基于样条有限点法的压电功能梯度板的动力分析
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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.
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.
引文
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[2]BEHJAT B,KHOSHRAVAN M R.Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates[J].Composite Structure,2012,94:874-882.
[3]XIA X K,SHEN H S.Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators[J].Composite Structure,2009,90:254-262.
[4]黄小林,沈惠申.热环境下功能梯度材料板的自由振动和动力响应[J].工程力学,2005,22(3):224-227.
[5]YANG J,SHEN H S.Vibration characteristic and transient response of shear-deformable functionally graded plates in thermal environment[J].Journal of Sound and Vibration,2002,255(3):579-602.
[6]SHENH S.Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties[J].International Journal of Mechanical Sciences,2007,49:466-478.
[7]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):1-3.
[8]FAKHARI V,OHADI A,YOUSEFIAN P.Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment[J].Composite Structures,2011,93:2310-2321.
[9]JOSHI S P.Non-linear constitutive relations for piezoceramic materials[J].Smart Materials and Structures,1992,1(1):80-83.
[10]KAPURIA S,YASIN M Y.A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field[J].Smart Materials and Structures,2013,22(5):1-10.
[11]李双蓓,顾春霞,黄君.强电场作用下压电层合板的非线性弯曲问题研究[J].广西大学学报:自然科学版,2013,38(6):1284-1291.
[12]李双蓓,黄君,顾春霞,等.强电场作用下压电FGM板非线性动力分析的样条有限点法[J],玻璃钢/复合材料,2014(4):8-12.
[13]黄小林.船舶与海洋工程中复合材料板构件的非线性振动和动力响应[D].上海交通大学船舶海洋与建筑工程学院,2005.
[14]秦荣.结构力学的样条函数方法[M].南宁:广西人民出版社,1985.
[15]秦荣.计算结构动力学[M].桂林:广西师范大学出版社,1997.
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