材料非线性圆板的1/21/4亚谐解  

1/21/4 SUBHARMONIC SOLUTION TO A CIRCULAR PLATE OF NONLINEAR MATERIAL

作　　者：李银山[1] 张善元[2] 张明路[1] 李彤[3] 

机构地区：[1]河北工业大学机械工程学院,天津300130 [2]太原理工大学应用力学研究所,太原030024 [3]华东理工大学机械工程学院,上海200237

出　　处：《振动与冲击》2006年第3期115-120,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(10472076);山西省自然科学基金项目(20001007)

摘　　要：计及材料的非线性弹性和粘性性质,研究了圆板在简谐载荷作用下的12 14亚谐解,导出了相应的非线性动力方程。提出一类强非线性动力系统的叠加-迭代谐波平衡法。将描述动力系统的二阶常微分方程,化为基本解的基本微分方程;和分岔解的增量微分方程。通过叠加-迭代谐波平衡法得出了圆板的12 14亚谐解。首次给出了强非线性强迫振动解的完整结构。将Arnold舌头的结构作了推广,不仅给出了亚谐解的分岔形式,而且给出了超谐解、超亚谐解和亚超谐解的分岔形式。同时给出了倍周期分岔解的叠加分布图。The nonlinear dynamic equationg of a circular plate consisting of nonlinear visco-elastic material under a harmonic excitation is derived.An iteration harmonic balance method is presented for the steady-state analysis of strongly nonlinear oscillators.Thus,a nonlinear oscillation system which is described by a second order ordinary differential equation can be expressed as a basic differential equation with basic harmonic solution and an incremental differential equation with bifurcation solution.The 1214subharmonic solution for the circular plates is investigated by the superpostion-iteration harmonic balance method.At the first time,a complete structure of solution to forced oscillations of systems with strong nonlinearity is obtained.The structure of Arnold tongue is extended.The structure of solution indudes four cases:superharmonic sodution,subharmonic solution,super subharmonic solution and sub-superharmonic solution.The superposition distributing structural graph of period-doubling bifurcation solution is drawed.

关 键 词：强非线性动力系统 叠加-迭代谐波平衡法 1/2+1/4亚谐解 分岔 

分 类 号：O322[理学—一般力学与力学基础]