不同边界条件下裂纹梁的固有频率分析  

The analysis on the natural frequency of cracked beam under different boundary conditions

作　　者：任伟 赵渭平 刘永豹 Ren Wei;Zhao Weiping;Liu Yongbao(School of Mechanical and Electrical Engineering,Tongchuan Vocational and Technical College,Shaanxi Tongchuan,727031,China)

机构地区：[1]铜川职业技术学院机电工程学院,陕西铜川727031

出　　处：《机械设计与制造工程》2024年第6期106-110,共5页Machine Design and Manufacturing Engineering

摘　　要：对裂纹Euler梁进行分析,将裂纹梁等效为两个子梁,通过弹簧将其连接在一起。根据Fernandez-Saez理论,获得裂纹等效柔度与裂纹相对深度的关系。基于Euler-Bernoulli梁振动方程,通过Ritz法获得梁的自由振动方程,研究一般边界条件下裂纹梁固有频率与裂纹深度、裂纹位置的关系。在弹性边界条件下,给出了不同弹性边界条件组合时基频与边界刚度的关系。The vibration of a cracked Euler beam is analyzed.The cracked beam is equivalent to two sub-beams connected with a spring.According to the Fernandez-Saez theory,the relationship between the equivalent flexibility of the crack and the relative depth of the crack is obtained.Based on the Euler-Bernoulli beam vibration equation,and the free vibration equation of the beam is obtained by the Ritz method.The relation between the natural frequency of the cracked beam and the crack depth and crack location under the generalized boundary conditions is studied.The relationship between the fundamental frequency and the boundary stiffness under different combinations of elastic boundary conditions is given.

关 键 词：Euler梁 裂纹 固有频率 边界条件 

分 类 号：O32[理学—一般力学与力学基础]