Nonlinear vibration of corrugated shallow shells under uniform load  

作　　者：袁鸿 刘人怀 

机构地区：[1]Institute of Applied Mechanics,Jinan University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第5期573-580,共8页应用数学和力学（英文版）

摘　　要：Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green＇s function. To solve the integral-differential equations, expansion method is used to obtain Green＇s function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells .Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green＇s function. To solve the integral-differential equations, expansion method is used to obtain Green＇s function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells .

关 键 词：corrugated shells spherical shells Green＇s function integral equation nonlinear vibration 

分 类 号：O322[理学—一般力学与力学基础]