基于非均匀光滑有限元法的功能梯度压电梁自由振动分析

摘要

In order to improve the solving precision of dynamic response problems of functionally gradient piezoelectric materials and soften the“over-stiffness”, an inhomogeneous Cell-based smoothed finite element method was presented. Based on gradient smoothing technique of elements and considering the change of gradient of material properties only in the breadth direction, the basic formula of inhomogeneous Cell-based smoothed finite element (ICS-FEM) was derived. Using this proposed method, free vibration characteristics of the functionally graded piezoelectric cantilever were analyzed when the material parameters followed different gradient distributions. The accuracy of the proposed method was confirmed by comparing the FEM results. The results show that the gradient smoothing technique can reduce the stiffness of the finite element system and improve the accuracy of the solution for electromechanical coupling systems by using ICS-FEM, which provides reference for further application of Cell-based smoothed finite element method.%为了提高求解功能梯度压电材料动响应的精度，克服有限元系统刚度偏硬的缺点，提出非均匀Cell-based 光滑有限元法。基于单元的梯度光滑操作，考虑材料物性沿宽度方向呈梯度连续变化，推导非均匀Cell-based光滑有限元法的基本公式，分析功能梯度压电悬臂梁的材料物性参数遵循不同梯度分布规律时结构自由振动的固有频率与振型，并与FEM求解结果进行对比。研究结果表明：光滑梯度操作可降低有限元系统的刚度，非均匀Cell-based光滑有限元法的数值解更加接近真实解，从而可为功能梯度压电材料的进一步应用提供参考。