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New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems

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Abstract

We present new analytical approach to the problem of energy pumping in strongly non- homogeneous nonlinear two-degree-of-freedom (2DOF) systems with single anchor spring under condition of initial impact. Energy pumping is a passive, almost irreversible transfer of mechanical energy from the main substructure of the system to the light auxiliary attachment. The mechanism of energy pumping in the system under consideration is a resonance capture. The approach is based on application of Laplace transformation to the principal asymptotic approximation of the equations of motion in complex form and using the power expansion of the solution in terms of time. Obtained temporal dependence of the system energetic characteristics gives a tool for estimation of energy pumping efficiency. In particular, we show that the system without an anchor spring in attachment is more efficient than the system with such a spring. Numerical simulations confirm the analytical results.

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Authors and Affiliations

  1. N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, 119991, Moscow, Russia

    Leonid I. Manevitch & Andrey I. Musienko

  2. LGM, URA CNRS 1652, Ecole Nationale des Travaux Publics de l’Etat, 3 Rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France

    Claude-Henri Lamarque

Authors
  1. Leonid I. Manevitch
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  2. Andrey I. Musienko
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  3. Claude-Henri Lamarque
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Correspondence to Andrey I. Musienko.

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Manevitch, L.I., Musienko, A.I. & Lamarque, CH. New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems. Meccanica 42, 77–83 (2007). https://doi.org/10.1007/s11012-006-9021-y

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  • DOI: https://doi.org/10.1007/s11012-006-9021-y

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