, stresses and the elasticity tensor are derived within the finite deformation context and then summarized for the considered transversely isotropic material with initial stress in terms of invariants, following which they are specialized for linear elastic response and, for an incompressible material, to the case of plane strain, which involves considerable simplification. The equations for two-dimensional motions in the considered plane are then applied to the study of Rayleigh waves in a rotating half-space with the initial stress parallel to its boundary and the preferred direction of transverse isotropy either parallel to or normal to the boundary within the sagittal plane. The secular equation governing the wave speed is then derived for a general strain-energy function in the plane strain specialization, which involves only two material parameters. The results are illustrated graphically, first by showing how the wave speed depends on the material parameters and the rotation without specifying the constitutive law and, second, for a simple material model to highlight the effects of the rotation and initial stress on the surface wave speed.Finite element computation of trapped and leaky elastic waves in open stratified waveguides.https://www.zbmath.org/1456.740752021-04-16T16:22:00+00:00"Treyssède, F."https://www.zbmath.org/authors/?q=ai:treyssede.fabien"Nguyen, K. L."https://www.zbmath.org/authors/?q=ai:nguyen.khoa-lu|nguyen.khac-lan"Bonnet-BenDhia, A.-S."https://www.zbmath.org/authors/?q=ai:bonnet-ben-dhia.anne-sophie"Hazard, C."https://www.zbmath.org/authors/?q=ai:hazard.christopheSummary: Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an \textit{open} waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.Rayleigh waves with impedance boundary conditions in anisotropic solids.https://www.zbmath.org/1456.740842021-04-16T16:22:00+00:00"Vinh, Pham Chi"https://www.zbmath.org/authors/?q=ai:vinh.pham-chi"Thanh Hue, Trinh Thi"https://www.zbmath.org/authors/?q=ai:hue.trinh-thi-thanhSummary: The paper is concerned with the propagation of Rayleigh waves in an elastic half-space with impedance boundary conditions. The half-space is assumed to be orthotropic and monoclinic with the symmetry plane \(x_3 = 0\). The main aim of the paper is to derive explicit secular equations of the wave. For the orthotropic case, the secular equation is obtained by employing the traditional approach. It is an irrational equation. From this equation, a new version of the secular equation for isotropic materials is derived. For the monoclinic case, the method of polarization vector is used for deriving the secular equation and it is an algebraic equation of eighth-order. When the impedance parameters vanish, this equation coincides with the secular equation of Rayleigh waves with traction-free boundary conditions.Extraction of bulk wave characteristics from a pulsed ultrasonic polar scan.https://www.zbmath.org/1456.741022021-04-16T16:22:00+00:00"Kersemans, Mathias"https://www.zbmath.org/authors/?q=ai:kersemans.mathias"Lammens, Nicolas"https://www.zbmath.org/authors/?q=ai:lammens.nicolas"Degrieck, Joris"https://www.zbmath.org/authors/?q=ai:degrieck.joris"Van Den Abeele, Koen"https://www.zbmath.org/authors/?q=ai:van-den-abeele.koen"Pyl, Lincy"https://www.zbmath.org/authors/?q=ai:pyl.lincy"Zastavnik, Filip"https://www.zbmath.org/authors/?q=ai:zastavnik.filip"Sol, Hugo"https://www.zbmath.org/authors/?q=ai:sol.hugo"Van Paepegem, Wim"https://www.zbmath.org/authors/?q=ai:van-paepegem.wimSummary: The pulsed ultrasonic polar scan (P-UPS) technique provides a map with characteristic contours reflecting the critical bulk wave angles, which directly relate to the in-plane elastic properties of the insonified material spot. Besides these contours, additional information is captured in a P-UPS experiment which has particular importance for the inspection of anisotropic materials. By extensive post-processing on a single P-UPS experiment, we successfully extracted the local directional (i) critical bulk wave angles, (ii) phase velocity profiles, (iii) slowness curves, (iv) walk-off angles and (v) energy velocity profiles, for the three different polarization states of bulk waves. The procedure is demonstrated and discussed for an isotropic aluminum sample as well as an autoclave manufactured orthotropic \([0]_8\) carbon/epoxy laminate. In addition, a numerical and experimental investigation of the role of the immersion liquid as a lens for the P-UPS result is performed. This lensing effect permits to zoom in/out on the P-UPS fingerprint, hence broadening the class of materials which can be inspected by the P-UPS technique.Analysis of traveling waveform of flexible waveguides containing absorbent material along flanged junctions.https://www.zbmath.org/1456.740852021-04-16T16:22:00+00:00"Afzal, Muhammad"https://www.zbmath.org/authors/?q=ai:afzal.muhammad-zeshan|afzal.muhammad-u"Shafique, Sajid"https://www.zbmath.org/authors/?q=ai:shafique.sajid"Wahab, Abdul"https://www.zbmath.org/authors/?q=ai:wahab.abdul-fatahSummary: The traveling waveform of a flexible waveguide bounded by elastic plates and with an inserted expansion chamber having flanges at two junctions and a finite elastic membrane atop is investigated through a mode-matching technique. The modeled problem is governed by Helmholtz's equation and includes Dirichlet and higher-order boundary conditions. An acoustically absorbent lining is placed along the inner sides of the flanges at the junctions while their outer sides are kept rigid. Moreover, the edge conditions are imposed to define the physical behavior of the elastic membrane and plates at finite edges. The configuration is excited with the structure as well as fluid-borne modes. The influence of the imposed edge conditions at the connections of the plates and the prescribed incident forcing on the