热环境下压电功能梯度板的非线性等几何建模与主动控制研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 38-50.

论文

刘涛1,2,3，张顺琦1，刘庆运2,3

作者信息 +

Nonlinear isogeometric modeling and active control of piezoelectric functionally graded plates in thermal environment

LIU Tao1,2,3，ZHANG Shunqi1，LIU Qingyun2,3

Author information +

文章历史 +

摘要

压电材料的压电参数（应力、应变和介电参数）对温度均较为敏感，且直接影响着压电智能结构工作时的性能。为更加准确地探究热环境中上、下表面覆盖有压电层的功能梯度板的非线性力学行为和非线性主动控制问题，首先在传统的线性压电本构方程中引入了温度对压电参数的影响，基于一阶剪切变形理论（First-order shear deformation theory, FSDT）和Von Kármán理论建立了压电功能梯度板（piezoelectric functionally graded plates, PFGPs）的非线性等几何分析（Isogeometric analysis, IGA）模型，并通过相关算例验证了模型的正确性和有效性。其次，对多种载荷作用下板的自由振动和非线性静态弯曲响应进行了分析。最后，利用位移-速度反馈控制方法研究了板的非线性主动控制。研究结果表明，压电参数的温度相关性对压电功能梯度板的自由振动、非线性静态弯曲响应以及非线性主动控制效果均有影响，且影响大小与压电层的厚度、梯度指数n和温度有关。

Abstract

The piezoelectric parameters (piezoelectric stress, strain and dielectric parameters) of piezoelectric materials are sensitive to temperature, and directly affect the performance of piezoelectric smart structures. In order to accurately analyze the nonlinear mechanical behavior and nonlinear active control of functionally graded plates (FGPs) with surface-bonded piezoelectric layers in thermal environment, firstly, the influences of temperature on piezoelectric parameters are introduced into the traditional linear piezoelectric constitutive equation. The nonlinear isogeometric analysis (IGA) model of piezoelectric functionally graded plates (PFGPs) is established based on the first-order shear deformation theory (FSDT) and Von Kármán theory, and the correctness and effectiveness of the model are verified by relevant numerical examples. Secondly, the free vibration and nonlinear static bending of the plates under various loads are analyzed. Finally, the displacement-velocity feedback control method is used to study the nonlinear active control of the plates. The results show that the temperature dependence of piezoelectric parameters have influences on the free vibration, nonlinear static bending response and nonlinear active control effect of piezoelectric functionally graded plates, and the influences are related to the thickness of piezoelectric layers, gradient index n and temperature.

导出引用

刘涛1,2,3，张顺琦1，刘庆运2,3. 热环境下压电功能梯度板的非线性等几何建模与主动控制研究[J]. 振动与冲击, 2023, 42(8): 38-50

LIU Tao1,2,3，ZHANG Shunqi1，LIU Qingyun2,3. Nonlinear isogeometric modeling and active control of piezoelectric functionally graded plates in thermal environment[J]. Journal of Vibration and Shock, 2023, 42(8): 38-50

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