Physical Sience and Technical Research

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.

Two-mode; Parametric resonance; Experiment; Portal frame; Coupling/Uncoupling