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Closed-form periodic solutions for piecewise-linear vibrating systems

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Abstract

In this paper, closed-form asymptotic solutions are derived for piecewise-linear one- and two-degrees-of-freedom systems. Deviations from perfectly linear restoring force characteristics play the role of small but nonsmooth perturbations. It is shown that the nonsmooth transformation of temporal argument enables one of justifying at least first several steps of the classic perturbation procedure which eventually gives the unit-form solutions. The form of the solutions is suitable for further manipulations including possible generalization on non-periodic cases.

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Author notes

  1. V. N. Pilipchuk

    Present address: General Motors Technical Center, Warren, MI, USA

Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, The National University, Dnepropetrovsk, Ukraine, 49050

    V. N. Pilipchuk

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  1. V. N. Pilipchuk
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Correspondence to V. N. Pilipchuk.

Additional information

Reported at Twelfth Conference on Nonlinear Vibrations, Dynamics, and Multibody Systems, Virginia Tech, June 1–5, 2008.

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Pilipchuk, V.N. Closed-form periodic solutions for piecewise-linear vibrating systems. Nonlinear Dyn 58, 169–178 (2009). https://doi.org/10.1007/s11071-009-9469-0

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  • DOI: https://doi.org/10.1007/s11071-009-9469-0

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