含双边呼吸式裂纹悬臂梁的自由振动分析  

Natural vibration analysis of the cantilever beam with bilateral breathing cracks

作　　者：马一江 李宇昕 王加夏 陈国平[2] 吴杰[1] 樊乐 马康佳 MA Yi-jiang;LI Yu-xin;WANG Jia-xia;CHEN Guo-ping;WU Jie;FAN Le;MA Kang-jia(School of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiang 212003,China;College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;University of Electronic Science and Technology of China,Zhongshan Institute,College of Mechanical and Electrical Engineering,Zhongshan 528400,China)

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212100 [2]南京航空航天大学航空学院,南京210016 [3]电子科技大学中山学院机电工程学院,广东中山528400

出　　处：《船舶力学》2023年第11期1718-1728,共11页Journal of Ship Mechanics

基　　金：国家重点研发计划资助(2022YFC2806600);国家自然科学基金项目(51809122)。

摘　　要：基于含双边裂纹梁的振动行为,本文提出一种含双边呼吸式裂纹悬臂梁自由振动的理论分析方法。考虑裂纹的倾斜角度,将裂纹模块转化成悬臂梁的局部柔度;根据双边裂纹的呼吸行为,建立含双边呼吸式裂纹悬臂梁的刚度模型;采用Galerkin方法,将梁结构的振动微分方程简化为多个单自由度系统的振动微分方程组,推导含双边呼吸式裂纹梁的固有频率和振型;通过ANSYS开展含双边呼吸式裂纹悬臂梁模态的数值分析,验证本文提出的理论方法。算例分析结果表明:与张开时裂纹模型相比,呼吸式裂纹模型更加接近工程实际;裂纹的倾斜角度是影响梁结构固有频率的重要因素,而裂纹对梁结构固有振型的影响很小。Based on vibration behaviors of beams with bilateral cracks,a theoretical method was proposed to conduct the natural vibration analysis of a cantilever beam with bilateral breathing cracks in this paper.Con-sidering the inclined angle of the cracks,the crack module was transformed into the local flexibility of the cantilever beam.According to breathing behavior of the bilateral cracks,the stiffness model of the cantilever beam with the bilateral breathing cracks was established.The vibration differential equation of the beam was simplified to vibration differential equations of several single-degree-of-freedom systems by Galerkin meth-od,and natural frequencies and modes of the cracked beam were derived.The numerical analysis of the cracked beam modal was carried out by ANSYS,and the theoretical method proposed in this paper was veri-fied.Results indicate that,compared with the opening crack model,the breathing crack model is closer to the engineering practice,and that the inclined angle of the crack is an important factor affecting natural frequen-cy of the beam while the crack has little impact on the natural mode of the beam.

关 键 词：呼吸式裂纹 双边裂纹 悬臂梁 GALERKIN方法 自由振动 

分 类 号：V224[航空宇航科学与技术—飞行器设计]