强电场下压电功能梯度板非线性动力分析的样条有限点法  

NONLINEAR VIBRATION ANALYSIS OF PIEZOELECTRIC FGM PLATE UNDER STRONG ELECTRIC FIELDS BY SPLINE FINITE POINT METHOD

作　　者：李双蓓[1,2] 黄君[1] 顾春霞 黄贤智[1] 

机构地区：[1]广西大学土木建筑工程学院,广西南宁530004 [2]广西大学工程防灾与结构安全教育部重点实验室,广西南宁530004 [3]广西壮族自治区人防设计研究院,广西南宁530029

出　　处：《玻璃钢／复合材料》2014年第4期8-12,共5页Fiber Reinforced Plastics/Composites

基　　金：国家自然科学基金项目(11262002);广西理工科学实验中心重点项目(LGZX201101)

摘　　要：针对强电场作用下基于线性压电本构方程求解压电功能梯度板固有频率存在误差的问题,本文考虑非线性压电效应,采用样条有限点法建立压电非线性动力分析模型,讨论强电场作用下压电非线性效应对固有频率的影响。研究表明,强电场作用下压电线性解与非线性解偏差较大,非线性效应不容忽视;由于功能梯度板的材料特性,相同电场强度下不同的施加方式,会得到不同的固有频率控制效果;基于样条有限点法建立的分析模型精确可靠,具有输入简单、处理边界条件简便等优点。In the strong electric field,the natural frequency of piezoelectric FGM plate cannot be accurately solved based on the linear constitutive equations.For this,a dynamic analysis model that considering the nonlinear piezoelectric constitutive relation is established by using the spline finite point method （SFPM） in this paper,and the impact of the nonlinear piezoelectric effect to the natural frequency is discussed in the environment of strong electric.Numerical results show that natural frequency of piezoelectric FGM plate has large deviation between nonlinear and linear results in strong electric field.And,nonlinear effects cant be ignored in this case.Owing to the special material properties of FGM,different control on the natural frequency can be obtained with different applying ways of the electric.The analysis modal based on the SPFM is accurate and reliable.Moreover,it is simple to make the input and easy to deal with the boundary conditions.

关 键 词：压电材料 功能梯度材料 非线性压电效应 固有频率 样条有限点法 

分 类 号：TB332[一般工业技术—材料科学与工程]