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A finite element formulation for multilayered and thick plates, based on a multilayered theory, which was previously applied to a static analysis is extended to include vibration and stability analyses. First, a mass matrix formulation is presented which is consistent with the stiffness coefficient derivation, namely a virtual work expression is obtained which is then evaluated through numerical differentiation. This is followed by a more general discussion of a geometric stiffness derivation which is seen within the concept of linear elastic stability. The geometric stiffness itself, in this context is the difference between the linear stiffness and the tangent stiffness where the tangent stiffness is evaluated, within the general nonlinear theory, usually at a unit load stress state. In both cases vibration and stability analysis, the usual generalized eigenvalue problem follows. In some applications for layered beams and plates the vibration and stability analysis presented is compared with exact solutions.

The method of singular surfaces was used in a recent paper to develop a numerical procedure for calculating the growth and decay of the amplitude of shock waves propagating into a one‐dimensional nonlinearly elastic body. Here we extend this approach to estimate the influence of such external effects as elastic support and viscous friction on the propagation of shocks. We conclude that even in the case of a homogeneous linearly elastic material these external effects account for some attenuation of the amplitude of the shock and/or the secondary waves. Further analysis of a nonlinear elastic material readily shows that an increase in the viscosity produces, among other things, a slower growth of the shock amplitude and that for some critical value it will even start with a decay. Numerical examples illustrate the applicability of the technique in the case of a homogeneous nonlinear elastic body subjected to external viscous friction.