The Wave Motion Analysis Of Piezoelectric Laminated Beam/bar Under Impulse Load

Due to the good electromechanical performance, piezoelectric material has been applied extensively as intelligent devices involving sensor and actuator. Further to the above, it is being important function devices in various scientific fields and application fields, especially in space technology, automatic monitored control system, energy field, ocean exploration and even in biological technology application. The study of dynamic performance of the piezoelectric material has developed rapidly recently since it has been applied extensively and more problems in productive practice appeared.In recent years, wave motion analysis has been a topic of considerable interest in vibration control with many applications in engineering structure involving beam, plate and chord. The main reason is that due to the simplicity and the systematicness of the wave motion analysis. The wave motion analysis can extend the analysis to periodic elastic structure and quasi-periodic elastic structure. The other side, it is thought to be one of the most prospect method in intelligent structure monitored system since besides providing the transient response of the structure directly, it can also research the rule of the system energy’s transmission effectively.In this paper, piezoelectric laminated beam structure is investigated.The basic equations of dynamics of piezoelectric-elastic laminated beam/bar are established. The basic equations are simplified as the laminated piezoelectric-elastic beam/bar structure and the direction of wave propagation are given. The dispersion relations of wave propagation are derived by using the continuum conditions and the boundary conditions and solving the basic equations. For numerical example, the influence of the thickness of elastic layer and the thickness of piezoelectric layers on dispersion relations is discussed. The characteristics of wave propagation in piezoelectric-elastic laminated beam/bar structure are obtained.Appling the theory of wave motion, the dynamic analysis of the piezoelectric- elastic laminated bar under longitudinal impulse at free end is performed. The equations of wave propagation in the laminated bar are established using plane cross-section assumption. Displacement and electric potential expressions are obtained by solving the equations with Laplace transfer. The relations between displacement and electric potential are given when the wave propagation in the laminated bar. The influences of elastic modular and the thickness ratio of piezoelectric layer and elastic layer on wave speed, displacement and electric potential are discussed. The result indicated that the electric potential along thickness direction for linear distribution. The velocity of longitudinal impulse increases along with the Young’s modulus increases, reduces along with the thickness of piezoelectric layer increases.The dynamic response of piezoelectric laminated cantilever beam under transverse impulsive loading is studied by the method of wave motion. The equations of wave propagation in piezoelectric laminated beam are established by the differential method. The characteristics of the dispersion of the wave propagation are calculated by using the condition of nonzero solution based on the given shape functions and boundary conditions. The Fourier series are used to simulate the pulse and considering the dispersion relation and the boundary conditions, the amplitude coefficients of the transverse displacement and electric potential are obtained by solving the motion equations. The response curves of displacement and electric potential are obtained.