【摘要】 研究了双层金属圆薄板在静态均匀变温下的轴对称非线性自由振动问题。通过对双层板坐标参考面的选择,建立了其与经典vonK rm n单层板理论相似的控制方程,而后借助于计算机代数系统Maple进行摄动变分求解,获得了受热双层板非线性振动频率与振幅间特征关系的三次近似解析解,并绘出了不同加热温度下的幅频曲线。得出受热双层板的振动呈现硬弹簧特性,且升温使板的振动频率降低,降温使其升高等结论。该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。更多还原

【Abstract】 The axisymmetrically nonlinear free vibration of bimetallic thin circular plates with uniformly stationary temperature changes was studied. With appropriate selection of the reference surface of coordinates, the governing equations for the doublelayered plates were similar to those of the classical von Karman singlelayer plate theory. The thirdorder approximate characteristic relation between the frequency and the amplitude for the nonlinear vibrations of the heated bimetallic plates was obtained using the perturbationvariational method with the aid of the mathematical analysis program Maple. The frequencyamplitude characteristic curve was plotted for various temperatures. The results show that the vibration of the heated bimetallic plate appears a hardening spring behavior, and increased temperatures will reduce the frequency, decreased temperatures will increase the frequency. The present method can easily be expanded to analyze nonlinear vibration of heated thin single or multilayer plates.更多还原