Mokeyev, Vladimir V. A generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures. (English) Zbl 1017.74026 Int. J. Numer. Methods Eng. 50, No. 9, 2271-2282 (2001). Summary: We describe a generalized complex eigenvector method which can be used for linear dynamic analysis of viscoelastic structures. Here the dynamic analysis is understood as transient analysis and frequency response analysis. The generalized complex eigenvector method is based on finite element discretization of structures on the approximation of viscoelastic properties by differential operators, and on mode superposition technique. Coefficients of differential operator are defined from the condition of best matching of complex characteristics of viscoelastic material and complex characteristics of differential operator in a pre-set frequency range. Advantage of this method is that it allows to take into account the real changes of viscoelastic properties in frequency range. Also, the generalized complex eigenvector method allows to describe viscoelastic properties by two functions: complex Young’s modulus, and complex Poisson’s ratio. The method is verified by comparing its results with solutions obtained by complex modulus method. The effect of viscoelastic Poisson’s ratio on transient and frequency responses of structures is demonstrated. Cited in 1 Document MSC: 74H15 Numerical approximation of solutions of dynamical problems in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74S05 Finite element methods applied to problems in solid mechanics 74D05 Linear constitutive equations for materials with memory Keywords:heterogeneous viscoelastic structures; frequency response analysis; generalized complex eigenvector method; transient analysis; finite element discretization; differential operators; mode superposition technique; complex Young’s modulus; complex Poisson’s ratio PDFBibTeX XMLCite \textit{V. V. Mokeyev}, Int. J. Numer. Methods Eng. 50, No. 9, 2271--2282 (2001; Zbl 1017.74026) Full Text: DOI References: [1] Vibration Damping. Wiley: New York, 1985. [2] Johnson, AIAA Journal 20 pp 1284– (1982) · doi:10.2514/3.51190 [3] De Wilde, International Journal for Numerical Methods in Engineering 27 pp 429– (1989) · Zbl 0724.73223 · doi:10.1002/nme.1620270213 [4] Barkanov, International Journal for Numerical Methods in Engineering 44 pp 393– (1999) · Zbl 0927.74065 · doi:10.1002/(SICI)1097-0207(19990130)44:3<393::AID-NME511>3.0.CO;2-P [5] Greenenko, Mechanics and Computer Materials N3 pp 475– (1989) [6] Mokeyev, Communications in Numerical Methods in Engineering 14 pp 1– (1998) · Zbl 0899.65017 · doi:10.1002/(SICI)1099-0887(199801)14:1<1::AID-CNM123>3.0.CO;2-8 [7] Shock and Vibration Handbook. McGraw-Hill: New York, 1976. [8] Pritz, Journal of Sound and Vibration 214 pp 83– (1998) · doi:10.1006/jsvi.1998.1534 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.