Nonlinear Natural Frequency of Shallow Conical Shiells With Variable Thickness
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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、变厚度参数的特征曲线图.为动力工程提供了有价值的参考.Abstract: 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.
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Key words:
- variable thickness /
- natural frequency /
- nonlinear /
- perturbation variation method
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[1] 叶开沅.变厚度弹性圆薄板问题[J].物理学报,1955,11(3):207—218. [2] 王新志.变厚度圆薄板在均布载荷下的大挠度问题[J].应用数学和力学,1983,4(1):103—112. [3] 徐加初,王乘,刘人怀.变厚度夹层环形板的非线性弯曲[J].工程力学,2001,18(4):28—37. [4] 叶志明.变厚度圆底扁薄球壳的非线性稳定问题[J].力学学报,1984,16(6):634—638. [5] Reddy J N,Huang C L.Large amplitude free vibrations of annular plates of varying thickness[J].Journal of Sound and Vibration,1981,79(3):387—395. doi: 10.1016/0022-460X(81)90317-5 [6] WANG xin-zhi,WANG Lin-xiang,HONG Xiao-bo.Large amplitude problem of circular plates with variable thickness[A].In:WANG Zhao-lin Ed,ICVC[C].Beijing:Peking University Press,1990,1065—1069. [7] 王新志,王林祥,胡小方.波纹圆薄板的非线性振动[J].应用数学和力学,1987,8(3):237—245.
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