Modulation of the bandgaps of in-plane elastic waves by out-of-plane wavenumber in the piezoelectric composite structures

摘要

We study theoretically the modulation of bandgaps of in-plane elastic waves by the out-of-plane wavenumber that is parallel to the piezoelectric material rod axis in piezoelectric composite structures. The dependence of bandgaps of in-plane elastic waves on the out-of-plane wavenumber and the filling fraction are calculated with and without the composite's piezoelectricity. The in-plane bandgaps can be opened (or closed) and the in-plane wave modes can be tuned by controlling the propagation of out-of-plane elastic waves. The in-plane bandgap in the low-frequency range can be easily obtained by introducing an out-of-plane wavenumber, and is almost independent of the composite's piezoelectricity. Meanwhile, the widths and starting frequencies of in-plane bandgaps in a relatively high-frequency range can be modulated by the filling fraction and the composite's piezoelectricity. The piezoelectric composite structure is very useful in the design of ultrasonic transducers to avoid the invalid modes of in-plane elastic waves without affecting the working modes corresponding to the out-of-plane wavenumber. The method to calculate the total transmission spectrum of elastic waves in this paper is useful to study piezoelectric composite structures with finite length in engineering applications.