基于梁裂纹在动静力荷载作用下的弯矩-转角曲线, 考虑裂纹开闭状态的过渡效应, 建立了一种新的呼吸裂纹的瞬变刚度扭转弹簧模型, 给出了具有任意裂纹数目梁瞬时模态的统一显式表达式, 以及一种呼吸裂纹梁非线性动力响应的近似计算方法. 数值分析了含单条呼吸裂纹简支梁的自由振动以及双裂纹悬臂梁在简谐荷载作用下的动力响应. 结果表明: 该裂纹等效瞬变刚度扭转弹簧模型可较好地描述裂纹的开闭合过程, 裂纹梁的瞬时频率介于完全开裂纹梁和完全闭合裂纹梁的自振频率之间, 并逐步趋于常数; 同时, 裂纹的开闭状态以及裂纹所处的梁上下表面位置对裂纹梁的非线性动力响应有显著影响.

Based on the curve of bending moment-rotation angle of the crack in beam under dynamic/static load and considering the transition effect between the open and closed states of the crack, a novel rotational spring model of the breathing crack with instant rigidity has been proposed, with a unified explicit formula of the vibration modes of the beam with an arbitrary number of breathing cracks, and an approximate computing method of the nonlinear dynamic response of the beam with breathing crack presented. The free vibration of the simply-supported beam with a breathing crack and dynamic response of the cantilever beam with two breathing cracks subjected to a harmonic load are analyzed numerically. The numerical results indicate that the open and closure procedure of the crack can be appropriately described with the rotational spring model of the breathing crack with instant rigidity as is presented in this paper, and that the instant frequency of the cracked beam is located between natural frequency of the beams with complete open crack and one of the beams with complete closed crack, which gradually converges to a constant. Furthermore, the open and closure state of the crack and its location on top or bottom surface of the beam have significant influences on the nonlinear dynamic response of the cracked beam.