On the piezoelectric signals of multilayer systems

We consider a longitudinal elastic standing wave propagating along the,dire ction of growth of a cubic piezoelectric multilayer system. The Stokes recu rrent relation connecting the generalized reflection coefficients of adjace nt interfaces are used to establish 2 x 2 transfer matrices relating the ne t wave displacements at such interfaces. Resonances in the standing piezoel ectric signals have been interpreted in terms of simple interference condit ions. It is shown that the peak value of the piezoelectric signals is propo rtional to the number of periods of the system, and is very sensitive to th e frequency of elastic waves. The piezoelectric signals are computed for an extensive range of frequencies. and the peak full width at half maximum is shown numerically to vary as the inverse of the number of periods. The sen sitivity itself varies quadratically with the number of periods.