匀布静载荷作用下锥壳轴对称非线性自由振动

用能量变分法和多重尺度法研究了静载荷作用下扁薄锥壳轴对称非线性自由振动问题，求得了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。作为算例，文中计算并绘出了给定初始条件下非线性一阶和二阶固有频率与振幅以及非线性一阶和二阶固有频率与静挠度的特征关系曲线，本文的方法具有较广的适用性，可用于解决其它板壳的非线性振动问题。

Axisymmetrical Nonlinearr Free Vibration of the Conic Shells Under the Static Uniformly Distributed Loads

The problem of axisymmetrical nonlinear free vibration of shallow thin conic shells under the static uniformly distributed loads is studied by using the energy variational method and the multiple scale method.The third-order approximate analytical solution is ob-tained and the relation of the nonlinear natural frequences versus the amplitude is presented.In this paper,as for a calculation example,the characteristic curves of the first and the second nonlinear natural frequences versus the amplitude under the given initial conditions are calcu-lated and plotted. The characteristic curves of the first and the second nonlinear natural fre-quences versus the static deflection are also derived and plotted.The method presented in this paper is of wider applicability and can be used to solve other nonlinear vibration prob-lems of plates and shells.