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| Analysis of natural vibration characteristics of cracked T-beams |
| ZHANG Shan1, ZHOU Ding1, HAN Huixuan2, ZHANG Jiandong1， HU Chaobin1 |
1.College of Civil Engineering, Nanjing Tech University, Nanjing 211816, China;
2.College of Civil Engineering and Architecture, Jiangsu University of Science and Technology, Zhenjiang 212000, China |
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Abstract Based on the 2-D elasticity theory, natural vibration characteristics of T-beams with a crack were studied using Chebyshev-Ritz method.Firstly, according to the principle of the same strain and the unchanged total internal force, the beam was equivalent to a rectangular cross-section beam composed of two material layers with different characteristics using the transfer section method.Then, the equivalent beam was divided into 4 sub-domains along the crack and layer interface.The natural vibration characteristic equation of each sub-domain was deduced using Rayleigh-Ritz method, and the natural vibration characteristic equation of the whole cracked T-beam was derived with displacement continuity conditions on interfaces of sub-domains.Chebyshev polynomials were applied to construct displacement trial functions of various sub-domains, and the fast convergence solutions were obtained using the orthogonality and completeness of Chebyshev polynomials.The correctness of the proposed method was verified by comparing its solving results with those using the finite element analysis for actual T-beams.Finally, a cracked T-beam fixed at both ends was taken as an example, effects of crack position and its depth on this beam’s natural vibration characteristics were analyzed.
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Received: 10 February 2020
Published: 15 May 2021
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