NONLIEAR BENDING WAVES OF A PIEZOELECTRIC LAMINATED BEAM WITH ELECTRICAL BOUNDARY1)

Abstract

Nonlinear science has been an important symbol in the development of modern science, especially the researches in nonlinear dynamics and nonlinear waves have extraordinary significance in solving the complex phenomena and problems encountered in various fields of natural science. In this paper, the nonlinear bending wave propagation of a piezoelectric laminated beam with electrical boundary conditions is studied. Firstly, considering the geometric nonlinear effect and piezoelectric coupling effect, the nonlinear equation of the one-dimensional infinite rectangular piezoelectric laminated beams is established by using Hamiltonian principle. Secondly, the Jacobi elliptic function expansion method is used to treat the nonlinear flexural wave equation, and the corresponding shock wave solution and solitary wave solution of the nonlinear flexural wave equation are obtained in the approximate case. Last, the nonlinear Schrodinger equation is obtained by using the reduced perturbation method, and the bright and dark soliton solutions are further obtained. Moreover, the effects of external voltage and the thickness of the piezoelectric layer on the characteristics of shock wave and solitary wave as well as bright and dark solitons are studied. The results show that when the wave velocity is small, the external voltage has a great influence on the shock wave, and when the wave velocity is large, the external voltage has no effect on the solitary wave. The bright solitons and the dark solitons can be obtained by adjusting the external voltage applied to the piezoelectric laminated beam. It is found that the amplitudes of bright and dark solitons increase with the increase of external voltages.