transmission-loss along the duct is elaborated. Specifically, the effects of edge conditions on the transmission-loss of structure-borne vibrations and fluid-borne noise are specified. The performance of low-frequency approximation is compared with that of the benchmark mode-matching method and is found to be in good agreement with relative merits. Apposite numerical simulations are performed to substantiate the validity of the mode-matching technique.Acoustic wave propagation in inhomogeneous, layered waveguides based on modal expansions and hp-FEM.https://www.zbmath.org/1456.761142021-04-16T16:22:00+00:00"Belibassakis, K. A."https://www.zbmath.org/authors/?q=ai:belibassakis.konstadinos-a"Athanassoulis, G. A."https://www.zbmath.org/authors/?q=ai:athanassoulis.gerassimos-a"Papathanasiou, T. K."https://www.zbmath.org/authors/?q=ai:papathanasiou.theodosios-k"Filopoulos, S. P."https://www.zbmath.org/authors/?q=ai:filopoulos.sotirios-p"Markolefas, S."https://www.zbmath.org/authors/?q=ai:markolefas.s-iSummary: A new model is presented for harmonic wave propagation and scattering problems in non-uniform, stratified waveguides, governed by the Helmholtz equation. The method is based on a modal expansion, obtained by utilizing cross-section basis defined through the solution of vertical eigenvalue problems along the waveguide. The latter local basis is enhanced by including additional modes accounting for the effects of inhomogeneous boundaries and/or interfaces. The additional modes provide implicit summation of the slowly convergent part of the local-mode series, rendering the remaining part to be fast convergent, increasing the efficiency of the method, especially in long-range propagation applications. Using the enhanced representation, in conjunction with an energy-type variational principle, a coupled-mode system of equations is derived for the determination of the unknown modal-amplitude functions. In the case of multilayered environments, \(h\)- and \(p\)-FEM have been applied for the solution of both the local vertical eigenvalue problems and the resulting coupled mode system, exhibiting robustness and good rates of convergence. Numerical examples are presented in simple acoustic propagation problems, illustrating the role and significance of the additional mode(s) and the efficiency of the present model, that can be naturally extended to treat propagation and scattering problems in more complex 3D waveguides.Temporal behavior of laser induced elastic plate resonances.https://www.zbmath.org/1456.741032021-04-16T16:22:00+00:00"Laurent, Jérôme"https://www.zbmath.org/authors/?q=ai:laurent.jerome"Royer, Daniel"https://www.zbmath.org/authors/?q=ai:royer.daniel"Prada, Claire"https://www.zbmath.org/authors/?q=ai:prada.claireSummary: This paper investigates the dependence on Poisson's ratio of local plate resonances in low attenuating materials. In our experiments, these resonances are generated by a pulse laser source and detected with a heterodyne interferometer measuring surface displacement normal to the plate. The laser impact induces a set of resonances that are dominated by Zero Group Velocity (ZGV) Lamb modes. For some Poisson's ratio, thickness-shear resonances are also detected. These experiments confirm that the temporal decay of ZGV modes follows a \(t^{- 0.5}\) law and show that the temporal decay of the thickness resonances is much faster. Similar decays are obtained by numerical simulations achieved with a finite difference code. A simple model is proposed to describe the thickness resonances. It predicts that a thickness mode decays as \(t^{- 1.5}\) for large times and that the resonance amplitude is proportional to \(D^{- 1.5}\) where \(D\) is the curvature of the dispersion curve \(\omega(k)\) at \(k = 0\). This curvature depends on the order of the mode and on the Poisson's ratio, and it explains why some thickness resonances are well detected while others are not.Three-dimensional mapped-grid finite volume modeling of poroelastic-fluid wave propagation.https://www.zbmath.org/1456.650842021-04-16T16:22:00+00:00"Lemoine, Grady I."https://www.zbmath.org/authors/?q=ai:lemoine.grady-iHybrid approaches for vibroacoustical problems based on the finite element method and statistical energy analysis.https://www.zbmath.org/1456.740362021-04-16T16:22:00+00:00"Müller, Gerhard"https://www.zbmath.org/authors/?q=ai:muller.gerhard|muller.gerhard-norbert"Buchschmid, Martin"https://www.zbmath.org/authors/?q=ai:buchschmid.martinSummary: The prediction of structure borne sound in vehicles or buildings and the induced sound fields in acoustic volumes is typically carried out either with a finite element (FEM) fluid-structure interaction (FSI) approach or with the help of energy methods like the statistical energy analysis (SEA). In the first part of the paper a coupled FEM/FSI approach for the calculation of vibrations and the radiated sound in adjacent cavities according to \textit{M. Buchschmid} [ITM-based FSI-models for rooms with absorptive boundaries. Aachen: Shaker Verlag; München: TU München (PhD Thesis) (2011)] is presented. For the description of the sound field in the cavity model reduction techniques are applied, superposing modes for reflective boundary conditions and form functions, which provide displacements at the FSI-interface. Wavenumber dependent impedances for complex boundaries like porous absorbers, which can be derived analytically, are introduced in the calculation scheme. In the second part of the paper an inverse SEA-like approach, which can be applied in the postprocessing of an FEM computation, is presented. For the description of the structural and acoustical response in the mid-frequency range time- and space-averaged subsystem energies are discussed as state variables. Consequently the excitation is described by means of the input power into the subsystems, which, in