压电圆盘的轴对称振动:改进的双勒让德多项式方法  

Axi-symmetric vibration of piezoelectric disc based on improved double-Legendre polynomial

作　　者：周红梅[1] 韩康乐 禹建功[1] 张会端[1] 王现辉[1] 张小明[1] ZHOU Hongmei;HAN Kangle;YU Jiangong;ZHANG Huiduan;WANG Xianhui;ZHANG Xiaoming(School of Mechanical and Power Engineering,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学机械与动力工程学院,河南焦作454000

出　　处：《振动与冲击》2023年第21期169-175,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(U1804134);中国博士后科学基金(2019M662492);河南省博士后项目(201902035)。

摘　　要：压电陶瓷的力电耦合特性使其广泛应用于结构的形状控制、振动和噪声控制以及结构损伤监测等诸多领域。双勒让德多项式法通过在本构方程中添加两个方向上的矩形窗函数而自动满足压电结构的边界条件,成功应用于压电圆盘的振动特性研究。但该方法在求解高阶模态时面临大量的数值积分计算,时间成本剧增。该文章在传统双勒让德多项式法振动分析基础上,利用勒让德多项式性质推导了其中积分的解析表达式,使得计算效率提高90%以上。并通过与已有文献结果比对验证了该方法的正确性。最后分析了压电圆盘固有频率与径厚比的关系,结果显示频率半径积随着径厚比增大趋于稳定,且低阶更快达到稳定值。Electro-mechanical coupled characteristics of piezoelectric ceramics make them be widely used in various fields of structural shape control,vibration and noise control and structural damage monitoring.Double-Legendre polynomial method automatically satisfies boundary conditions of piezoelectric structures by adding rectangular window functions in two directions into constitutive equation,and it is successfully applied in vibration characteristics study of piezoelectric discs.However,this method faces a large amount of numerical integration calculations when solving high-order modes,and the time cost increases sharply.Here,based on vibration analysis with traditional double-Legendre polynomial method,the analytical expression of integration was derived by using properties of Legendre polynomial to make calculation efficiency increase by more than 90%.The correctness of this method was verified by comparing calculation results obtained with this method to those in existing literature.Finally,the relation between natural frequencies of piezoelectric disc and its diameter to thickness ratio was analyzed.The results showed that the disc's frequency-radius product tends to be stable with increase in its diameter-thickness ratio,and the lower order one reaches a stable value more quickly.

关 键 词：压电圆盘 轴对称振动 双勒让德多项式 解析积分法 

分 类 号：O323[理学—一般力学与力学基础]