功能梯度压电材料梁的热-机-电耦合振动及屈曲特性分析  

Vibration and Buckling Behaviors of Functionally Graded Piezoelectric Material Beams Subjected to Thermal-mechanical-electrical Loads

作　　者：周凤玺[1] 蒲育 ZHOU Fengxi;PU Yu(School of Civil Engineering,Lanzhou University of Technology,Lanzhou 730050;College of Civil Engineering,Lanzhou Institute of Technology,Lanzhou 730050)

机构地区：[1]兰州理工大学土木工程学院,兰州730050 [2]兰州工业学院土木工程学院,兰州730050

出　　处：《机械工程学报》2021年第8期166-174,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51978320,11962016);甘肃省基础研究创新群体基金(20JR5RA478);甘肃省自然科学基金(20JR5RA379);甘肃省高等学校创新能力提升(2019B-180);兰州工业学院“启智”人才培养计划基金(2018QZ-05)资助项目。

摘　　要：为提高梁理论对静动态响应预测的可靠性和准确性,基于一种n阶广义梁理论,研究外驱动电压及轴向机械载荷共同作用下功能梯度压电材料(Functionally graded piezoelectric material,FGPM)梁在热环境中的耦合振动及屈曲特性。考虑温度沿梁厚按不同类型稳态分布,采用Voigt混合幂率模型表征FGPM梁的材料属性,应用Hamilton原理统一实施静动态建模,采用Navier法求解FGPM简支梁的动态响应。分析不同梁理论、不同温度分布、热-机-电耦合效应、材料组份梯度指标、跨厚比等诸多参数对梁振动频率和屈曲临界载荷特性的影响,揭示多因素影响下FGPM梁耦合屈曲和耦合振动这两类静动态力学行为之间的二元耦联性。结果表明,通过改变外驱动电压大小和极化方向均可实现FGPM梁在热-机-电耦合作用下的振动控制以及稳定性安全设计。In order to improve the reliability and accuracy for beam models in predicting static and dynamic responses,vibration and buckling behaviors of functionally graded piezoelectric material(FGPM)beams in thermal environment and under the action of external electric voltage and axial mechanical load are studied based on an n-th order generalized beam theory.Various types of temperature distributions through the thickness of a beam are considered and the piezoelectric material properties are described by Voigt mixture power-law model,static and dynamic models for the system are built using Hamilton principle as a unity and Navier method is utilized to solve the dynamic response for FGPM simply supported beams.The effects of various beam theories,different cases of temperature distribution,thermal-mechanical-electrical loads,material graded index and slenderness ratio on the frequency and critical buckling load of FGPM beams are analyzed.Considering various factors,the binary relations between the coupling buckling and vibration behaviors are also illustrated.The results show that the vibration control and stability design of FGPM beams subjected to thermal-mechanical-electrical loads can be performed by changing the external voltage and polarization direction.

关 键 词：功能梯度压电材料梁 热-机-电效应 n阶广义梁理论 耦合振动 耦合屈曲 

分 类 号：O343[理学—固体力学] TB34[理学—力学]