Recursive surface impedance matrix methods for ultrasonic wave propagation in piezoelectric multilayers

Two recursive surface impedance methods are described for acoustic wave propagation in multilayered piezoelectric structures. Both methods have the advantage of conceptual simplicity and flexibility brought about by the transfer matrix method. Moreover they do not have a priori computational limitations with respect to the total number of layers of the stratified structure nor with respect to the thickness of individual layers; nor is the computational stability limited by the frequency range. For both methods, numerical simulations were carried out in order to illustrate their performances and robustness when combined with suitable recursive numerical algorithms.