框架结构空间自参数共振的试验与数值研究

Experimental and numerical studies on spatial self-parametric resonance of frame structure

工程中的框架结构经常受到周期性荷载的作用。在周期荷载作用下,框架结构可能发生空间自参数共振。采用数值计算和试验相结合的方法,研究了框架结构空间自参数共振的稳定性。首先基于哈密顿原理给出了一般框架结构空间动力失稳的理论公式,采用Newmark方法求解不稳定位移响应,用能量增长指数(EGE)确定了框架结构的参数共振稳定边界。此外对框架结构进行了空间自参数共振试验。通过数值计算和试验结果确定和比较了空间自参数内共振和非内共振的稳定边界,数值稳定边界与试验结果吻合较好。结果表明,小的外部激励可以激发框架结构的大振幅自参数共振,自参数内共振的不稳定区域远大于非内共振(一般情况)的不稳定区域,在框架结构设计中应尤其重视和避免空间自参数内共振的风险。

Frame structures in engineering are often subjected to periodic loads.Under action of periodic load,frame structure may have spatial self-parametric resonance.Here,the stability of spatial self-parametric resonance of frame structure was studied with numerical calculation and experiments.Firstly,based on Hamilton principle,the theoretical formula of spatial dynamic instability of general frame structures was derived,their unstable displacement responses were solved numerically with Newmark method,and the parametric resonance stability boundary of frame structure was determined using the energy growth exponent(EGE).Meanwhile,spatial self-parametric resonance experiments for frame structures were conducted.Stable boundaries of spatial self-parametric internal resonance and non-internal resonance were determined and compared with numerical calculation and experimental results.The results showed that numerical stable boundaries agree better with experimental results;small external excitation can excite large-amplitude self-parametric resonance of frame structure;the unstable region of self-parametric internal resonance is much larger than that of non-internal resonance under general situation;in frame structure design,special attention should be paid to the risk of spatial self-parametric internal resonance,and this risk should be avoided.