Effective elastic and piezoelectric constants of superlattices

It is shown that the determination of a set of equivalent elastic constants for periodically layered anisotropic materials to predict the acoustic performance in the long wavelength limit can be extended on the one hand to include piezoelectricity of the component materials and on the other to allow multiple layers within each period. The necessary matrices are shown in a form which can be programmed easily. The validity of the use of these equivalent constants is shown by comparison of results obtained with them and with an exact layer-by-layer calculation both for bulk-wave slowness surfaces and for surface-wave propagation velocities in two quite different examples of material combinations.