Universal solving program and Application in the strongly nonlinear oscillation system
Zhang Qi-chang1,2, Zhao Qiang-wei1, Wang Wei1,2
1.Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, School of Mechanical Engineering, Tianjin University, 300072, China; 2. State Key Laboratory of Engines, Tianjin 300072, China
Abstract：The universal solving procedure to calculate steady-state asymptotic solution of strongly nonlinear vibration system with multi-degree of freedom was presented, by using the undetermined fundamental frequency method and computer algebra Mathematica. With the aim of promoting traditional theory to high-dimensional complex systems, the systematization and routinization of coupled ordinary differential systems in application and calculation of higher order normal form was realized, which improved the theoretical derivation efficiently. A class of strongly nonlinear vibration of carbon nanotube system was researched for its normal form and steady-state asymptotic solution, and then the exciting force and damping effect for the vibration amplitude were discussed. Finally, the results of quantitative analysis and numerical results were compared to verify the effectiveness of the programming methodology.
2012, Vol. 31 
