发表机构
Technion – Israel Institute of Technology; University of Illinois Urbana-Champaign（以色列理工学院; 伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非标准弱频率调制激励下线性谐振器的共振现象，通过wNSFM信号激发振荡器，发现弱阻尼和无阻尼振荡器有独特共振特性，给出非简单共振条件，揭示了一类新的有趣共振现象，且共振响应参数变化鲁棒。
AI 中文摘要
研究表明，包含新型弱非标准频率调制（wNSFM）的谐波信号具有意外的频谱特性，即随时间推移宽带频谱不断扩展，代表了一类具有强频率-时间耦合的新信号。将此wNSFM信号应用于激励经典单自由度线性、时不变阻尼/无阻尼振荡器，产生了新的独特的高度鲁棒共振现象。弱阻尼振荡器在有限时间间隔内有两个涉及相对高振幅不同谐波的瞬态共振捕获，整体响应随\(t\rightarrow\infty\)衰减为\(~t^{-1/2}\)。无阻尼振荡器有简单和非简单共振两种类型，给出了非简单共振的充要条件定理，其共振谐波会无界增长，与传统线性谐振器不同。这些共振响应对wNSFM参数变化具有鲁棒性。
英文摘要
It is shown that harmonic signals incorporating a type of weak non-standard frequency modulation (wNSFM) have interesting spectral properties, namely, time-dependent bandwidths that become increasingly broader with increasing time. As such, they represent a class of signals with frequency-time coupling in their spectra. Specifically, the weakly damped oscillator exhibits always two transient resonance captures involving two distinct harmonics possessing relatively high amplitudes over finite time intervals, while the overall response decays as $~t^{-1/2}$ as $t\rightarrow\infty$. Considering the undamped oscillator, it possesses two types of resonances, referred to as simple and non-simple resonances. Simple resonances correspond to finite-amplitude steady-state responses caused by two sustained resonance captures, in the form of two distinct modulated quasi-periodic responses, which, however are "activated" at different time instances. The necessary and sufficient conditions for non-simple resonances are given in the form of a theorem which predicts the existence of resonant harmonics and specifies the special phase conditions that the resonant harmonics must satisfy for constructive interference; the resulting undamped non-simple resonance grows unboundedly as $~t^{-1/2}$ as $t\rightarrow\infty$, in contrast to the classical resonance growth of the linear resonator with unmodulated harmonic excitation whose response grows as $~t$ as $t\rightarrow\infty$. These resonant responses are persistent to changes in the parameters of the wNSFM. Our results reveal interesting infinite sets of resonances in linear SDOF resonators under frequency-modulated excitations.
