Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method  

作　　者：原培新 李永强 

机构地区：[1]Mechanical Engineering and Automation School,Northeastern University(Shenyang) [2]College of Science,Northeastern University(Shenyang)

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第10期1293-1304,共12页应用数学和力学（英文版）

基　　金：supported by the Fundamental Research Funds for the Central Universities(No.N090405009)

摘　　要：A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.

关 键 词：homotopy analysis method primary resonance series solution strong nonlinearity MULTI-DEGREE-OF-FREEDOM 

分 类 号：O322[理学—一般力学与力学基础]