Parker, D. F. Waveform evolution for nonlinear surface acoustic waves. (English) Zbl 0627.73022 Int. J. Eng. Sci. 26, No. 1, 59-75 (1988). A new nonlinear analysis is given for the propagation of surface waves on a homogeneous, elastic half-space of general anisotropy. Avoiding the need for a multiple scale analysis, it yields the evolution equation for the Fourier transform of the surface elevation as a criterion ensuring that corrections to the displacements within linear theory are everywhere sufficiently small. For second-order elasticity, this equation is similar to that of R. W. Lardner [J. Elasticity 16, 63-73 (1986; Zbl 0575.73032)]. For periodic waveforms it reduces to an infinite set of ordinary differential equations governing the Fourier coefficients. The behaviour of special solutions is illustrated by numerical integration for a particular isotropic material. This confirms that initially sinusoidal waveforms steepen until the vertical velocities develop a singularity within each wavelength. However, waveforms which are initially close to be ‘nondistorting waveforms’ of Parker and Talbot [see P. Chadwick, ibid. 6, 73-80 (1976; Zbl 0332.73034)] may travel large distances without significant alteration to their dominant feature, which is one sharp peak per wavelength. Cited in 16 Documents MSC: 74J15 Surface waves in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 74E10 Anisotropy in solid mechanics 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:quadratic approximation; nonlinear analysis; homogeneous, elastic half- space; evolution equation; Fourier transform; surface elevation; second- order elasticity; periodic waveforms; infinite set of ordinary differential equations; Fourier coefficients; behaviour of special solutions; numerical integration; initially sinusoidal waveforms; nondistorting waveforms Citations:Zbl 0575.73032; Zbl 0332.73034 PDFBibTeX XMLCite \textit{D. F. Parker}, Int. J. Eng. Sci. 26, No. 1, 59--75 (1988; Zbl 0627.73022) Full Text: DOI References: [1] Kalyanasundaram, N., Int. J. Engng Sci., 19, 279 (1981) [2] Kalyanasundaram, N.; Ravindran, R.; Prasad, P., J. Acoust. Soc. Am., 72, 488 (1982) [3] Kalyanasundaram, N., J. Sound Vib., 96, 411 (1984) [4] Lardner, R. W., Int. J. Engng Sci., 21, 1331 (1983) [5] Lardner, R. W., Int. J. Engng Sci., 23, 113 (1985) [6] Lardner, R. W., J. Elast., 16, 63 (1986) [7] Planat, M., J. Appl. Phys., 57, 4911 (1985) [8] Parker, D. F.; Talbot, F. M., (Nigul, U.; Engelbrecht, J., Nonlinear Deformation Waves (1983), Springer: Springer Berlin) [9] Parker, D. F.; Talbot, F. M., J. Elast., 15, 389 (1985) [10] Chadwick, P., J. Elast., 6, 73 (1976) [11] A. SOKOLOV, private communication.; A. SOKOLOV, private communication. [12] Farnell, G. W.; Adler, E. L., (Mason, W. P.; Thurston, R. N., Physical Acoustics IX (1972), Academic Press: Academic Press New York) [13] David, E. A., Int. J. Engng Sci., 23, 699 (1985) [14] Murnaghan, F., Finite Deformation of an Elastic Solid (1951), Dover: Dover New York · Zbl 0045.26504 [15] Parker, D. F., (Maiellaro, M., Waves and Stability in Continuous Media III (1987)), Bari This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.