Analysis of the impedance resonance of piezoelectric stacks

Inversion techniques to determine the complex material constants from the impedance data of a zero bond-length stack resonator are studied. The impedance equation examined in this paper is based on the derivation by Martin [G.E. Martin, JASA, 36, pp. 1496-1506, 1964]. The asymptotic solutions for the case where the number of layers n is large (n>8) and n small (n⩽2) are presented in terms of the complex material constants of the piezoelectric. When n =1 or 2, it is shown that the wave speed in the stack is determined by the open circuit elastic constant S^D₃₃. In the limit of large n, the wave speed is determined by the short circuit elastic constant S^E₃₃. Techniques to invert the impedance data to determine complex material constants are presented for all values of n. The error associated with using the impedance equations derived from fully short and fully open electrical boundary conditions is investigated. Since the model is based on material properties rather than circuit constants, it allows for the direct evaluation of specific aging or degradation mechanisms