The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

Abstract

Vibrations may shorten the lifetime of structures and machines, cause discomfort in many cases (noise radiation) and are totally unwanted in precision engineering. The latter requires also static shape control. The method of unique decomposition of eigenstrains into two constituents, namely in impotent eigenstrains, that do not cause stress and in the complementary nilpotent eigenstrains that do not induce any deformation in the linear elastic solid is considered in detail. These two complete classes of eigenstrains render optimal solutions by keeping shape and stress-control problems well separated. Assuming a common time function of the dynamic load, a novel approach is addressed to annihilate the forced vibrations. This optimal benchmark solution may serve the purpose in practical application to select properly shaped actuator patches and the control current.