Kovaleva Agnessa
Space Research Institute, Russian Academy of Sciences, Moscow 117997, Russia.
Phys Rev E. 2016 Aug;94(2-1):022208. doi: 10.1103/PhysRevE.94.022208. Epub 2016 Aug 10.
Localization of energy in oscillator arrays has been of interest for a number of years, with special attention paid to the role of nonlinearity and discreteness in the formation of localized structures. This work examines a different type of energy localization arising due to the presence of dissipation in nonlinear resonance arrays. As a basic model, we consider a Klein-Gordon chain of finite length subjected to a harmonic excitation applied at an edge of the chain. It is shown that weak dissipation may be a key factor preventing the emergence of resonance in the entire chain, even if its nondissipative analog is entirely captured into resonance. The resulting process in the dissipative oscillator array represents large-amplitude resonant oscillations in a part of the chain adjacent to the actuator and small-amplitude oscillations in the distant part of the chain. The conditions of the emergence of resonance as well as the conditions of energy localization are derived. An agreement between the obtained analytical results and numerical simulations is demonstrated.
振荡器阵列中的能量局域化问题已被关注多年，人们特别关注非线性和离散性在局域结构形成中的作用。这项工作研究了由于非线性共振阵列中存在耗散而产生的一种不同类型的能量局域化。作为一个基本模型，我们考虑一个有限长度的克莱因 - 戈登链，在链的一端施加谐波激励。结果表明，即使其无耗散的类似物完全进入共振状态，微弱的耗散也可能是阻止整个链中出现共振的关键因素。耗散振荡器阵列中产生的过程表现为靠近激励器的链的一部分出现大幅共振振荡，而链的远处部分出现小幅振荡。推导了共振出现的条件以及能量局域化的条件。证明了所获得的分析结果与数值模拟之间的一致性。
