摘要
本文通过一个门式框架的参数共振试验，发现了涉及两种振动模态参与的新的参数共振现象。当框架的平面内频率近似等于扭转频率，并且外部周期性激励参数位于结构参数共振的不稳定区域内时，结构系统将发生新奇的双模态参数共振。在不稳定域内观察到四种不同的参数共振现象，第一种现象是单模态扭转参数共振，其特征为大振幅的扭转共振和较小的不规则平面内振动；第二、三种现象是双模态参与的同相位和异相位参数共振，其中大振幅平面内和扭转模式运动分别表现出同步和异步行为，这两种模式运动之间存在显著的耦合和能量传递；第四种现象是双模态非耦合参数共振，其特征是振幅相对较小，双模运动之间没有相互作用或能量交换，平面内振动表现出间歇性的参数共振，而扭转模态参数共振保持相对稳定的极限环振荡。本文进一步讨论了不稳定区域内不同位置的结构参数共振的特征。复杂的双模态参数共振对实际工程结构可能构成潜在的危害，本文的试验发现可为复杂非线性参数共振的潜在技术应用提供参考。
关键词： 双模态；参数共振；试验；门式框架；耦合/非耦合
Abstract
This paper discovers new parametric resonance phenomena involving two vibration modes through a parametric resonance test of a portal frame. When the in-plane frequency of the frame is approximately equal to the torsional frequency, and the external periodic excitation falls within the instability region of structural parametric resonance, special two-mode parametric resonances occur in the structural system. Four distinct parametric resonance phenomena are observed within the instability domain. The first type is the one-mode torsional instability, characterized by a predominant large-amplitude torsional resonance with minor irregular in-plane vibrations. The second and third types are the two-mode in-phase and out-of-phase instabilities, where the large-amplitude in-plane and torsional mode motions exhibit synchronous and asynchronous behavior, respectively. There are significant coupling and energy transfer between these two mode motions. The fourth type is the two-mode uncoupled parametric resonance, characterized by relatively smaller vibration amplitude and no interaction or energy exchange between the two mode motions. The in-plane mode motion demonstrates intermittent parametric resonance, whereas the torsional-mode parametric resonance maintains a relatively stable limit-cycle oscillation. The characteristics of parametric resonance at different locations within the instability region are also addressed. The complex two-mode dynamic instabilities pose potential hazards to practical engineering structures. The present study can serve as a valuable reference for potential applications of complex nonlinear parameter resonances.
Key words： Two-mode; Parametric resonance; Experiment; Portal frame; Coupling/Uncoupling
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