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Experimental and Numerical Analyses for Auto-Parametric Internal Resonance of a Framed Structure

The auto-parametric internal resonance experiment of a [Formula: see text]-shaped frame is first conducted in this research. A non-contact electromagnetic vibration exciter is used to exert a periodic force on the vertical beam of the frame. The phenomena of internal resonance and non-internal resonance are observed and measured in this test. A common resonance of the vertical beam is excited by the external electromagnetic force, and the auto-parametric internal resonance of the horizontal beam is subsequently induced by the common resonance. The numerical method is also used to simulate the internal resonance and non-internal resonance. The stability boundaries of internal resonance and non-internal resonance are numerically and experimentally determined and compared. The numerical stability boundaries are in agreement with the experimental results. The results indicate that a small external excitation can excite a strong internal resonance response of a framed structure. The unstable domain of the internal resonance is much bigger than that of the non-internal resonance. The auto-parametric internal resonance is much more dangerous than the non-internal resonance. The risk of auto-parametric internal resonance should be emphasized and avoided in the designs of engineering structures.