On forced vibrations in the linear theory of micropolar elasticity

Abstract

This study is concerned with the problem of determining the dynamic response of a finite micropolar elastic body subject to time-dependent surface loads, body forces, and body moments. Under the assumption of the existence of an infinite set of natural frequencies and eigenfunctions for the general free vibration problem, the general orthogonality condition is derived. The solution of the general forced motion problem consists of a superposition or the ‘quasi static’ and ‘dynamic’ portions of the displacements, rotations, force stresses, and couple stresses. A convenient, simple expression for the generalized forces is developed on the basis of certain symmetry properties of the general theory of micropolar elasticity. As a specific example, the forced thickness-shear vibrations of an infinite plate are studied.