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Chaos in a Mapping Describing Elastoplastic Oscillations

In memoriam: Pat Sethna

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Advances in Nonlinear Dynamics: Methods and Applications

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Abstract

We study the local and global dynamical behavior of a two dimensional piecewise linear map which describes the asymptotic motions of a single degree of freedom, parametrically excited, elastoplastic oscillator after it has settled down to purely elastic oscillations. We give existence and stability conditions for periodic orbits and prove that chaos, in the form of a Smale horseshoe, exists at specific, but representative, parameter values. We interpret simulations of the elastoplastic oscillator itself in the light of these results.

Partially supported by NSF grant number MSS-9016626.

Partially supported by AFOSR 91–0329.

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Author information

Authors and Affiliations

  1. Department of Theoretical & Applied Mechanics, Cornell University, 14853, Ithaca, NY, USA

    Rudra Pratap & Philip Holmes

Authors
  1. Rudra Pratap
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  2. Philip Holmes
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Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, Purdue University, West Lafayette, USA

    Anil K. Bajaj

  2. Department of Mechanical Engineering, Michigan State University, East Lansing, USA

    Steven W. Shaw

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© 1995 Springer Science+Business Media Dordrecht

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Pratap, R., Holmes, P. (1995). Chaos in a Mapping Describing Elastoplastic Oscillations. In: Bajaj, A.K., Shaw, S.W. (eds) Advances in Nonlinear Dynamics: Methods and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0367-1_6

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  • DOI: https://doi.org/10.1007/978-94-011-0367-1_6

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4164-5

  • Online ISBN: 978-94-011-0367-1

  • eBook Packages: Springer Book Archive

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