求强非线性系统共振解的渐近法  

ASYMPTOTIC METHOD FOR SOLVING RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

作　　者：彭献[1] 盛国刚[2] 

机构地区：[1]湖南大学工程力学系,长沙410082 [2]长沙交通学院桥梁与结构工程系,长沙410076

出　　处：《振动与冲击》2004年第1期45-46,60,共3页Journal of Vibration and Shock

基　　金：湖南省自然科学基金资助项目 (0 1JJY2 0 0 7)

摘　　要：本文通过引入参数变换α=ε/(υ2 +ε) ,并假设ω20 =(pυ/q) 2 +α△ ,把强非线性系统转化为弱非线性系统 ,再将解展开为傅氏级数 ,利用参数待定法可方便地求出强非线性系统的共振解。算例表明近似解与数值解非常接近。By introducing a parameter transformation α=Ε(v2+Ε) and supposing ω02=(pv/q)2+αΔ the strongly nonlinear system is transformed into a weak nonlinear system. The solution of the weak nonlinear system is expanded by Fourier series, and then the resonance solution of strongly nonlinear system can be found by undetermined parameter method. An example shows that approximate solution is in good agreement with numerical solution.

关 键 词：强非线性系统 共振解 参数变换 傅氏级数 渐近法 

分 类 号：O322[理学—一般力学与力学基础] O241.82[理学—力学]