Dynamic approach for finding effective elastic and piezoelectric constants of superlattices

Abstract

A dynamic approach is presented for determining a set of equivalent elastic, piezoelectric, and permittivity constants for a superlattice consisting of a periodic multilayer of anisotropic materials. The objective is to predict the acoustic properties of such a periodic structure in the long-wavelength (low-frequency) limit. It is shown that the acoustic wave propagation properties for propagation in any plane defined by an arbitrary direction and the superlattice axis are contained in a 6×6 system matrix requiring only a subset of at most 29 material constants (from a total of 46) for its construction. The computation of an equivalent system matrix for a superlattice is demonstrated and the manner of obtaining the equivalent density, six permittivities, 21 stiffness, and 18 piezoelectric constants is given.