contrast to the SEA, do not have to be weakly coupled. The resulting kinetic and potential energies can be visualized for all substructures. The ratio between these energies provides an insight into the coupling-characteristics of adjacent structures.Weakly nonlinear wave interactions in multi-degree of freedom periodic structures.https://www.zbmath.org/1456.740282021-04-16T16:22:00+00:00"Manktelow, Kevin L."https://www.zbmath.org/authors/?q=ai:manktelow.kevin-l"Leamy, Michael J."https://www.zbmath.org/authors/?q=ai:leamy.michael-j"Ruzzene, Massimo"https://www.zbmath.org/authors/?q=ai:ruzzene.massimoSummary: This work presents a multiple time scales perturbation analysis for analyzing weakly nonlinear wave interactions in multi-degree of freedom periodic structures. The perturbation analysis is broadly applicable to (discretized) periodic systems in any dimensional space and with a wide range of constitutive nonlinearities. Specific emphasis is placed on cubic nonlinearity, as dispersion shifts typically arise from the cubic components in nonlinear restoring forces. The procedure is first presented in general. Then, application to the diatomic chain and monoatomic two-dimensional lattice demonstrates, individually, the treatment of multiple degree of freedom systems and higher dimensional spaces. The dispersion relations are modified by weakly nonlinear wave interactions and lead to additional opportunities to control wave propagation direction, band gap size, and group velocity. Numerical simulations validate the expected dispersion shifts. An amplitude-tunable focus device demonstrates the viability of utilizing dynamically-introduced dispersion to produce beam steering that may, ultimately, lead to a phononic superprism effect as well as multiplexing/demultiplexing behavior.Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures.https://www.zbmath.org/1456.740792021-04-16T16:22:00+00:00"Ge, Luyao"https://www.zbmath.org/authors/?q=ai:ge.luyao"Wang, Xinwei"https://www.zbmath.org/authors/?q=ai:wang.xinwei"Jin, Chunhua"https://www.zbmath.org/authors/?q=ai:jin.chunhua.1Summary: This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.Two dimensional self-similar expanding crack problems in elastic half-space.https://www.zbmath.org/1456.741432021-04-16T16:22:00+00:00"De, Ajit"https://www.zbmath.org/authors/?q=ai:de.ajitSummary: The application of the property of dynamic similarity is useful to the solution which admits a self-similarity or homogeneous form. One independent variable has been dropped in the present equivalent set of the governing equations. The displacement discontinuity on the crack face and also the displacement field on the surface due to an in-plane shear model over an expanding zone of slippage of arbitrary dip have been obtained. The moving slip edge extends towards the surface with a constant velocity. Cagniard De-Hoop technique has been used here to obtain the two dimensional exact transient response due to the slip in the vertical mode via body force equivalent. The results of the present paper are valid at least up to the time when the diffracted waves from the crack edge have not reached the receiving station. The spectral behavior of the source time function has also been discussed.Explicit expression of polarization vector for surface waves, slip waves, Stoneley waves and interfacial slip waves in anisotropic elastic materials.https://www.zbmath.org/1456.740822021-04-16T16:22:00+00:00"Ting, T. C. T."https://www.zbmath.org/authors/?q=ai:ting.thomas-c-tSummary: We present explicit expression of the polarization vector for surface waves and slip waves in an anisotropic elastic half-space, and Stoneley waves and interfacial slip waves in two dissimilar anisotropic elastic half-spaces. An unexpected result is that, in the case of interfacial slip waves, the polarization vector for the material in the half-space \(x_2 \geq 0\) does not depend explicitly on the material property in the half-space \(x_2 \leq 0\). It depends on the material property in the half-space \(x_2 \leq 0\) implicitly through the interfacial slip wave speed \(\upsilon\). The same is true for the polarization vector for the material in the half-space \(x_2 \leq 0\).From the Newton equation to the wave equation: the case of shock waves.https://www.zbmath.org/1456.741012021-04-16T16:22:00+00:00"Blanc, Xavier"https://www.zbmath.org/authors/?q=ai:blanc.xavier"Josien, Marc"https://www.zbmath.org/authors/?q=ai:josien.marcSummary: We study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, and Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show numerically and mathematically that if the distances between particles remain bounded, it is not the case any more when there are shocks at least for a convex nearest-neighbor interaction potential with convex derivative.The discrete Lamb problem: elastic lattice waves in a block medium.https://www.zbmath.org/1456.740772021-04-16T16:22:00+00:00"Aleksandrova, N. I."https://www.zbmath.org/authors/?q=ai:aleksandrova.n-iSummary: We study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the directions of the axes \(x, y\), and in the diagonal directions. The problem is solved by two methods. Analytically, we obtain asymptotic solutions in the vicinity of the Rayleigh wave at large time intervals. Numerically, we obtain a solution for any finite time interval. We compare these solutions with each other and with the solution to the Lamb problem for an elastic medium.The nonlinear analysis of elastic wave of piezoelectric crystal plate with perturbation method.https://www.zbmath.org/1456.740722021-04-16T16:22:00+00:00"Fan, Yanping"https://www.zbmath.org/authors/?q=ai:fan.yanping"Ji, Xiaojun"https://www.zbmath.org/authors/?q=ai:ji.xiaojun|ji.xiaojun.1"Liu, Xianping"https://www.zbmath.org/authors/?q=ai:liu.xianping"Cai, Ping"https://www.zbmath.org/authors/?q=ai:cai.pingSummary: