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
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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 can't 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.
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 can't 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.
引文
[1]李信,刘海昌,滕元成,鲁伟员.功能梯度材料的研究现状及展望[J].材料导报,2012,26:370-373.
[2]沈惠申.功能梯度复合材料板壳结构的弯曲、屈曲和振动[J].力学进展,2004,34:53-60.
[3]曹志远.功能梯度壳体力学的一般理论[J].玻璃钢/复合材料,2008,(2):7-11.
[4]黄立新,姚祺,张晓磊,阳明.基于分层法的功能梯度材料有限元分析[J].玻璃钢/复合材料,2013,(2):43-48.
[5]王明禄,马文蕾,魏高峰.热荷载下功能梯度梁的热弹性弯曲[J].玻璃钢/复合材料,2009,(1):7-9.
[6]Shen Huishen.Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties[J].Mechanical Sciences,2007,49:466-478.
[7]丁丽霞,刘玮.压电元件驱动的功能梯度弹性薄板的屈曲[J].玻璃钢/复合材料,2006,(8):1229-1238.
[8]伍晓红,沈亚鹏.压电功能梯度板自由振动的三维解[J].固体力学学报,2003,(1):75-82.
[9]林超,陈凤,袁莉,梁国正.智能复合材料研究进展[J].玻璃钢/复合材料,2012,(2):74-77.
[10]Shiv P Joshi.Non-linear constitutive relations for piezo-ceramic materials[J].Smart Mater Struct,1992,(1):80-83.
[11]X.Q.He,T.Y.Ng,S.Sivashanker,K.M.Liew.Active control of FGM plates with integrated piezoelectric sensors and actuators[J].International Journal of Solids and Structures,2001,38:1641-1655.
[12]刘玮,闫铂.具有压电元件的功能梯度弹性薄板的振动特性[J].振动与冲击,2007,26(5):1-8.
[13]B.Behjat,M.R.Khoshravan.Geometrucally nonlinear static and free vibration analysis of functionally graded piezoelectric plates[J].Composite Structures,2012,94:874-882.
[14]Xian-Kun Xia,Hui-Shen Shen.Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators[J].Composite Structures,2009,90:254-262.
[15]Vahid Fakhari,Abdolreza Ohadi,Peyman Yousefian.Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment[J].Composite Structures,2011,93:2310-2321.
[16]J.Yang,S.Kitipornchai,K.M.Liew.Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates[J].Computer methods in applied mechanics and engineering,2003,192:3861-3885.
[17]姚林泉,丁睿.非线性压电效应下压电弯曲执行器的动力分析[J].力学学报,2005,37(2):183-189.
[18]秦荣,计算结构力学[M].北京:科学出版社,2001.
[2]沈惠申.功能梯度复合材料板壳结构的弯曲、屈曲和振动[J].力学进展,2004,34:53-60.
[3]曹志远.功能梯度壳体力学的一般理论[J].玻璃钢/复合材料,2008,(2):7-11.
[4]黄立新,姚祺,张晓磊,阳明.基于分层法的功能梯度材料有限元分析[J].玻璃钢/复合材料,2013,(2):43-48.
[5]王明禄,马文蕾,魏高峰.热荷载下功能梯度梁的热弹性弯曲[J].玻璃钢/复合材料,2009,(1):7-9.
[6]Shen Huishen.Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties[J].Mechanical Sciences,2007,49:466-478.
[7]丁丽霞,刘玮.压电元件驱动的功能梯度弹性薄板的屈曲[J].玻璃钢/复合材料,2006,(8):1229-1238.
[8]伍晓红,沈亚鹏.压电功能梯度板自由振动的三维解[J].固体力学学报,2003,(1):75-82.
[9]林超,陈凤,袁莉,梁国正.智能复合材料研究进展[J].玻璃钢/复合材料,2012,(2):74-77.
[10]Shiv P Joshi.Non-linear constitutive relations for piezo-ceramic materials[J].Smart Mater Struct,1992,(1):80-83.
[11]X.Q.He,T.Y.Ng,S.Sivashanker,K.M.Liew.Active control of FGM plates with integrated piezoelectric sensors and actuators[J].International Journal of Solids and Structures,2001,38:1641-1655.
[12]刘玮,闫铂.具有压电元件的功能梯度弹性薄板的振动特性[J].振动与冲击,2007,26(5):1-8.
[13]B.Behjat,M.R.Khoshravan.Geometrucally nonlinear static and free vibration analysis of functionally graded piezoelectric plates[J].Composite Structures,2012,94:874-882.
[14]Xian-Kun Xia,Hui-Shen Shen.Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators[J].Composite Structures,2009,90:254-262.
[15]Vahid Fakhari,Abdolreza Ohadi,Peyman Yousefian.Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment[J].Composite Structures,2011,93:2310-2321.
[16]J.Yang,S.Kitipornchai,K.M.Liew.Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates[J].Computer methods in applied mechanics and engineering,2003,192:3861-3885.
[17]姚林泉,丁睿.非线性压电效应下压电弯曲执行器的动力分析[J].力学学报,2005,37(2):183-189.
[18]秦荣,计算结构力学[M].北京:科学出版社,2001.