不同边界条件下裂纹梁的固有频率分析  

Natural Frequency Analysis of Cracked Beam under Different Boundary Conditions

作　　者：冯小庭 王航 梁新平[1] Feng Xiaoting;Wang Hang;Liang Xinping(Xi’an Railway Vocational and Technical Institute,Xi’an,Shaanxi 710026,China)

机构地区：[1]西安铁路职业技术学院,陕西西安710026

出　　处：《西安轨道交通职业教育研究》2023年第1期21-27,共7页Xi'an Rail Transit Vocational Education Research

摘　　要：本文对有裂纹Euler梁的固有振动进行了分析。裂纹梁等效为两个子梁,通过一个弹簧连接在一起。使用Fernandez-Saez的理论,获得裂纹等效柔度同裂纹相对深度之间的关系。基于Euler-Bernoulli梁振动方程,并用Ritz法获得梁的自由振动方程。研究了一般边界条件下裂纹梁固有频率同裂纹深度与裂纹位置之间的关系。裂纹梁在弹性边界条件下,给出了不同弹性边界条件组合时基频与边界刚度之间的关系。This paper analyzes the natural vibration of the cracked Euler beam.The cracked beam is equivalent to two sub-beams,connected together by a spring.Using the theory of Fernandez-Saez,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,the free vibration equation of the beam is obtained by the Ritz method.The relationship between the natural frequency of the cracked beam and the crack depth and crack position under general boundary conditions is studied.For cracked beams under elastic boundary conditions,the relationship between fundamental frequency and different elastic boundary conditions is investigated.

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]