Global Convergence Methods for Determining Periodic Solution of Nonlinear Dynamic Systems
Chen Hongkui(1,2),Xu Qingyu(1),Zhang Tao(3)
(1 Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an 710049, China)
(2 Institute of Science, Chang'an University, Xi'an, 710064)
(3 Department of admission and employment, Xi'an Institute of post and Telecommun ications, Xi'an, 710061)

Abstract: The analysis of dynamic system with multiple degrees of freedom usually encounter extreme nonlinearity,which exactly interpret the mechanisms of some phenomena. The fundamental response of a nonlinear nonautonomous system, may bifurcatate from periodic motion as system parameter varies, thus to determine the periodic solution is required in such case. An efficient method to evaluate nonlinear vibration periodic solution is proposed where a global convergence of periodic solutions can be achieved, and Euler-Newton algorithm based on predictor corrector method is used to trace the solution path. The examples confirm efficiency of this continuation algorithm.
Keywords: nonlinear dynamics, periodic motion, continuation method, bifurcation.