When investigating or designing acoustic wave sensors, the behavior of piezoelectric devices is supposed to be linear. However, if the sensors are subjected to a strong elastic field, the amplitude of the elastic strain induced in the piezoelectric material is so large that the nonlinearity, which affects the stability and performance of the piezoelectric sensors, can no longer be ignored. In this paper, we perform a theoretical analysis on nonlinear anti-symmetric thickness vibration of thin-film acoustic wave resonators made from quartz. Using Green's identity, under the usual approximation of neglecting higher time harmonics, a perturbation analysis is performed from which the resonator frequency-amplitude (A-F) relation is obtained. Numerical calculations are made. Furthermore, the validity of the method is examined.Modulation of solitary waves and formation of stable attractors in granular scalar models subjected to on-site perturbation.https://www.zbmath.org/1456.740972021-04-16T16:22:00+00:00"Ben-Meir, Y."https://www.zbmath.org/authors/?q=ai:ben-meir.y"Starosvetsky, Y."https://www.zbmath.org/authors/?q=ai:starosvetsky.yuliSummary: Present work concerns the propagation of solitary waves in the array of coupled, uncompressed granular chains subjected to onsite perturbation. We devise a special analytical procedure depicting the modulation of solitary pulses caused by the inter-chain interaction as well as by the on-site perturbations of a general type. The proposed analytical procedure is very efficient in depicting both the transient response characterized by significant energy fluctuations between the chains as well as in predicting the formation of stable attractors corresponding to a steady state response. We confirm the validity of a general analytical procedure with several specific setups of granular scalar models. In particular we consider the response of the array of coupled granular chains free of perturbation as well as the arrays subject to the basic type of on-site perturbations such as the ones induced by the uniform and random elastic foundation, dissipation. Additional interesting finding made in the present study corresponds to the granular arrays subject to a special type of on-site perturbation containing the terms leading to the two opposing effects namely dissipation and energy sourcing. Interestingly enough this type of perturbation may lead to the formation of stable attractors. By the term attractors we refer to the stable, stationary pulses simultaneously forming on all the coupled chains and propagating with the same phase speed. It is important to emphasize that the analytical procedure developed in the first part of the study predicts the formation of stable attractors through a typical saddle-node bifurcation. Moreover, results of the reduced model are found to be in a spectacular agreement with those of the direct numerical simulations of the true model.Wave modelling in predictive vibro-acoustics: applications to rail vehicles and aircraft.https://www.zbmath.org/1456.740032021-04-16T16:22:00+00:00"Orrenius, Ulf"https://www.zbmath.org/authors/?q=ai:orrenius.ulf"Liu, Hao"https://www.zbmath.org/authors/?q=ai:liu.hao.1|liu.hao|liu.hao.2"Wareing, Andrew"https://www.zbmath.org/authors/?q=ai:wareing.andrew"Finnveden, Svante"https://www.zbmath.org/authors/?q=ai:finnveden.svante"Cotoni, Vincent"https://www.zbmath.org/authors/?q=ai:cotoni.vincentSummary: Three different predictive methods based on wave descriptions of the acoustic field are presented and used to calculate transmission and radiation properties of typical rail and aerospace structures. First, a transfer matrix method assesses the sound transmission and wavenumbers of composite sandwich fuselage structures in a wide frequency range. The method is computationally effective and can be used for numerical optimization of sandwich lay-ups common in rail and aerospace engineering. Further, an approach for which a small finite element model of a periodic cell is applied to create a statistical model of a near periodic structure is shown to determine transmission and radiation properties of stiffened fuselage structures and an extruded train floor structure. Finally, a novel combination of the waveguide FE method with the Rayleigh-Ritz method is applied to: (i) calculate the transmission through a double wall structure; (ii) again assess the sound transmission of an extruded floor structure and also (iii) determine the sound pressure inside a large section of a rail car excited by external sound sources. All three methods presented can be used to effectively support decision making in the design process of trains and aircraft.Bifurcations of traveling wave solutions for a generalized Camassa-Holm equation.https://www.zbmath.org/1456.350752021-04-16T16:22:00+00:00"Wei, Minzhi"https://www.zbmath.org/authors/?q=ai:wei.minzhi"Sun, Xianbo"https://www.zbmath.org/authors/?q=ai:sun.xianbo"Zhu, Hongying"https://www.zbmath.org/authors/?q=ai:zhu.hongyingSummary: In this paper, the traveling wave solutions for a generalized Camassa-Holm equation \(u_t-u_{xxt}=\frac{1}{2}(p+1)(p+2)u^pu_x-\frac{1}{2}p(p-1)u^{p-2}u_x^3-2pu^{p-1}u_xu_{xx}-u^pu_{xxx}\) are investigated. By using the bifurcation method of dynamical systems, three major results for this equation are highlighted. First, there are one or two singular straight lines in the two-dimensional system under some different conditions. Second, all the bifurcations of the generalized Camassa-Holm equation are given for \(p\) either positive or negative integer. Third, we prove that the corresponding traveling wave system of this equation possesses peakon, smooth solitary wave solution, kink and anti-kink wave solution, and periodic wave solutions.Traveling waves in trimer granular lattice. II: Asymptotic prediction of weakly attenuated