基于弹性力学的裂缝梁自由振动分析

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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，并使本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。

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	赵佳雷
	周叮
	张建东
	胡朝斌

关键词 ：平面应力理论, Chebyshev-Ritz法, 裂缝梁, 频率和振型

Abstract：Free vibration characteristics of the beam with a crack is presented using Chebyshev-Ritz method in this paper. The analysis procedure is based on the plane stress theory of elasticity. In the analysis, the cracked beam is divided into three sub-beams. The product of boundary function and Chebyshev polynomials is 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 Ritz method. The vibration characteristic equation of the whole cracked beam is 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 are performed.

Key words： plane stress theory Chebyshev-Ritz method cracked beam frequency and mode shape

收稿日期: 2018-12-12 出版日期: 2020-06-15

引用本文:

赵佳雷，周叮，张建东，胡朝斌. 基于弹性力学的裂缝梁自由振动分析[J]. 振动与冲击, 2020, 39(12): 78-84.
ZHAO Jialei，ZHOU Ding，ZHANG Jiandong，HU Chaobin. Free vibration of a beam with a crack based on elasticity. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(12): 78-84.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I12/78

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