论文标题
能量定位和自动散发性弱耗散链链中的转移
Energy localization and transfer in autoresonant weakly dissipative anharmonic chains
论文作者
论文摘要
在这项工作中，我们开发了一个分析框架，以解释耗散参数对强烈非线性弱阻尼的链中自动持持续性的出现和稳定性的影响，该链受到谐波强迫的频率缓慢。使用渐近过程，我们构建了进化方程，该方程描述了在1：1共振的条件下阵列的行为，然后大约计算慢速振幅和相位以及自动兑换持续时间。结果表明，与在无孔链中具有无界能量生长的非隔离性链中的自动兑换相反，最初静止的弱阻尼阵列中的能量仅在有界的时间间隔内生长，直到同时从所有自动振荡器的共振中同时逃脱。通过数值模拟证实了自动耐药性出现和稳定性的分析条件。
In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with a slowly-varying frequency. Using the asymptotic procedures, we construct the evolutionary equations, which describe the behavior of the array under the condition of 1:1 resonance and then approximately compute the slow amplitudes and phases as well as the duration of autoresonance. It is shown that, in contrast to autoresonance in a non-dissipative chain with unbounded growth of energy, the energy in a weakly damped array being initially at rest is growing only in a bounded time interval up to an instant of simultaneous escape from resonance of all autoresonant oscillators. Analytical conditions of the emergence and stability of autoresonance are confirmed by numerical simulations.
