比例粘性減衰を有する内部共振衝突振動系に現れる減衰概周期振動の波動アルゴリズムによる解析（釣合位置で完全弾性衝突する場合）

概要

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In this paper, we study periodic energy transfer in multiple vibro-impact oscillators under proportional viscous damping by using wave algorithm. Internal resonance frequency is obtained by the condition that some off-diagonal elements become to 0 in state transition matrix. Under equivalent modal damping rate, we derive the condition of periodic damped and periodic energy transfer that contains sub-harmonic resonance which depends on mass ratio between the impact and non-impact small oscillators. Under non-equivalent modal damping rate, modulation of the frequency in imperfect damped energy transfer is observed. We obtain a state transition matrix of non-equivalent modal damping rate as the perturbation of that in equivalent. The modulation of periodic damped energy transfer depends on the decay of the modal damping rate in the small impact oscillator.