扁薄锥壳轴对称非线性自由振动

本文用能量变分法和多重尺度法研究了扁薄锥壳轴对称非线性自由振动问题,求得了一般问题的三次近似解析解,并给出了非线性固有频率与振幅的特征关系式。文中通过变分方程和假定振型把原问题化为二阶非线性常微分方程组,结合特征向量的正交性利用多重尺度法求解了该问题。通过算例将三次近似解析斛与前人所得的有关结果作了比较,可以看出本文的方法是正确的。本文的方法不但具有较广的适用性,且所得结果精度较高。

Axisymmetrical Nonlinear Free Vibration of Shallow Thin Conic Shells

In this paper,by using the energy variation method and the method of multiple scales, the problem of axisymmetrical nonlinear free vibration of shallow thin conic shells is studied,a third-order approximate analytic solution is obtained ,and the characteristic curves of nonlinear natural frequencies versus amplitude are plotted. Using variational equation and assuming the mode of vibration, the original problem is turned into a system of second order nonlinear ordinary differential equations. Using the method of mutiple scales and the orthogonality of the eigenvectors,the problem is solved and a third-order approximate analytic solution is obtained. Comparing the results of the calculated example in this paper with the existing relevant results,it can be seen that the method developed in this paper is valid . This method can be used not only for a wider range,but also gives the results with higher accuracy.