Band Gaps Of Periodic Piezoelectric Composite Plates

Since the periodic structure exhibits a unique dynamic character, the so-called frequency band gap in which the wave can not propagate; Piezoelectric material has been known as low-cost, lightweight, and easy-to-implement which can be used in many engineering field. The present thesis is to employ piezoelectric material to periodic structure, a type of composite periodic plate on which piezoelectric patches are periodically mounted is designed. Elastic waves whose frequency fall into the frequency gap can not propagate in periodic plate. So this thesis carries out theoretical analysis and numerical analysis on periodic piezoelectric plate, and the active control of the plate's band gaps by adjusting the gain constant of the controlling circuit has been investigated.The main works include four parts as following:1. The basic theory of periodic structure is introduced, including periodicity description and Bloch-Floquet theorem. The principle of differential quadrature method is elaborated, including the selection of weighting coefficients and the choice of sampling points.2. Band gap characteristics of periodic piezoelectric plate are studied. By changing the physical parameter and the geometric parameter of the unit cell, analyses the influencing factors on band gaps. The numerical results show that piezoelectric plate can generate complete band gaps or directional band gaps by designing reasonable parameters of unite cell.3. By numerical simulation of the finite periodic plate with mounted piezoelectric patches, the plate's vibration performances are researched. The simulation results show that elastic waves whose frequency fall into the frequency gap can not propagate in periodic plate.4. The active controllers are designed on the piezoelectric composite plate. By properly adjusting the gain parameters of controllers, the band gaps of the periodic piezoelectric plate can be changed actively, and the control process is simple and convenient.