pulses.https://www.zbmath.org/1456.740992021-04-16T16:22:00+00:00"Shiffer, A."https://www.zbmath.org/authors/?q=ai:shiffer.a"Jayaprakash, K. R."https://www.zbmath.org/authors/?q=ai:jayaprakash.k-r"Starosvetsky, Y."https://www.zbmath.org/authors/?q=ai:starosvetsky.yuliSummary: In the present study we consider the impulsive response of perfectly aligned, uncompressed, tri-atomic (trimer) granular lattice. In this study, we demonstrate that under particular choice of the system parameters -- impulsively loaded, trimer granular lattice can support formation of highly localized, weakly attenuated pulses. These pulses are manifested by the completely non-symmetric wave profiles and can be attributed to the special family of solitary like waves forming in the non-homogenous, periodic trimer granular lattice in the state of acoustic vacuum. Using the recently developed analytical procedure based on the singular, multi-scale perturbation analysis, we derive a simplified reduced order model predicting the special regions in the space of the system parameters corresponding to the formation of the weakly attenuated pulses. Predictions of the asymptotical model are found to be in very good agreement with the results of numerical simulations of the full trimer granular lattice. From a practical point of view, these results can have important implications in complex, structural optimization problems of wave manipulation in the repetitive granular metamaterials.
For Part I, see [the authors, Commun. Nonlinear Sci. Numer. Simul. 38, 8--22 (2016; Zbl 07247740)].High frequency vibroacoustics: a radiative transfer equation and radiosity based approach.https://www.zbmath.org/1456.740902021-04-16T16:22:00+00:00"Le Bot, A."https://www.zbmath.org/authors/?q=ai:le-bot.alain"Sadoulet-Reboul, E."https://www.zbmath.org/authors/?q=ai:sadoulet-reboul.emelineSummary: This paper is a review of the theoretical framework for the application of radiative transfer equations to structural dynamics and acoustics. It is shown that under the assumption of geometrical acoustics and when the phase of rays is neglected, a representation of a sound field in terms of incoherent fictitious sources provides a sufficiently large framework to embody diffuse as well as specular reflection, steady-state or transient phenomena and even diffraction. Two special cases are mentioned. The so-called radiosity method in acoustics corresponds to a purely diffusing boundary and statistical energy analysis when the sound field is diffuse.Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media.https://www.zbmath.org/1456.740702021-04-16T16:22:00+00:00"Craster, R. V."https://www.zbmath.org/authors/?q=ai:craster.richard-v"Joseph, L. M."https://www.zbmath.org/authors/?q=ai:joseph.l-m"Kaplunov, J."https://www.zbmath.org/authors/?q=ai:kaplunov.julius-dSummary: This article explores the deep connections that exist between the mathematical representations of dynamic phenomena in functionally graded waveguides and those in periodic media. These connections are at their most obvious for low-frequency and long-wave asymptotics where well established theories hold. However, there is also a complementary limit of high-frequency long-wave asymptotics corresponding to various features that arise near cut-off frequencies in waveguides, including trapped modes. Simultaneously, periodic media exhibit standing wave frequencies, and the long-wave asymptotics near these frequencies characterise localised defect modes along with other high-frequency phenomena. The physics associated with waveguides and periodic media are, at first sight, apparently quite different, however the final equations that distill the essential physics are virtually identical. The connection is illustrated by the comparative study of a periodic string and a functionally graded acoustic waveguide.Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach.https://www.zbmath.org/1456.740582021-04-16T16:22:00+00:00"Renno, Jamil M."https://www.zbmath.org/authors/?q=ai:renno.jamil-m"Mace, Brian R."https://www.zbmath.org/authors/?q=ai:mace.brian-rSummary: The vibration modelling of waveguide structures is considered. These structures comprise waveguides connected via joints. Traditionally, analytical models of the wave behaviour of such structures can be developed if they are simple (beams or rods connected at point joints, etc.). However, if the waveguides are of complicated constructions (truss-like, layered media, etc.) or the joints are complicated (e.g. of significant physical dimensions), obtaining the wave characteristics might be a formidable task. In this paper, such structures are modelled using a hybrid finite element/wave and finite element (FE/WFE) approach. The waveguides are modelled using the WFE method and thus their wave characteristics are obtained regardless of the complexity of their cross-section. The joints are modelled using standard FE, and the WFE and FE models are coupled to yield the scattering properties of the joints. The propagation and scattering models are assembled to describe the behaviour of the structure using relatively small models, while also providing information for other applications such as structure-borne sound, statistical energy analysis, etc. Numerical examples are presented to illustrate the approach.The wave based method: an overview of 15 years of research.https://www.zbmath.org/1456.350062021-04-16T16:22:00+00:00"Deckers, Elke"https://www.zbmath.org/authors/?q=ai:deckers.elke"Atak, Onur"https://www.zbmath.org/authors/?q=ai:atak.onur"Coox, Laurens"https://www.zbmath.org/authors/?q=ai:coox.laurens"D'Amico, Roberto"https://www.zbmath.org/authors/?q=ai:damico.roberto"Devriendt, Hendrik"https://www.zbmath.org/authors/?q=ai:devriendt.hendrik"Jonckheere, Stijn"https://www.zbmath.org/authors/?q=ai:jonckheere.stijn"Koo, Kunmo"https://www.zbmath.org/authors/?q=ai:koo.kunmo"Pluymers, Bert"https://www.zbmath.org/authors/?q=ai:pluymers.bert"Vandepitte, Dirk"https://www.zbmath.org/authors/?q=ai:vandepitte.dirk"Desmet, Wim"https://www.zbmath.org/authors/?q=ai:desmet.wimSummary: