具有压电元件的功能梯度弹性薄板的振动特性  

VIBRATION CHARACTERISTICS OF FUNCTIONAL GRADIENT THIN ELASTIC PLATES BONDED WITH PIEZOELECTRIC PATCHES

作　　者：刘玮[1] 闫铂[1] 

机构地区：[1]吉林大学数学学院力学与工程科学系,长春130012

出　　处：《振动与冲击》2007年第5期1-3,7,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10472037)

摘　　要：考虑一功能梯度薄板,其上下表面嵌有压电执行元件。根据逆压电效应,将电场强度转换成作用于板上的等效电载荷。假设梯度材料的物性参数为板厚度方向坐标的幂函数,应用达朗贝尔原理,导出了具有压电元件的功能梯度弹性薄板的动力学方程。采用变量分离与Navier解,得到四边简支功能梯度板的固有特性与电场强度间的关系。并进一步通过数值例子讨论了电场强度、材料的梯度指数等对板固有特性的影响。研究结果表明,调整作用于执行元件上的电场强度可以实现对板的振动特性的控制,而材料的梯度化可影响板的固有频率,在设计中应予以考虑。A functional gradient thin elastic plate bonded with piezoelectric patches on its top and bottom surfaces,is analyzed here.The equivalent loads are obtained by considering the inverse piezoelectric effect on it.We assume its physical properties are functionally graded in its thickness direction according to a power function.Based on d'Alembert principle,its dynamic equation is derived.By using separation of variables and Navier solution,relations between its natureal characteristics and electric field are presented.The influence of electric field and gradient index on its natural characteristics is discussed by using numerical examples.It's found that its vibration characteristics can be controlled effectively by means of regulating the electric field of actuators.The effects of gradient index on the natural frequencies of the plate are obvious,so we should pay attention to it in structural design.

关 键 词：振动特性 压电元件 功能梯度材料 弹性薄板 

分 类 号：O326[理学—一般力学与力学基础]