Aspects of Saint-Venant's Principle in the Dynamical Theory of Linear Micropolar Elasticity

Abstract

A principle of Saint-Venant type is established for the theory of linear micropolar elastodynamics, and the connection that exists between this principle and the domain of influence theorems, uniqueness theorems, and continuous dependence theorems is discussed. The body, which is assumed to be of arbitrary regular shape and is subjected to loadings that possess a bounded support DT for the time interval [0, T], can be bounded or unbounded. According to this principle, there exists a constant c > 0 such that a certain energetic measure of the displacement vanishes for r > ct and decays to zero for r < ct, where r is the distance from a generic point to the support DT, and t is any time in the interval [0, T]. The decay rate is controlled by the factor 1 -r/(ct).