The Wave Based Method is a deterministic prediction technique to solve steady-state dynamic problems and is developed to overcome some of the frequency limitations imposed by element-based prediction techniques. The method belongs to the family of indirect Trefftz approaches and uses a weighted sum of so-called wave functions, which are exact solutions of the governing partial differential equations, to approximate the dynamic field variables. By minimising the errors on boundary and interface conditions, a system of equations is obtained which can be solved for the unknown contribution factors of each wave function. As a result, the system of equations is smaller and a higher convergence rate and lower computational loads are obtained as compared to conventional prediction techniques. On the other hand, the method shows its full efficiency for rather moderately complex geometries. As a result, various enhancements have been made to the method through the years, in order to extend the applicability of the Wave Based Method. This paper gives an overview of the current state of the art of the Wave Based Method, elaborating on the modelling procedure, a comparison of the properties of the Wave Based Method and element-based prediction techniques, application areas, extensions to the method such as hybrid and multi-level approaches and the most recent developments.Formulas for the slowness of Stoneley waves with sliding contact.https://www.zbmath.org/1456.740802021-04-16T16:22:00+00:00"Giang, P. T. H."https://www.zbmath.org/authors/?q=ai:giang.pham-thi-ha"Vĩnh, P. C."https://www.zbmath.org/authors/?q=ai:vinh.pham-chi"Anh, V. T. N."https://www.zbmath.org/authors/?q=ai:anh.vu-thi-ngocSummary: The main aim of this paper is to derive formulas for the slowness of Stoneley waves traveling along the sliding interface of two isotropic elastic half-spaces. These formulas have been obtained by employing the complex function method. From the derivation of them, it is shown that if a Stoneley wave exists, it is unique. Based on the obtained formulas, it is proved that a Stoneley wave is always possible for two isotropic elastic half-spaces with the same bulk wave velocities. This result leads to the fact that a Stoneley wave is always possible for two elastic half-spaces satisfying the Wiechert condition, a condition that plays an important role in acoustic analyses. The obtained formulas are of theoretical interest and they will be useful in practical applications, especially in nondestructive evaluations.Scattering of a plane harmonic SH wave by multiple layered inclusions.https://www.zbmath.org/1456.740922021-04-16T16:22:00+00:00"Sheikhhassani, Ramtin"https://www.zbmath.org/authors/?q=ai:sheikhhassani.ramtin"Dravinski, Marijan"https://www.zbmath.org/authors/?q=ai:dravinski.marijanSummary: Scattering of a plane harmonic SH wave by an arbitrary number of layered inclusions in a half-space is investigated by using a direct boundary integral equation method. The inclusions of arbitrary shape and placement are embedded within an elastic half-space. The effects of multiple scattering, the geometry, and the impedance contrast of the materials for layered inclusions and pipes are considered in detail.Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact.https://www.zbmath.org/1456.740832021-04-16T16:22:00+00:00"Vinh, Pham Chi"https://www.zbmath.org/authors/?q=ai:vinh.pham-chi"Anh, Vu Thi Ngoc"https://www.zbmath.org/authors/?q=ai:anh.vu-thi-ngoc"Thanh, Vu Phuong"https://www.zbmath.org/authors/?q=ai:thanh.vu-phuongSummary: In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.Resonances of three transverse standing-wave modes in a waveguide with periodic wall undulations.https://www.zbmath.org/1456.741002021-04-16T16:22:00+00:00"Tao, Zhi-Yong"https://www.zbmath.org/authors/?q=ai:tao.zhiyong"Fan, Ya-Xian"https://www.zbmath.org/authors/?q=ai:fan.ya-xianSummary: Interactions of three transverse modes are investigated in a waveguide with periodic walls. Resonances of two guided wave modes always result in forbidden bands for wave propagations when the wavenumber matching conditions are satisfied. As a third mode is involved due to the selected wall corrugations, we find that a single high-order mode can penetrate through the forbidden band based on the complex interactions. A method for generating a single high-order transverse mode is proposed by manipulating the multimode interactions. The numerical simulations on acoustic waveguides, showing the extreme suppression of the unwanted modes in the Bragg and non-Bragg gaps, demonstrate the validity and the efficiency of the proposed method.Elastic wave scattering and dynamic stress concentrations in exponential graded materials with two elliptic holes.https://www.zbmath.org/1456.740942021-04-16T16:22:00+00:00"Zhou, Chuanping"https://www.zbmath.org/authors/?q=ai:zhou.chuanping"Hu, Chao"https://www.zbmath.org/authors/?q=ai:hu.chao"Ma, Fai"https://www.zbmath.org/authors/?q=ai:ma.fai"Liu, Diankui"https://www.zbmath.org/authors/?q=ai:liu.diankuiSummary: Based on the elastodynamics, employing complex functions and conformal mapping methods, and local coordinates, the scattering of elastic waves and dynamic stress concentrations in infinite exponential graded materials with two holes are investigated. A general solution of the problem and expression satisfying the given boundary conditions are derived. The problem can be reduced to the solution of an infinite system of algebraic equations. As an example, numerical results of dynamic stress concentration factors for two elliptic holes in exponential graded materials are presented, and the influence of incident wave number and holes spacing on dynamic stress distributions is analyzed.Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides.https://www.zbmath.org/1456.740712021-04-16T16:22:00+00:00"Duru, Kenneth"https://www.zbmath.org/authors/?q=ai:duru.kenneth"Kreiss, Gunilla"https://www.zbmath.org/authors/?q=ai:kreiss.gunillaSummary: Perfectly matched layers (PMLs) are now a standard approach to simulate the absorption of waves in open domains. Wave propagation in elastic waveguides has the possibility to support back-propagating modes (propagating modes with oppositely directed group and phase velocities) with long wavelengths. Back-propagating modes can lead to temporally growing solutions in the PML. In this paper, we demonstrate that back-propagating modes in a two space dimensional isotropic elastic waveguide are not harmful to a discrete and finite width PML. Analysis and numerical experiments confirm the accuracy and stability of the PML.Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence.https://www.zbmath.org/1456.740952021-04-16T16:22:00+00:00"Blanloeuil, P."https://www.zbmath.org/authors/?q=ai:blanloeuil.philippe"Meziane, A."https://www.zbmath.org/authors/?q=ai:meziane.abdelouafi|meziane.anissa|meziane.ahmed|meziane.a-mohamed"Bacon, C."https://www.zbmath.org/authors/?q=ai:bacon.christopheSummary: A Finite Element (FE) model is proposed to study the interaction between in-plane elastic waves and a crack of different orientations. The crack is modeled by an interface of unilateral contact with Coulombs friction. These contact laws are modified to take into account a pre-stress \(\sigma_0\) that closes the crack. Using the FE model, it is possible to obtain the contact stresses during wave propagation. These contact stresses provide a better understanding of the coupling between the normal and tangential behavior under oblique incidence, and explain the generation of higher harmonics. This new approach is used to analyze the evolution of the higher harmonics obtained as a function of the angle of incidence, and also as a function of the excitation level. The pre-stress condition is a governing parameter that directly changes the nonlinear phenomenon at work at the interface and therefore the harmonic generation. The diffracted fields obtained by the nonlinear and linear models are also compared.Scattering of monochromatic elastic waves on a planar crack of arbitrary shape.https://www.zbmath.org/1456.740892021-04-16T16:22:00+00:00"Kanaun, S."https://www.zbmath.org/authors/?q=ai:kanaun.sergey|kanaun.sergei-kSummary: Scattering of monochromatic elastic waves on~an isolated planar crack of arbitrary shape is considered. The 2D-integral equation for the crack opening vector is discretized by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem have forms of standard one-dimensional integrals that can be tabulated. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz structure, and the corresponding matrix-vector products can be calculated by the fast Fourier transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. Examples of calculations of crack opening vectors, dynamic stress-intensity factors, and differential cross-sections of circular (penny-shaped) and non-circular cracks for various incident wave fields are presented. For a penny-shaped crack and longitudinal incident waves normal to the crack plane, an efficient semi-analytical method of the solution of the scattering problem is developed. The results of both methods are compared in a wide frequency region of the incident field.Complex wavenumber Fourier analysis of the B-spline based finite element method.https://www.zbmath.org/1456.741492021-04-16T16:22:00+00:00"Kolman, R."https://www.zbmath.org/authors/?q=ai:kolman.radek"Plešek, J."https://www.zbmath.org/authors/?q=ai:plesek.jiri"Okrouhlík, M."https://www.zbmath.org/authors/?q=ai:okrouhlik.miloslavSummary: We present the results of one-dimensional complex wavenumber Fourier analysis of the B-spline variant of Finite Element Method (FEM). Generally, numerical results of elastic wave propagation in solids obtained by FEM are polluted by dispersion and attenuation. It was shown for the higher-order B-spline based FEM, that the optical modes did not occur in the case of infinite domains, unlike the higher-order Lagrangian and Hermitian finite elements, and also the dispersion errors are smaller. The paper's main focus is on the wave propagation through B-spline multi-patch/segment discretization with the \(C0\) connection of B-spline segments and, chiefly, to the determining of dispersion and attenuation dependences. The numerical approach employed leads to substantial minimization of dispersion errors. Furthermore, the errors decrease in line with the increasing order of the B-spline elements/segments, with the local refinement, and also by the particular choice of the positions of control points through the optimizing procedure.Lamb wave mode decomposition for structural health monitoring.https://www.zbmath.org/1456.741042021-04-16T16:22:00+00:00"Park, Ilwook"https://www.zbmath.org/authors/?q=ai:park.ilwook"Jun, Yongju"https://www.zbmath.org/authors/?q=ai:jun.yongju"Lee, Usik"https://www.zbmath.org/authors/?q=ai:lee.usikSummary: Lamb waves propagate over large distances in plate-like thin structures and they have received great attention in the structural health monitoring (SHM) field as an efficient means to inspect a large area of a structure by using only a small number of sensors. The times-of-flight of the Lamb wave modes are useful for detecting damage generated in a structure. However, due to the dispersive and multi-mode nature of Lamb waves, it is very challenging to decompose Lamb wave modes into symmetric and anti-symmetric modes for potential applications to structural health monitoring. Thus, we propose an efficient Lamb wave mode decomposition