双层旋转扁壳非线性振动分析的同伦摄动法

采用能量变分法和同伦摄动法研究了双层金属旋转扁壳在均匀静态变温下的非线性轴对称自由振动问题。首先通过对坐标参考面的重新定位,建立了本问题控制方程的单层旋转壳简化形式,然后基于空间模态的假设,利用变分法导出了时间模态满足的非线性微分方程,最后由同伦摄动法获得了扁壳以温度为参数的非线性振动频率与振幅间特征关系的二次近似解析解。数值结果表明,变温对双层扁壳非线性振动的频率有明显的影响,而扁壳矢高可以改变振动的弹簧特性。

Homotopic perturbation method for nonlinear vibrations of bimetallic shallow shells of revolution

Axisymmetric nonlinear free vibrations of bimetallic shallow shells of revolution with uniformly distributed stationary temperature changes are investigated using the energy variational method and the homotopic perturbation method.The governing equations are similar to those of classical single-layer shell theory after re-determination of the reference coordinate surface.The nonlinear differential equation in time mode is derived using the variational method with an assumed spatial mode.The resulting equation is then solved with the homotopic perturbation method to get the second-order approximate characteristic relation of the frequency vs.amplitude for various temperature changes for nonlinear vibrations of the shell.Numerical results show that the temperature change strongly influences the shell vibration characteristics.The nonlinear behavior changes from hard to soft spring as the shell height is increased.