General relationships for guided acoustic waves in anisotropic plates

Abstract

Some universal identities for plane elastic waves in free and clamped homogeneous plates of arbitrary anisotropy are obtained and analysed. Insight is gained by linking the dispersion of guided–wave phase velocity (or, more precisely, its derivative in wavenumber or frequency) to the Stroh matrix, i.e. to the coefficients of the governing system of wave motion equations in the sextic form, on the one hand, and to the energetic parameters, on the other. The derivation also involves the residues of the plate admittance (Gree's function in the transform domain) along a dispersion branch. Combining these complementary perspectives enables a general criterion for increasing or decreasing trends in the dispersion branches and provides useful interpretations of the difference between the phase velocity and the in–plane group velocity. Explicit examples at low, high and cut–off frequencies are presented. Limitations for the case of transversely inhomogeneous plates are discussed.