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Global dynamics of an autoparametric spring–mass–pendulum system

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Abstract

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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Authors and Affiliations

  1. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Khalid El Rifai & George Haller

  2. School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907-2088, USA

    Anil K. Bajaj

Authors
  1. Khalid El Rifai
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  2. George Haller
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  3. Anil K. Bajaj
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Correspondence to Anil K. Bajaj.

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Rifai, K.E., Haller, G. & Bajaj, A.K. Global dynamics of an autoparametric spring–mass–pendulum system. Nonlinear Dyn 49, 105–116 (2007). https://doi.org/10.1007/s11071-006-9116-y

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  • DOI: https://doi.org/10.1007/s11071-006-9116-y

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