Variational principles for dynamic problems for inhomogeneous elastic media

Abstract Some new variational principles for elastodynamic problems, which reduce to the Hashin-Shtrikman principle in the static limit, are presented. They are deduced from dynamical analogues of the classical energy principles of elastostatics by performing appropriate rearrangements and then neglecting certain terms that are quadratic in a measure of the error associated with the approximating trial fields. One of the new principles is then employed to develop equations that provide an approximate description of waves in a random composite. These equations make optimal use of the pair correlations of the composite, in the sense that better approximation (relative to the variational principle) would unavoidably involve correlations of higher order.