A generalized formulation of elastodynamics: Small on rigid

The conventional theory of linearized elastodynamics addresses the case of motions that have small displacement gradients with respect to a reference configuration of the elastic body that is unstressed and at rest. Here, we develop a theory of much wider applicability in which the linearization is with respect to a reference configuration that is in rigid motion. More specifically, with an eye toward application of the theory to analysis of the motions of relatively inflexible machine parts, we view the motion as being composed of a rigid motion, which corresponds to the applied loads and initial conditions for the body under consideration, and an infinitesimal motion, in which the displacement from the rigid motion has a small gradient.