裂纹梁固有频率近似计算方法

Approximate Calculation Method for the Natural Frequencies of Cracked Beam

损伤裂纹会导致结构局部刚度减小,降低结构自振频率。在结构自振频率的计算中,采用理论或数值分析方法得到的结构刚度系数均不能根据裂纹的状态而变化,无法很好地考虑裂缝张开闭合状态对结构固有频率的影响。基于接触非线性理论,提出呼吸裂纹梁固有频率近似计算法。通过对裂缝悬臂梁在受激振力后的自由振动分析,得到考虑接触非线性的呼吸裂纹梁的动力响应,再通过快速傅里叶变换,得到裂缝梁的频响函数,进一步由频率位移关系确定呼吸裂纹梁的固有频率。实例计算表明,采用考虑接触非线性的动力识别方法确定非线性梁的固有频率具有一定的可行性,能够保证一定的精度。

The presence of crack in structure usually causes a local reduction in stiffness and the reduction of natural frequencies. At present, in the calculation of the natural frequencies, the stiffness coefficient of the structure is unchanged with the different states of crack, no matter by the theoreti- cal analysis or numerical analysis. The computing on natural frequencies could not take different state of crack＇ s opening or shutting into consideration well. The dynamic responses of any structure contain the inherent characteristics, at the same time, the contact states can be considered by the nonlin- ear theory of contact. Thus, according to this thinking, by the free vibration of the cantilever beam after an excitation force, we got the dynamic re- sponse of a breathing cracked beam, which considered the contact nonlinear. By the Fast Fourier Transform （FFF）, we got the frequency-response function of the concrete cracked beam. So, the natural frequencies of breathing cracked beam could be determined by the relationship between fre- quency and displacement. The examples show that the proposed method is feasible ,at the same time, the method can ensure the certain engineering precision.