压电复合悬臂梁非线性模型及求解

基于功能材料的复合悬臂梁涉及多物理场耦合，其本构关系的非线性影响悬臂梁的输出及控制精度，采用Helmholtz Gibbs自由能关系建立压电材料的非线性本构模型。基于Boltzmann原理，该模型的内核函数由热能和Gibbs能量平衡决定。将模型与悬臂梁结构进行耦合，利用边界和初始条件导出压电复合悬臂梁的强解形式，并对强解进行弱化，采用Galerkin法对弱解进行离散化，利用三次B样条函数得到悬臂梁的数值解。研究结果表明，与已有文献的实验进行比较，所建立的压电材料非线性本构模型能够较好地预测复合悬臂梁的行为。

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.