Nonlinear modeling and numerical solution of piezoelectric cantilever beam

Cantilever beam compositing functional material involves multi-physics, and the nonlinearity with its constitutive equations have unstable output performance and low control accuracy. A nonlinear constitutive model for piezoelectric materials is proposed in this paper, adopting Helmholtz and Gibbs energy relations. While establishing this model, the core functions are determined using the equilibrium between thermal and Gibbs energies according to Boltzmann principles. Then the model is coupled with the cantilever structure through the following steps: deriving the strong solutions of the piezoelectric cantilever beam by using the boundary and initial conditions, weakening the strong solutions, and discretizing the weak solutions by using the Galerkin method, in order to acquire the numerical solutions of the cantilever beam combining cubic B-spline function. The results of this paper show that compared with the experimental data in existing references, the nonlinear constitutive model for piezoelectric materials is capable of precisely predicting the behavior of the cantilever beam. ©, 2014, Nanjing University of Aeronautics an Astronautics. All right reserved.