基于固有频率的呼吸式裂纹梁损伤识别方法

将呼吸裂纹梁简化为由扭转弹簧连接的两段弹性梁，在假定振动响应随振幅变化的基础上推导出呼吸裂纹梁的固有频率方程；考虑振动过程中呼吸裂纹的开合情况，假定裂纹梁的刚度是振幅的非线性函数，建立了呼吸裂纹梁的多项式刚度模型；结合等高线裂纹识别理论和方法，提出了一种基于固有频率的呼吸裂纹梁损伤识别方法，算例验证了方法的可行性与有效性。研究表明，该方法的识别精度取决于实验固有频率的精度。

A Damage Identification Method of a Breathing Cracked Beam by Natural Frequency

Firstly, a cracked cantilever beam was simplified into two elastic beams connected by a torsion spring. It was supposed that the vibration response varied as the vibration amplitude of the beam. And the natural frequency equation of a breathing cracked beam was derived. Then, the open and close conditions of the breathing crack during vibrations were considered. A polynomial stiffness model of the breathing cracked beam was built up by the postulation that the stiffness of the cracked beam was one of nonlinear functions of the vibration amplitudes. Thereafter, a damage identification method of a breathing cracked beam by natural frequency was proposed combined with the natural frequency equation and the stiffness model. The feasibility and effectiveness of this method was verified by case studies in the end. Results indicate that the identification precision of this method depends on the testing precision of the experimental natural frequency.