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.

中文翻译：

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框架结构自参数内部共振的实验和数值分析

本研究首先进行了[公式：见正文]形框架的自参数内共振实验。采用非接触式电磁激振器对框架的垂直梁施加周期性的力。在该试验中观察和测量了内部共振和非内部共振的现象。垂直梁的共共振由外部电磁力激发，水平梁的自参内部共振随后由共共振引起。数值方法也用于模拟内部共振和非内部共振。内部共振和非内部共振的稳定性边界通过数值和实验确定和比较。数值稳定性边界与实验结果一致。结果表明，小的外部激励可以激发框架结构的强内部共振响应。内部共振的不稳定域远大于非内部共振的不稳定域。自参数内部共振比非内部共振危险得多。在工程结构设计中应强调和避免自参数内部共振的风险。