基于样条有限点法的压电功能梯度板的动力分析  

Dynamic analysis of piezoelectric FGM plate based on spline finite point method

作　　者：黄君[1,2] 莫春美 李双蓓[2,3] 

机构地区：[1]桂林理工大学南宁分校土木与测绘工程系,广西南宁530001 [2]广西大学土木建筑工程学院,广西南宁530004 [3]广西防灾减灾与工程安全重点实验室,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2015年第1期127-134,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11262002);广西大学科研基金资助项目(XBZ030060)

摘　　要：为了研究热环境中强电场作用下压电材料的电致非线性效应对压电功能梯度(P/FGM/P)板自由振动的影响,基于高阶剪切变形理论,采用压电材料电致非线性本构关系,同时考虑电场和热荷载的作用,通过样条有限点法建立P/FGM/P板动力分析模型,讨论了压电线性与非线性效应的差别,以及热环境中强电场对P/FGM/P板自振频率的控制效果。结果表明:随电场增大,压电线性解与非线性解偏差增大,且偏差大小同时还受边界约束影响。随温度升高,由于板的刚度减小,电场对P/FGM/P板自振频率的控制效果变好。同时也证明了样条有限点法具有编程简便、精度好及效率高等优点。In order to understand the impact of nonlinear electric property of piezoelectric material on the free vibration behavior of piezoelectric FGM（P / FGM / P） plate,the high-order shear deformation theory and nonlinear piezoelectric constitutive relations were introduced.A dynamic model of P / FGM / P plates was established using the spline finite point method with the role of electric load and thermal load taken into account to understand the influence of these characteristics on the free vibration behavior of P / FGM / P plates.According to the analysis model,the difference between linear and nonlinear effects was discussed.The control effect of a strong electric field on the vibration frequency of P / FGM / P plates in the thermal environment was studied.The studies show that the deviation between linear solution and nonlinear solution is affected by the boundary and increased with the increase of electric field.Due to the reduction of plate stiffness,the control effect of electricfield on the vibration frequency of the P / FGM / P plates increases with the increase of temperature.It also shows that the spline finite point method has advantages of easy programming,good accuracy and high efficiency,which was good for the analysis of the P / FGM / P plates.

关 键 词：样条有限点法 压电材料 功能梯度材料 压电非线性特性 热环境 自由振动 

分 类 号：O342[理学—固体力学]