裂纹梁无效损伤位置的理论分析和实验研究

Theoretical Analysis and Experimental Study on Non-effective Damage Locations of Cracked Beams

以两端固支裂纹梁为例,通过理论和实验方法探讨无效损伤位置。首先将梁的裂纹模拟为无质量的等效扭转弹簧,得到裂纹梁的特征方程,并求解特征方程解得固有频率。数值计算结果表明,某阶模态的无效损伤位置就是该阶模态固有频率与裂纹深度无关的位置,并且该位置出现裂纹时无法通过计算相应模态的曲率模态差来判断是否出现损伤。不同阶模态的无效损伤位置也会不同。随后用质量块模拟裂纹进行实验研究,利用移动质量块的方法模拟不同损伤位置得到的梁固有频率曲线,与健康梁固有频率对比,从而得到梁的无效损伤位置。最后将质量块放置在梁无效损伤位置上模拟裂纹,实验测得该梁的曲率模态,实验结果表明:当质量块布置在梁某阶无效损伤位置时,梁该阶固有频率几乎不发生变化,且相应模态的曲率模态差无法检测出损伤信息,与数值计算结果相符。

The non-effective damage locations of a cracked beam with both ends clamped are investigated theoretically and experimentally. First of all, the crack is modeled as an equivalent massless rotational spring. The natural frequency is obtained by solving the characteristic equation of the cracked beam. The numerical calculation results show that the noneffective damage locations of some modal are the positions where the natural frequency of the modal is independent of the depth of the crack. When the crack appears at these locations one cannot judge whether the damage occurs by calculating the curvature modal difference only. The non-effective damage locations are different for the modals of different orders. Later on, experiment is done by replacing the crack by equivalent mass blokes. The natural frequency curve is obtained by using the method of moving auxiliary mass block. The natural frequency curve is then compared with that of a healthy beam so asto obtain the non- effective damage zones of the cracked beam. Finally, the auxiliary mass block is placed on the noneffectivedamage locations to simulate the crack and the curvatures modal is obtained experimentally. The experimental results show that when the mass arranged at the non-effective damage location corresponding to the modal of some order,the natural frequency of this order hardly changes, and the corresponding curvatures modal difference cannot detect the damage information. This conclusion is consistent with the results of numerical calculation.