On the dynamic behavior of thin elastic plates

摘要

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.Two wave propagation problems are considered: the propagation of acoustic waves in a fluid slab and the propagation of elastic waves in an elastic slab.When formulated in terms of nondimensional variables these problems depend explicitly on two small parameters [epsilon] and [delta]. The parameter [epsilon] provides a measure of the thinness of the slabs considered and the parameter [delta] measures the impulsiveness of the applied excitation or loading. Approximation solutions of the problems considered are obtained consisting of several parts, each part having the form of a power series expansion in the parameters [epsilon] and [delta].The most important result obtained is the development of the approximate theories - the plate wave equation and the Euler-Bernoulli plate equation - directly from the full equations of dynamic elasticity using a rational perturbation expansion technique.