王 蕴. 压电层合圆板驻波振动的非线性动力学分析[J]. 工程力学, 2009, 26(11): 46-052.
引用本文: 王 蕴. 压电层合圆板驻波振动的非线性动力学分析[J]. 工程力学, 2009, 26(11): 46-052.
WANG Yun. NONLINEAR DYNAMIC ANALYSIS OF PIEZOELECTRIC LAMINATED DISK UNDER STANDING WAVE VIBRATION[J]. Engineering Mechanics, 2009, 26(11): 46-052.
Citation: WANG Yun. NONLINEAR DYNAMIC ANALYSIS OF PIEZOELECTRIC LAMINATED DISK UNDER STANDING WAVE VIBRATION[J]. Engineering Mechanics, 2009, 26(11): 46-052.

压电层合圆板驻波振动的非线性动力学分析

NONLINEAR DYNAMIC ANALYSIS OF PIEZOELECTRIC LAMINATED DISK UNDER STANDING WAVE VIBRATION

  • 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贴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。

     

    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 under 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 current components. 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. Numerical analysis verifies the feasibility of the analytical analysis.

     

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