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Analysis of Natural Vibration Characteristics of Timoshenko Cracked Beam Based on Transfer Matrix Method

DOI：

 作者 单位 邮编 王亚波0 长安大学 710061 马乾瑛* 长安大学 吴宗欢 长安大学

首先基于传递矩阵法，将裂纹截面假定一无质量扭转弹簧，通过扭转弹簧建立起各段子梁在裂纹截面处的矩阵传递关系，推导出含任意裂纹Timoshenko梁及无裂纹Timoshenko梁的传递矩阵，引入边界条件简化矩阵方程，并利用Matlab对方程进行求解。其次讨论了裂纹位置、相对深度对单裂纹简支梁自振频率的影响，与文献结果进行对比，误差最多不超过1%；然后通过ABAQUS建立悬臂梁及两端固支梁有限元模型，分析相对裂纹深度对自振频率的影响，计算结果与有限元结果进行对比，误差不超过3.86%；最后研究了不同跨高比下相对裂纹深度对Timoshenko简支梁自振频率的影响，计算结果与文献最大误差为4.56%，验证了本文方法的有效性及适用性。

Firstly, based on the transfer matrix method, the crack section is assumed to be a mass free torsional spring. The matrix transfer relation of each section beam at the crack section is established by the torsional spring. The transfer matrix of Timoshenko beam with arbitrary crack and Timoshenko beam without crack is derived. And using Matlab to solve the equation. Secondly, the effect of crack location and relative depth on the natural vibration frequency of the simple supported beam with single crack is discussed. The error is less than 1% compared with the results in the literature. Then, the finite element model of the cantilever beam and the fixed beam at both ends was established by ABAQUS, and the influence of the relative crack depth on the natural vibration frequency was analyzed. The calculated results were compared with the finite element results, and the error was less than 3.86%. Finally, the effect of the relative crack depth on the natural vibration frequency of Timoshenko simply supported beams with different span to height ratios is studied. The maximum error between the calculated results and the literature is 4.56%, which verifies the validity and applicability of the proposed method.
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