Bending waves of a rectangular piezoelectric laminated beam

A simple nonlinear model is proposed in this paper to study the bending wave in a rectangular piezoelectric laminated beam of infinite length. Based on the constitutive relations for transversely isotropic piezoelectric materials and isotropic elastic materials, combined with some electric conditions, we derive the bending wave equation in a long rectangular piezoelectric laminated beam by using energy method. The nonlinearity considered is geometrically associated with the nonlinear normal strain in the longitudinal beam direction. The shock-wave solution, solitary-wave solution and other exact solutions of the bending wave equation are obtained by the extended F-expansion method. And by using the reductive perturbation method we derive the nonlinear Schrodinger (NLS) equation, further more, the bright and dark solitons are obtained. For those soliton solutions, and some parameters derived by the process of solving soliton solutions, some conclusions are drawn by numerical analysis with some fixed conditions.