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Oscillatory chain with grounding support in conditions of acoustic vacuum. (Russian. English summary) Zbl 1381.70037

Summary: In this work we investigate dynamics of a string with uniformly distributed discrete masses without tension both analytically and numerically. Each mass is also coupled to the ground through lateral spring which provides effect of cubic grounding support. The most important limiting case of low-energy transversal oscillations is considered accounting for geometric nonlinearity. Since such oscillations are governed by motion equations with purely cubic stiffness nonlinearities, the chain behaves as a nonlinear acoustic vacuum. We obtained adequate analytical description of resonance non-stationary processes in the system which correspond to intensive energy exchange between parts (clusters) of the chain in low-frequency domain. Conditions of energy localization are given. Obtained analytical results agree well with results of computer simulations. The considered system is shown to be able to be used as very effective energy sink.

MSC:

70K30 Nonlinear resonances for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
70K75 Nonlinear modes
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