Uniqueness in elastodynamics for systems with nonlocal impedance boundary conditions

Abstract

It is shown that an elastodynamic initial-value boundary-value problem is unique if the stiffness and mass density are positive definite, and if the boundary conditions are such that the boundary is passive, i.e., that cannot do more work on the body than the body has done on the boundary. This includes impedance boundary conditions of the sort that are now being considered in structural acoustics to represent the effect of uncertain substructures on a known master structure. Uniqueness follows if the impedance is local or nonlocal, in space as well as time. The only requirement is that it be passive.