环形薄圆板的非线性振动分析  

Nonlinear Vibration of an Annular Thin Plate

作　　者：侯朝胜[1] 李磊[1] 

机构地区：[1]天津大学建筑工程学院,天津300072

出　　处：《天津大学学报（自然科学与工程技术版）》2005年第6期538-542,共5页Journal of Tianjin University：Science and Technology

摘　　要：为研究环形薄圆板非线性振动特性,用伽辽金法消除动态卡门偏微分方程的残值,推导出了环形薄圆板的受迫振动控制方程,即硬弹簧型达芬方程;用KBM法求解达芬方程,定性地探讨了边界条件、阻尼比、外激振力和内外半径比对环形薄圆板振动的影响,得到了4种边界条件下共振时激起的振幅均随半径比或阻尼比的增大而减少的结论;取外激振力作为控制参数,进行理论分析和数值仿真,发现随着外激振力的增大,动力系统从围绕1个焦点的周期运动转变成围绕2个焦点的周期运动.结果表明非齐次项(即外激振力项)不会导致动力系统不稳定.The Duffing equation was derived to analyze the non-linear behavior of an annular thin plate. An advantage of Galerkin method was that, for a given trial function, the residuals of the dynamic von Karman partial differential equations could be eliminated easily, thereby the governing equation of an annular thin plate for forced vibration, namely the hard-spring type of Duffing equation, could be obtained. Then Krylov-Bogoliubov-Mitropolskii (KBM) method was used to solve the Duffing equation, because the solutions were used to analyze qualitatively the effect of boundary conditions, ratio of damp, external excitation, and ratio of inner radius to outer radius on the vibration of an annular thin plate.Finally, by stability theory and numerical simulation, the results show as non-homogeneous term (namely external excitation term) increases, it will not make the dynamic system unstabilized because it makes dynamic system no bifurcation but from periodic motion around one focus to periodic motion around two focuses.

关 键 词：环形薄圆板 动态卡门偏微分方程 硬弹簧型达芬方程 周期吸引子 

分 类 号：O322[理学—一般力学与力学基础]