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This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flugge and Timoshenko-Mindlin. The linear model, a general standard viscoelastic body, of the rheologic properties of a viscoelastic material was applied. The time and coordinate curves of the basic quantities displacement, rotation, velocity, stress and deformation are compared. The results obtained by an approximate analytic method are compared with numerical results for 3D plate generated by FEM application and with experimental investigation.

The grid dispersion for a harmonic Rayleigh wave propagating along a straight boundary of a thin elastic solid, modelled by finite elements, is investigated. It is shown that with an increase of dimensionless wavenumber γ · q , a phase velocity of Rayleigh waves increases from the long wave limit C R . For sufficiently short waves it follows the dispersion curve referring to quasitransverse waves in an unbounded discretized medium.

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.