压电层合圆板的非线性动力学模型与主共振响应

Nonlinear Dynamic Model and Primary Resonance of Piezoelectric Laminated Disk

考虑非线性压电效应,即电致弹性和电致伸缩效应,根据Hamilton原理和Rayleigh-Ritz假设模态方法建立了表面粘贴压电陶瓷片薄圆板的非线性动力学模型,使用多尺度方法计算压电层合板驻波振动的主共振一次近似响应,给出解的特性与系统参数的关系.结果表明,在一定条件下,主共振响应存在多解和跳跃现象.改变激励频率(调谐参数)时,主共振解可能是唯一的,也可能有2个,主共振解的真正实现取决于其稳定性条件及初始条件;当激励频率由高向低变化时,存在振幅突跳和滞后.根据分析结果,计算出了在给定的参数条件下用软特性压电材料层合圆板的工作频率选取范围.数值积分的结果验证了解析解的正确性.

A nonlinear dynamic model of laminated disk affixed with piezoelectric materials was established while considering the nonlinear constitutive relations of piezoelectric materials by means of Hamilton＇ s principle and Rayleigh-Ritz method. With the use of the method of multiple scales, the standing wave primary resonance of the laminated disk was investigated. The results show that the primary resonance has multi-solutions and jump phenomena when excitation frequency varies from low value to high value. The steady-state primary resonance can be single or multiple （two） when the excitation frequency changes. The realization of primary resonance lies on the stability conditions and initial conditions. To the laminated disk using piezoelectric materials with soft character, the reasonable area of detuning parameter was proposed according to the analytical results. Numerical results verify the solution of analytical analysis.