均布载荷作用下波纹扁壳的非线性振动

Nonlinear Vibration of Corrugated Shallow Shells Under Uniform Load

应用轴对称旋转扁壳的非线性大挠度动力学方程,研究了波纹扁壳在均布载荷作用下的非线性受迫振动问题.采用格林函数方法,将扁壳的非线性偏微分方程组化为非线性积分微分方程组.再使用展开法求出格林函数,即将格林函数展开为特征函数的级数形式,积分微分方程就成为具有退化核的形式,从而容易得到关于时间的非线性常微分方程组.针对单模态振形,得到了谐和激励作用下的幅频响应.作为算例,研究了正弦波纹扁球壳的非线性受迫振动现象.该文的解答可供波纹壳的设计参考.

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load had been investigated. The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations by using the method of Green＇ s function. To solve the integral-differential equations, expansion method was used to obtain Green＇ s function. Then the integral-differential equations were reduced to the form with degenerate core by expanding Green＇ s function as series of characteristic function. Therefore, the integral-differential equations became nonlinear ordinary differential equations with regard to time. The ampUtude-frequency response under harmonic force was obtained by considering single mode vibration. As a numerical exanple, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions axe available for reference to design of corrugated shells.