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Analyzing and tuning longitudinal-wave bands in periodic piezoelectric rods

A hybrid method, which combines the method of reverberation-ray matrix (MRRM) and the transfer matrix method (TMM), is presented for the analysis of longitudinal-wave bands in periodic piezoelectric rods. The unit cell of the periodic rods is made of alternate piezoelectric and elastic rods modeled by the Love Rod Theory. The transversal effect of the piezoelectric rods is exploited. The MRRM is introduced to derive the member transfer matrix of the constituent rods. The global transfer matrix of the unit cell is obtained by further considering the continuous conditions between the adjacent rods. Due to the Floquet-Bloch principle, the propagation constants are found to be the natural logarithm of the eigenvalues of the global transfer matrix. The frequency spectra representing the longitudinal-wave bands can then be drawn. Numerical examples are given to validate the proposed hybrid method and to illustrate the influences of high frequency, the Poisson's effect of the constituent rods, the thickness of the electrodes and the applied electric capacity and voltage on the frequency bands. These effects can be used to passively or actively tune the longitudinal-wave bands in periodic piezoelectric composite structures.