Vibrations of multilayer plates under the effect ofimpulse loads. Three-dimensional theory

Abstract

A new analytical–numerical approach to investigation of the response of multilayerplates to impulse loading is described in this paper. The plates behaviour is described by theequations of the three-dimensional elasticity theory. According to the approach being proposed,the sought for functions included in the system of equations and the boundary and initialconditions are presented as Fourier series expansions in the tangential directions. The derivativesof these functions in the transverse direction are replaced by their finite-difference presentations.As a result of such transforms, the problem of vibration of a multilayer plate is reduced tointegration of a system of ordinary differential equations with constant coefficients. Integration isperformed by expansion into the Taylors series. The possibilities of the approach proposed andthe validity of results obtained is illustrated by several examples of calculating vibration processesand the processes of propagation of elastic waves. A comparison of the results obtained on thebasis of other approaches has been performed.