【作者】 张俊； 李天匀； 朱翔； 陈繁；

【Author】 ZHANG Jun;LI Tianyun;ZHU Xiang;CHEN Fan;School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology;Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics;Collaborative Innovation Center for Advanced Ship and Deep-sea Exploration;

【机构】 华中科技大学船舶与海洋工程学院； 船舶与海洋水动力湖北省重点实验室； 高新船舶与深海开发装备协同创新中心；

【摘要】 本文基于能量泛函变分的思想提出了一种求解圆锥壳振动特性的方法。采用适用于任意边界条件的改进傅立叶级数为型函数,得到结构的能量泛函。通过引入拉格朗日乘子处理边界条件,最终得到关于条件矩阵与结构刚度矩阵、质量矩阵的控制方程,求解该方程即可得到各阶固有频率。结果对比表明方法准确可靠。通过应用拉格朗日乘子法对不同边界条件及不同半顶角下圆锥壳的固有频率进行计算,得到边界条件和半顶角的变化对圆锥壳固有频率的影响,以及圆锥壳固有频率随周向波数的变化规律。更多还原

【Abstract】 An method based on the energy method is proposed to solve the vibration characteristics of conical shells.Adopting the improved Fourier series which is applicable to all boundary condition as shape function,the energy functional is obtained.By citing the Lagrangian Multiplier to dispose the boundary condition,the governing equation of the conditional matrix,the structural stiffiness matrix and mass matrix can be received,and solving the equation,each order natural frequency is obtained.Setting the conical shells with the SS-SS support as the example,the effects to the natural frequency with 0 force and moment is analyzed,and the conclusion that the effect of the discribed boundary condition can be neglected is made,and the support that the boundary condition in the engineering of vibration analysis can be ignored is provided.更多还原