Dynamic approach for finding effective elastic and piezoelectric constants of superlattices

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 properties for propagation in any plane defined by an arbitrary direction and the superlattice axis are contained in a 6×6 system matrix requiring for its construction only 29 (at most) material constants from a total of 46. The computation of an equivalent system matrix for a superlattice is demonstrated, and the manner of obtaining the equivalent density, 6 permittivities, 21 stiffness, and 18 piezoelectric constants is given