Winkler基础上裂纹Euler-Bernoulli梁弯曲解析解  

Analytical solution for bending of the cracked Euler-Bernoulli beam on the Winkler foundation

作　　者：杨骁 刘昕[2] 郑超引[1] YANG Xiao;LIU Xin;ZHENG Chaoyin(Department of Basic Education,Shanghai Customs College,Shanghai 201204,China;School of Mechanic and Engineering Science,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海海关学院公共教学部,上海201204 [2]上海大学力学与工程科学学院,上海200444

出　　处：《上海大学学报（自然科学版）》2023年第3期491-501,共11页Journal of Shanghai University:Natural Science Edition

基　　金：上海市自然科学基金资助项目(18ZR1414500)。

摘　　要：基于梁横向贯通开裂纹的线性扭转弹簧模型,采用Laplace变换及其逆变换,得到了Winkler基础上具有任意裂纹数目Euler-Bernoulli梁弯曲变形的解析通解.在验证解析解正确性的基础上,研究了Winkler基础上均布荷载作用下简支裂纹梁和悬臂裂纹梁的弯曲变形,参数分析了裂纹数目和位置、地基反力系数和梁长高比等参数对裂纹梁弯曲变形的影响.结果表明:在梁裂纹处,Winkler基础上裂纹梁的挠度存在尖点,转角存在跳跃;基础反力系数及裂纹深度对裂纹梁弯曲的影响较大,而裂纹数目、位置以及梁长高比对裂纹梁弯曲的影响相对较小.这些结论对结构健康检测及监测具有一定指导意义.Based on the linear torsional spring model of a transverse crack in a beam,the general analytical solution of the Euler-Bernoulli beam considering an arbitrary num-ber of cracks on the Winkler foundation was presented through Laplace transform and its inverse transformation.The bending deformation for simply-supported and cantilever cracked beams under uniform loads were investigated to evaluate the analytical solution.The influences of the numbers and locations of cracks,foundation reaction coefficient and beam length-height ratio on the bending deformation of the cracked beam were analyzed.At the crack location,a cusp in deflection and a gap rotational angle of the beam were identified.The influences of the foundation reaction coefficient and crack depth on the bending of cracked beam were significant,in contrast to the effects caused by the number and locations of the crack and the length-height ratio of beam.These conclusions can be used for structural health detection and monitoring.

关 键 词：Winkler基础 Euler-Bernoulli裂纹梁 广义函数 解析解 参数研究 

分 类 号：TU223[建筑科学—建筑设计及理论] TU317