非对称强非线性振动特征分析  

ASYMMETRIC,STRONGLY NONLINEAR OSCILLATION CHARACTERISTIC ANALYSIS

作　　者：李银山[1] 潘文波[1] 吴艳艳[1] 李欣业[1] 

机构地区：[1]河北工业大学机械工程学院力学系,天津300130

出　　处：《动力学与控制学报》2012年第1期15-20,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金重点资助项目(10632040)~~

摘　　要：提出了构造一类非线性振子解析逼近周期解的的初值变换法.用Ritz-Galerkin法,将描述动力系统的二阶常微分方程,化为以振幅、角频率和偏心距为独立变量的不完备非线性代数方程组;关键是考虑初值变换,增加补充方程,构成了以角频率、振幅和偏心距为变量的完备非线性代数方程组.作为例子利用初值变换法求解了相对论修正轨道方程的六种分岔周期解.给出了非对称振动的幅频曲线和偏频(偏心距与角频率的关系)曲线.发现了固有角频率漂移现象.A method of initial-value transformation was presented to obtain the approximate analytic periods of a class of nonlinear oscillators. The periodic solutions can be expressed in the forms of basic harmonics and bifurcate harmonics. Thus,an oscillation system,which is described as a second order ordinary differential equation, can be expressed as a set of non-linear algebraic equations with a frequency,amplitudes as the independent variables using Ritz-Galerkin’s method. But the set of equations is incomplete,and the key is to consider initial-value transformation. After adding supplementary equations,a set of non-linear algebraic equations with angular frequencies,amplitudes as the independent variables was constituted completely. For examples,six asymmetric periodic solutions bifurcating about a nonlinear differential equation arising in general relativity were solved by using the method of initial-value transform. Amplitude-frequency curves and central offset-frequency curves of the asymmetrically vibration systems were derived. In addition,the drift phenomenon of natural angular frequency was discovered.

关 键 词：初值变换法 非对称振动 分岔 偏-频曲线 固有角频率漂移 

分 类 号：O322[理学—一般力学与力学基础]