Methods for Computing 3D Steady-State Vibrations of Composites Using Green’s Functions

Abstract

Spatial steady-state harmonic vibrations of an infinite layered composite plate with an arbitrary elastic anisotropy of each layer are considered in this paper. The required vector of mechanical displacements of arbitrary points for a layered structure can be represented in the form of a double inverse Fourier transform of the product of the Fourier transform of the Green’s matrix and the Fourier transform of the surface load vector. An algorithm for computing the Fourier inverse transform with the given load vector is presented. Reducing of the initial double integral to the repeated one and using Jordan’s lemma make it possible to present the displacement vector in terms of residues in real and complex poles of the Green’s matrix. The stationary phase method is applied for computing asymptotic representations of the displacement field in the far-field zone. Displacements on the surface of some various composites on the basis of graphite-epoxy material for two types of surface load were computed as numerical examples.