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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。
Taking the cracked beam with both ends as an example, the location of the invalid damage is discussed by theoretical and experimental methods. First, the crack of the beam is modeled as a massless equivalent torsion spring, the characteristic equation of the cracked beam is obtained, and the eigenvalue equation is solved to obtain the natural frequency. The numerical results show that the ineffective damage location of a mode is the position irrelevant to the crack’s natural frequency and the crack can not be judged by the modal difference of the corresponding modes. Different modes of ineffective damage location will be different. Then the crack was simulated by mass and the mass of the beam was simulated by moving the mass. The natural frequency of the beam was simulated and compared with the natural frequency of the healthy beam to obtain the ineffective position of the beam. Finally, the mass is placed on the simulated crack at the ineffective damage location of the beam, and the curvature mode of the beam is measured experimentally. The experimental results show that the inherent frequency of the beam is almost unchanged when the mass is placed at the ineffective damage location of the beam , And the modal curvature mode difference can not detect the damage information, which is consistent with the numerical calculation.