Numeric Research of Chaotic Response for a Cubic Nonlinear Dynamic System
Longitudinal vibration of a nonlinear viscoelastic rod system with one end fixed and another end subjected to an axial periodical excitation was studied under the consideration of transverse inertia. By using Galerkin method and for hard stiffness nonlinear material, a combined Parametric and Forcing Excited cubic nonlinear dynamic system is derived. Here, arc-length method is used for an accurate integral procedure, and numeric results are given detailedly. The process of the system evolved from stable periodic motion to chaos is illustrated in the period-doubling bifurcation graph of the parameter space, and the Lyapunov exponent spectrum is also given that is perfectly consistent with bifurcation process. The strange attractor obtained from Poincare Map is present, which has different fractal dimension from Duffings one, so it may be a new chaotic attractor.
cubic nonlinear viscoelastic Galerkin method arc-length method bifurcation strange attractor
Jingwu Gao Xiaoli Wang Zhixiang Zhang
School of Science North University of China Taiyuan 030051, China School of Mechatronic Engineering North University of China Taiyuan 030051, China
国际会议
太原
英文
396-399
2010-10-22（万方平台首次上网日期，不代表论文的发表时间）