一类强非线性振动系统的改进能量解析法  

MODIFIED ENERGY METHOD FOR A CLASS OF STRONGLY NONLINEAR VIBRATION SYSTEM

作　　者：鲍文博[1] 闻邦椿[2] 

机构地区：[1]沈阳工业大学建筑工程学院,沈阳110023 [2]东北大学机械工程与自动化学院,沈阳110004

出　　处：《工程力学》2006年第6期1-5,10,共6页Engineering Mechanics

基　　金：辽宁省教育厅高等学校科学研究项目(202063287);沈阳工业大学学科基金资助项目(521100401)

摘　　要：能量法是求解强非线性系统常用的一种近似解析方法,由于忽略了激励力和阻尼力所做的瞬时功的影响,计算上比较方便。但是当扰力水平较高时,能量解法往往会产生较大误差。揭示了能量法产生误差的原因,并对传统的能量法进行了修正,提出了一种新的解析法-改进能量法。以动力基础为研究对象,用改进能量法给出了此类强非线性非自治系统的解析解,并用Runge-Kutta法对该系统进行了数值计算。分析表明,改进能量法比传统的能量法有了很大的改进,即便是在扰力水平较高的亚谐振动条件下,仍然能够给出较为准确的解。The energy method is a approximately analytical approach frequently used in solving strongly nonlinear systems. The calculation is simplified due to ignoring the affection of instantaneous work done by exciting and damping force. But it will generate biggish error when the system suffers high disturbance. The cause of the error is unveiled and the classical energy method is improved in the paper. A new analytical approach, modified energy method （MEM）, is developed at last. Analytical solution of strongly nonlinear nonautonomous systems is proposed based on MEM for dynamic foundations, and numerical calculation is carried out with Runge-Kutta method for the system. The results of numerical analysis show that MEM is more accurate than classical energy method, even under subharmonic vibration with high disturbance.

关 键 词：振动理论 强非线性 改进能量法 能量法 非自治系统 

分 类 号：O322[理学—一般力学与力学基础]