Smart Structures and Systems

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Perturbation method for the dynamic analysis of a bistable oscillator under slow harmonic excitation

  • Luongo, Angelo (M&MoCS, International Research Center on Mathematics and Mechanics of Complex Systems, University of L'Aquila) ;
  • Casciati, Sara (DICAr-Dipartimento di Ingegneria Civile e Architettura, University of Catania) ;
  • Zulli, Daniele (M&MoCS, International Research Center on Mathematics and Mechanics of Complex Systems, University of L'Aquila)
  • Received : 2015.09.26
  • Accepted : 2016.05.06
  • Published : 2016.07.25
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Abstract

In this paper a nonlinear, bistable, single degree of freedom system is considered. It consists of a Duffing oscillator externally excited by a non-resonant, harmonic force. A customized perturbation scheme is proposed to achieve an approximate expression for periodic solutions. It is based on the evaluation of the quasi-steady (slow) solution, and then on a variable change followed by two perturbation steps which aim to capture the fast, decaying contribution of the response. The reconstructed solution, given by the sum of the slow and fast contributions, is in a good agreement with the one obtained by numerical integration.

Keywords

Acknowledgement

Supported by : Natural Science Foundation

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