method based on two fundamental rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of \(A_0\) and \(S_0\) modes must be constant. The mode amplitude ratio rule means that the ratio of the magnitudes of \(A_0\) and \(S_0\) modes in a measured response signal must be always greater than one once the center frequency of the input signal is determined, such that the magnitude of the \(A_0\) mode in the excited signal is larger than that of the \(S_0\) mode, and \textit{vice versa}. The proposed method is verified through experiments conducted for a plate specimen.Low-frequency wave propagation in post-buckled structures.https://www.zbmath.org/1456.740982021-04-16T16:22:00+00:00"Maurin, Florian Paul Robert"https://www.zbmath.org/authors/?q=ai:maurin.florian-paul-robert"Spadoni, Alessandro"https://www.zbmath.org/authors/?q=ai:spadoni.alessandroSummary: Nonlinear wave propagation in solids and material structures provides a physical basis to derive nonlinear canonical equations which govern disparate phenomena such as vortex filaments, plasma waves, and traveling loops. Nonlinear waves in solids however remain a challenging proposition since nonlinearity is often associated with irreversible processes, such as plastic deformations. Finite deformations, also a source of nonlinearity, may be reversible as for hyperelastic materials. In this work, we consider geometric bucking as a source of reversible nonlinear behavior. Namely, we investigate wave propagation in initially compressed and post-buckled structures with linear-elastic material behavior. Such structures present both intrinsic dispersion, due to buckling wavelengths, and nonlinear behavior. We find that dispersion is strongly dependent on pre-compression and we compute waves with a dispersive front or tail. In the case of post-buckled structures with large initial pre-compression, we find that wave propagation is well described by the KdV equation. We employ finite-element, difference-differential, and analytical models to support our conclusions.In-plane wave motion and resonance phenomena in periodically layered composites with a crack.https://www.zbmath.org/1456.740732021-04-16T16:22:00+00:00"Golub, Mikhail V."https://www.zbmath.org/authors/?q=ai:golub.mikhail-v"Zhang, Chuanzeng"https://www.zbmath.org/authors/?q=ai:zhang.chuanzengSummary: This paper investigates the transmission and propagation of two-dimensional (2D) time-harmonic plane waves in periodically multilayered elastic composites with a strip-like crack. The total wave field in the composite structure is represented as a sum of the incident wave field determined by the transfer matrix method and the scattered wave field described by integral representations in terms of the Green's matrices and the crack-opening-displacements. A numerical scheme is developed to compute the wave propagation characteristics and the crack-characterizing quantities. The effects of the crack location and size as well as the angle of wave incidence are investigated using the averaged crack-opening-displacements and the stress intensity factors. Special attention of the paper is devoted to resonance wave motion and wave localization phenomena in a stack of periodical elastic layers weakened by a single strip-like crack. Numerical results are presented and discussed to reveal the usual and the resonant wave transmission by using the power-density vector and the energy streamlines in the vicinity of the crack. Wave localization due to interior and interface cracks is analyzed by considering the energy captured by a crack, and resonance induced crack growth is also discussed.\(N\) masses on an infinite string and related one-dimensional scattering problems.https://www.zbmath.org/1456.740912021-04-16T16:22:00+00:00"Martin, P. A."https://www.zbmath.org/authors/?q=ai:martin.paul-andrew|martin.philippa-a|martin.paulo-aSummary: One-dimensional time-harmonic waves interact with a finite number of scatterers: they could be beads on a long string, for example. If the scatterers are identical and equally spaced, such periodic problems can be solved exactly. One problem solved here arises when one scatterer in a periodic row is forced to oscillate, giving the Green function for the row. Our main interest is with disordered problems, where a periodic configuration is disturbed. Two problems are studied. First, just one scatterer in a finite periodic row is displaced: an exact solution is obtained for the transmission coefficient and its average over all allowable displacements. Second, a similar problem is treated where each scatterer is displaced by a small distance from its position in the periodic row. The main tools used are perturbation theory and transfer matrices.On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves.https://www.zbmath.org/1456.740782021-04-16T16:22:00+00:00"Bonnet-Ben Dhia, Anne-Sophie"https://www.zbmath.org/authors/?q=ai:bonnet-ben-dhia.anne-sophie"Chambeyron, Colin"https://www.zbmath.org/authors/?q=ai:chambeyron.colin"Legendre, Guillaume"https://www.zbmath.org/authors/?q=ai:legendre.guillaumeSummary: An efficient method to compute the scattering of a guided wave by a localized defect, in an elastic waveguide of infinite extent and bounded cross section, is considered. It relies on the use of perfectly matched layers (PML) to reduce the problem to a bounded portion of the guide, allowing for a classical finite element discretization. The difficulty here comes from the existence of backward propagating modes, which are not correctly handled by the PML. We propose a simple strategy, based on finite-dimensional linear algebra arguments and using the knowledge of the modes, to recover a correct approximation to the solution with a low additional cost compared to the standard PML approach. Numerical experiments are presented in the two-dimensional case involving Rayleigh-Lamb modes.