王永岗, 戴诗亮. 受热双层圆薄板的轴对称非线性振动[J]. 工程力学, 2003, 20(2): 76-79,8.
引用本文: 王永岗, 戴诗亮. 受热双层圆薄板的轴对称非线性振动[J]. 工程力学, 2003, 20(2): 76-79,8.
WANG Yong-gang, DAI Shi-liang. NONLINEAR AXISYMMETRIC VIBRATIONS OF HEATED DOUBLE-LAYER CIRCULAR THIN PLATES[J]. Engineering Mechanics, 2003, 20(2): 76-79,8.
Citation: WANG Yong-gang, DAI Shi-liang. NONLINEAR AXISYMMETRIC VIBRATIONS OF HEATED DOUBLE-LAYER CIRCULAR THIN PLATES[J]. Engineering Mechanics, 2003, 20(2): 76-79,8.

受热双层圆薄板的轴对称非线性振动

NONLINEAR AXISYMMETRIC VIBRATIONS OF HEATED DOUBLE-LAYER CIRCULAR THIN PLATES

  • 摘要: 通过对双层薄板坐标参考面的选择,基于Von Kár mán理论和Hamilton原理,建立了受热双层圆板轴对称非线性振动控制方程的简化形式.采用Galerkin法进行时空变量分离后,由Lindstedt-Poincaré 摄动法获得了受热双层板非线性振动频率与振幅间的特征关系.文末以某热致微型泵的驱动膜片为例,研究了不同温度对其振动特性的影响.本文的方法极易推广到单层和多层受热薄板非线性振动的分析中.

     

    Abstract: By the selection of reference surface of coordinates and based on Von Ká r mán's theory, the compact control equations of nonlinear axisymmetric vibrations of heated double-layer thin plates are established using Hamilton's principle. The time-spatial variables are separated by Galerkin抯 technique, and the characteristic relation of frequency vs. amplitude for nonlinear vibrations of heated double-layer plates is obtained from Lindstedt-Poincaré perturbation method. Taking the driving membrane of a thermally actuated micropump as example, the effects of temperature on its vibration behavior are studied. The present method can be extended easily to the analysis of nonlinear vibrations of heated thin single or multi-layer plates.

     

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