Wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam

The wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam is investigated in this paper by considering the mechanical–electrical coupling behavior. The strain energy and kinetic energy of each sub-cell are first formulated to extract the dynamic stiffness matrices, and then the compatibility and continuity conditions at the interface between the adjacent cells are utilized to derive the transfer matrix that governs the propagation of the wave along the periodic piezoelectric beam. By employing the Lyapunov exponent method, the dynamic behaviors of the periodic beam structure are evaluated with different base beam materials, dimension ratios, piezoelectric constants and elastic stiffness. The results indicate that regardless of the length ratio, there exist certain frequency intervals, where the width and magnitude of the prominent stop band of the aluminum beam with periodic piezoelectric patches are always broader and larger than those of the steel base system. In addition, as the thickness ratio decreases, the location of the stop band tends to move toward a higher frequency. Numerical studies also demonstrate that different piezoelectric constants and elastic stiffness affect the characteristics of wave propagation in completely different fashions. The investigation in the present study provides basic guidelines to design periodic elastic-piezoelectric laminate structures in order to achieve desired filtering characteristics.