Global dynamics of an autoparametric spring–mass–pendulum system

被引：0
作者：
Khalid El Rifai
George Haller
Anil K. Bajaj
机构：
[1] Massachusetts Institute of Technology,Department of Mechanical Engineering
[2] Purdue University,School of Mechanical Engineering
来源：
Nonlinear Dynamics | 2007年 / 49卷
关键词：
Autoparametric pendulum; Domains of attraction; Finite-time Lyapunov exponents; Global dynamics; Internal resonance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a study of the global dynamics of an autoparametric four degree-of-freedom (DOF) spring–mass–pendulum system with a rigid body mode is presented. Following a modal decoupling procedure, typical approximate periodic solutions are obtained for the autoparametrically coupled modes in 1:2 internal resonance. A novel technique based on forward-time solutions for finite-time Lyapunov exponent is used to establish global convergence and domains of attraction of different solutions. The results are compared to numerically constructed domains of attraction in the plane of initial position and initial velocity for the pendulum. Simulations are also provided for a few interesting cases of interest near critical values of parameters. Results also shed some light on the role played by other modes present in a multi-DOF system in shaping the overall system response.
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页码：105 / 116
页数：11
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