变厚度扁锥壳的非线性固有频率  

Nonlinear Natural Frequency of Shallow Conical Shiells With Variable Thickness

作　　者：王新志[1] 韩明君[1] 赵永刚[1] 叶开沅[2] 

机构地区：[1]兰州理工大学理学院,兰州730050 [2]兰州大学物理学院,兰州730000

出　　处：《应用数学和力学》2005年第3期253-258,共6页Applied Mathematics and Mechanics

基　　金：甘肃省自然科学基金资助项目(ZS021_A25_007_Z)

摘　　要：　借助于变厚度圆薄板非线性动力学变分方程和协调方程,给出了变厚度扁薄锥壳的非线性动力学变分方程和协调方程·　假设薄膜张力由两项组成,将协调方程化为两个独立的方程,选取变厚度扁锥壳中心最大振幅为摄动参数,采用摄动变分法,将变分方程和微分方程线性化·　对周边固定的圆底变厚度扁锥壳的非线性固有频率进行了求解;一次近似得到了变厚度扁锥壳的线性固有频率,三次近似得到了变厚度扁锥壳的非线性固有频率,且绘出了固有频率与静载荷、最大振幅。The nonlinear dynamical variation equation and compatible equation of the shallow conical shell with variable thickness are obtained by the theory of nonlinear dynamical variation equation and compatible equation of the circular thin plate with variable thickness. Assuming the thin film tension is composed of two items. The compatible equation is transformed into two independent equations. Selecting the maximum amplitude in the center of the shallow conical shells with variable thickness as the perturbation parameter, the variation equation and the differential equation are transformed into linear expression by theory of perturbation variation method. The nonlinear natural frequency of shallow conical shells with circular bottom and variable thickness under the fixed boundary conditions is solved; in the first approximate equation, the linear natural frequency of shallow conical shells with variable thickness is obtained, in the third approximate equation, the nonlinear natural frequency of it is obtained. The figures of the characteristic curves of the natural frequency varying with stationary loads, large amplitude, and variable thickness coefficient are plotted. A valuable reference is given for dynamic engineering.

关 键 词：变厚度 固有频率 非线性 摄动变分法 

分 类 号：O322[理学—一般力学与力学基础]