基于弹性力学的裂缝梁自由振动分析  

Free vibration of a beam with a crack based on elasticity

作　　者：赵佳雷 周叮[1] 张建东[1] 胡朝斌[1] ZHAO Jialei;ZHOU Ding;ZHANG Jiandong;HU Chaobin(College of Civil Engineering,Nanjing Tech University,Nanjing 211816,China)

机构地区：[1]南京工业大学土木工程学院,南京211816

出　　处：《振动与冲击》2020年第12期78-84,102,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51778288);江苏省交通厅重大专项课题(2014Y01)。

摘　　要：基于弹性力学平面应力理论,采用Chebyshev-Ritz法分析裂缝梁的自由振动特性。将梁分成三个子梁,取边界函数与Chebyshev多项式的乘积作为每个子梁的位移试函数,保证解的快速收敛性,并使该方法适用于不同的几何边界条件。用里兹法列出每个子梁的振动特征方程,并根据各子梁在界面上的位移连续性条件得到整个裂缝梁的振动特征方程。计算结果与文献数据和有限元分析吻合很好。最后分析了裂缝深度和梁的高跨比对动力特性的影响。Free vibration characteristics of a beam with a crack were presented using the Chebyshev-Ritz method in this paper.The analysis procedure was based on the plane stress theory of elasticity.In the analysis,the cracked beam was divided into three sub-beams.The product of boundary function and Chebyshev polynomials was taken as the admissible functions of the displacement functions.This ensures the fast convergence of the solution and makes the method suitable for different geometric boundary conditions.The eigenvalue equations of each sub-beam can be established using the Ritz method.The vibration characteristic equation of the whole cracked beam was obtained by the displacement continuity condition of each sub-beam at the joint.The results are consistent with that of in literature and the finite element analysis,and it verified the accuracy of the method in this paper.Finally,the effects of the structural parameters such as height-span ratio,crack depth on non-dimensional natural frequencies and mode shapes were performed.

关 键 词：平面应力理论 Chebyshev-Ritz法 裂缝梁 频率和振型 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3