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Smart Structures and Systems Volume 18, Number 1, July 2016 , pages 183-196 DOI: https://doi.org/10.12989/sss.2016.18.1.183 |
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Perturbation method for the dynamic analysis of a bistable oscillator under slow harmonic excitation |
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Angelo Luongo, Sara Casciati and Daniele Zulli
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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. | ||
| Key Words | ||
| energy harvesting; duffing oscillator; slow-fast dynamics; perturbation method | ||
| Address | ||
| Angelo Luongo and Daniele Zulli: M&MoCS, International Research Center on Mathematics and Mechanics of Complex Systems, University of L\'Aquila, Via Giovanni Gronchi, 18, 67100 L\'Aquila AO Italy Sara Casciati: DICAr-Dipartimento di Ingegnera Civile e Architettura, University of Catania, Italy | ||