DYNAMIC DISPLACEMENT TRACKING OF FORCE-LOADED LINEAR ELASTIC OR VISCOELASTIC BODIES BY EIGENSTRAIN-INDUCED ACTUATION STRESSES

摘要

The present paper is concerned with the dynamics of linear elastic or viscoelastic bodies under the action of transient forces, with prescribed time-dependent boundary conditions, and with given initial conditions, or with a given initial past history. We consider anisotropic linear elastic bodies, or anisotropic linear viscoelastic bodies that are described by a hereditary law of the Boltzmann type. We ask for an additional distribution of actuation stresses such that the resulting displacements of the body under consideration follow exactly some desired trajectories in every point and at every time instant. We present relations that must be satisfied for the actuation stresses in order that this goal of displacement tracking is reached. In order to promote practical realizations, we present several versions of our formulations. To our best knowledge, the theoretical results we are presenting in the present contribution are new. They extend some previous results of our group concerning elastic shape control, i.e. for the case that zero trajectories are tracked; the body then maintains its undistorted initial shape. The actuation stresses we have in mind for enforcing tracking of displacements are induced by eigenstrains, such as thermal expansion strains or piezoelectric parts of strain. Practical applications of our formulations seem to be visible for the dynamics of smart structures.