梁的强非线性超、次谐波共振  

SUPERHARMONIC AND SUBHARMONIC RESONANCES OF STRONGLY NONLINEAR VIBRATION OF BEAMS

作　　者：黄建亮[1] 黄惠仪[1] 陈恒[1] 陈树辉[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275

出　　处：《振动与冲击》2004年第1期1-3,共3页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目 (1 0 2 72 1 1 7);广东省自然科学基金资助项目 (0 1 1 2 0 3)

摘　　要：本文采用改进的L -P法研究梁的强非线性振动 ,分析了超谐波共振和次谐波共振两种情况。首先建立了梁振动的Duffing方程 ,然后采用改进的L -P法分别求解超谐波响应和次谐波响应 ,最后给出两个典型算例 ,其计算结果与增量谐波平衡法和经典的L -P法进行比较。算例表明 ,改进的L -P法得出的计算值与增量谐波平衡法所得出的结果非常吻合 ,但是经典的L -P法就失效了。The modified Lindstedt-Poincae method (MLP) is used to analyze strongly nonlinear vibration of beams. Attention is focused on the superhamonic and subharmonic resonances. Firstly the governing dynamic equation of a strongly non-linear beam is set up. Then the modified Lindstedt-Poincae method is formulated for analyzing the superharmonic and subharmonic resonances. Finally, two examples are presented to show the effectiveness of the present method. The numerical results of the modified Lindstedt-Poincae method are in good agreement with those of the Incremental Harmonic Balance (IHB) method, while the classical Lindstedt-Poincae method is invalid here.

关 键 词：梁 超谐波共振 次谐波共振 DUFFING方程 L-P法 增量谐波平衡法 

分 类 号：O327[理学—一般力学与力学基础]