Abstract
We present results of analytical and numerical study of planar dynamics of a membrane consisting of one longitudinal and N transversal strings without a preliminary stretching with uniformly distributed discrete masses. In the previous paper it was shown that in the most significant case of predominantly transversal dynamics an effective non-local axial force is formed in longitudinal string and equations of motion cannot be linearized. Therefore the membrane oscillates in the conditions of “non-local” acoustic vacuum and can be used as an efficient energy trap. Adequate analytical description of non-stationary resonance dynamics at such conditions is achieved in terms of limiting phase trajectories (LPT) corresponding to maximum possible energy exchange between different parts (clusters) of the membrane. We have revealed also in these terms the conditions of energy localization in the initially excited cluster. Analytical results are confirmed by numerical simulation data.
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Acknowledgements
We are grateful to the Russian Foundation for Basic Research (Grants No. 17-01-00582, 16-02-00400) for financial support of this work.
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Koroleva (Kikot), I.P., Manevitch, L.I. (2019). Is Energy Localization Possible in the Conditions of Non-local Acoustic Vacuum?. In: Andrianov, I., Manevich, A., Mikhlin, Y., Gendelman, O. (eds) Problems of Nonlinear Mechanics and Physics of Materials. Advanced Structured Materials, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-92234-8_3
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DOI: https://doi.org/10.1007/978-3-319-92234-8_3
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