基于等几何方法的压电功能梯度板动力学及主动振动控制分析  

ANALYSIS FOR DYNAMIC AND ACTIVE VIBRATION CONTROL OF PIEZOELECTRIC FUNCTIONALLY GRADED PLATES BASED ON ISOGEOMETRIC METHOD

作　　者：刘涛[1,2] 汪超[1] 刘庆运[1] 胡文锋[1] 胡晓磊 LIU Tao;WANG Chao;LIU Qing-yun;HU Wen-feng;HU Xiao-lei(Department of Mechanical Engineering,Anhui University of Technology,Ma'anshan 243002,China;Department of Mechatronic Engineering and Automation,Shanghai University,Shanghai 200072,China)

机构地区：[1]安徽工业大学机械工程学院,马鞍山243002 [2]上海大学机电工程与自动化学院,上海200072

出　　处：《工程力学》2020年第12期228-242,共15页Engineering Mechanics

基　　金：安徽高校协同创新项目(GXXT-2019-048);国家重点研发计划项目(2017YFC0805100);安徽教育厅高校自然科学研究项目(KJ2018A0069,KJ2019A0091)。

摘　　要：针对表面粘贴有压电层的功能梯度板的动力学及主动振动控制问题,建立了一种基于三阶剪切变形理论的等几何分析求解方法。其中,功能梯度板的材料属性为板厚方向的幂函数分布,并假设电势沿着压电层的厚度方向呈线性变化。利用线性压电本构方程以及哈密顿变分原理,推导了压电功能梯度板的相关等几何分析有限元方程。通过分析压电智能结构的静态弯曲行为验证了该方法的有效性与精确性。运用模态叠加技术与Newmark-β直接积分法分析了两种不同结构的压电功能梯度板的动力学响应与主动振动控制问题。在主动振动控制分析中,引入了物理中面的概念避免当传感器与驱动器分别粘贴于功能梯度的上、下表面时,由拉伸-耦合效应引起的控制不稳定的问题,并着重分析了振动控制过程中两种结构传感器层和驱动器层的电压响应。An isogeometric analysis method based on third-order shear deformation theory is proposed to solve the dynamic response and active vibration control of functionally graded plates(FGPs) with surface-bonded piezoelectric layers. The material properties of FGPs are assumed to be graded through the thickness by a power law distribution, and the variation of electric potential is assumed to be linear in the direction of the thickness of the piezoelectric layer. The isogeometric-analysis finite-element formulation of the piezoelectric functionally graded plates(PFGPs) is derived by utilizing the linear piezoelectric constitutive equation and Hamiltonian principle. The availability and accuracy of the present method are verified by the analysis of the static bending responses of smart piezoelectric structures. The dynamic response and active vibration control analyses of the plate are calculated via Newmark-β direct integration method. The neutral plane is introduced to avoid the control instability caused by stretching-bending coupling effect when the sensor and the actuator are bonded on the upper and lower surfaces of the FGPs, respectively. Besides, the voltage responses of the sensor and the actuator of the two structures in the vibration control process are analyzed.

关 键 词：压电功能梯度板 等几何分析 三阶剪切变形理论 动力学 主动振动控制 物理中面 

分 类 号：TB115[理学—数学]