文档介绍：压电层合圆板驻波振动的
非线性动力学分析
王蕴
(白城师范学院机械电子工程系,吉林白城 137000)
摘要:考虑压电材料二次非线性本构关系,应用广义Hamilton原理和Rayleigh-Ritz假设模态方法建立了表面粘帖压电陶瓷片薄圆板的非线性动力学模型,使用多尺度法计算压电层合板驻波振动的二阶主共振响应,给出解的特性与系统参数的关系。结果表明,驻波振动的二次近似解包含二次超谐成分和由于二次非线性引起的直流分量;当激励频率变化时,二阶主共振响应存在多解和跳跃现象,主共振解的真正实现取决于其初始条件。数值积分的结果验证了解析解的正确性。
关键词:压电材料,非线性,二次非线性本构关系,主共振,稳定性
中图分类号:O322 TM331 文献标识码:A
Nonlinear Dynamic Analysis of Piezoelectric Laminated
Disk for Standing Wave Vibration
WANG Yun
(Department of Mechanical & Electrical Engineering,BaiCheng Normal College,
BaiCheng, JiLin 137000 China)
Abstract: Considering the quadratic stiffness in nonlinear constitutive relations of piezoelectric materials, a nonlinear dynamic model of laminated disk affixed with piezoelectric materials is established using Hamilton’s principle and the Rayleigh-Ritz method. Applying the method of multiple scales, the second-order approximation of the primary resonance for standing wave vibration of the laminated disk is investigated. The results show that the second-order primary resonance includes not only the quadratic harmonic but also the direct ponents. The second-order approximation can be single or multiple when the excitation frequency changes, the realization of primary resonance lies on the stability conditions and initial conditions. The results give the relation between the responses and system parameters. Numerical analysis verifies the feasib