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Journal of Shanghai University >

2020 , Vol. 26 >Issue 3: 443 - 455

DOI: https://doi.org/10.12066/j.issn.1007-2861.2051

Research Articles

Nonlinear vibration of beam with breathing crack

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  • Department of Civil Engineering, Shanghai University, Shanghai 200444, China

Received date: 2018-03-08

  Online published: 2018-12-23

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Abstract

Based on the curve of bending moment-rotation angle of the crack in beam under dynamic/static load and considering the transition effect between the open and closed states of the crack, a novel rotational spring model of the breathing crack with instant rigidity has been proposed, with a unified explicit formula of the vibration modes of the beam with an arbitrary number of breathing cracks, and an approximate computing method of the nonlinear dynamic response of the beam with breathing crack presented. The free vibration of the simply-supported beam with a breathing crack and dynamic response of the cantilever beam with two breathing cracks subjected to a harmonic load are analyzed numerically. The numerical results indicate that the open and closure procedure of the crack can be appropriately described with the rotational spring model of the breathing crack with instant rigidity as is presented in this paper, and that the instant frequency of the cracked beam is located between natural frequency of the beams with complete open crack and one of the beams with complete closed crack, which gradually converges to a constant. Furthermore, the open and closure state of the crack and its location on top or bottom surface of the beam have significant influences on the nonlinear dynamic response of the cracked beam.

Key words： breathing crack; cracked beam; nonlinear vibration; instant frequency; dynamic response

Cite this article

WANG Tianyu, YANG Xiao . Nonlinear vibration of beam with breathing crack[J]. Journal of Shanghai University, 2020 , 26(3) : 443 -455 . DOI: 10.12066/j.issn.1007-2861.2051

References

[1] 胡家顺, 冯新, 李昕, 等. 裂纹梁振动分析和裂纹识别方法研究进展[J]. 振动与冲击, 2007,26(11):146-152.
[2] Dimarogonas A D. Vibration of cracked structures: a state of the art review[J]. Engineering fracture mechanics, 1996,55(5):831-857.
[3] Fan W, Qiao P. Vibration-based damage identification methods: a review and comparative study[J]. Structural Health Monitoring, 2011,10(1):83-111.
[4] Challamel N, Xiang Y. On the influence of the unilateral damage behaviour in the stability of cracked beam columns[J]. Engineering Fracture Mechanics, 2010,77(9):1467-1478.
[5] Kisa M. Vibration and stability of multi-cracked beams under compressive axial loading[J]. International Journal of the Physical Sciences, 2011,6(11):2681-2696.
[6] Fekrazadeh S. Khaji N. An analytical method for crack detection of Timoshenko beams with multiple open cracks using a test mass[J]. European Journal of Environmental and Civil Engineering, 2017,21:24-41.
[7] Rezaee M, Hassannejad R. Free vibration analysis of simply supported beam with breathing crack using perturbation method[J]. Acta Mechanica Solida Sinica, 2010,23(5):459-470.
[8] Jun O S, Eun H J, Earmme Y Y, et al. Modelling and vibration analysis of a simple rotor with breathing crack[J]. Journal of Sound and Vibration, 1992,155(2):273-290.
[9] 胡家顺, 冯新, 周晶. 呼吸裂纹梁非线性动力特性研究[J]. 振动与冲击, 2009,28(1):76-80.
[10] Gudmundson P. The dynamic behaviour of slender structures with cross-sectional cracks[J]. Journal of the Mechanics and Physics of Solids, 1983,31(4):329-345.
[11] Andreausa U, Casini P, Vestroni F. Non-linear dynamics of a cracked cantilever beam under harmonic excitation[J]. International Journal of Non-linear Mechanics, 2007,42(3):566-575.
[12] Semperlotti F, Wang K W, Smith E C. Localization of a breathing crack using super-harmonic signals due to system nonlinearity[J]. Aiaa Journal, 2012,47(9):2076-2086.
[13] Cheng S M, Swamidas A S J, Wu X J, et al. Vibrational response of a beam with a breathing crack[J]. Journal of Sound and vibration, 1999,225(1):201-208.
[14] Rezaee M, Hassannejad R. A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method[J]. Acta Mechanica Solida Sinica, 2011,24(2):185-194.
[15] Chondros T G, Dimarogonas A D, Yao J. Vibration of a beam with a breathing crack[J]. Journal of Sound and vibration, 2001,239(1):57-67.
[16] Wang G, Yu D, Wen J, et al. One-dimensional phononic crystals with locally resonant structures[J]. Physics Letters A, 2004,327(5):512-521.
[17] 杨海燕, 杨秉玉. 疲劳裂纹叶片振动的非线性特性研究[J]. 西北工业大学学报, 1999,17(2):198-204.
[18] Allison J E, Ku R C, Pompetzki M A. A comparison of measurement methods and numerical procedures for the experimental characterization of fatigue crack closure[M]// Newman J, Elber W. Mechanics of fatigue crack closure. Conshohocken: ASTM International, 1988: 185.
[19] Cicirello A, Palmeri A. Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads[J]. International Journal of Solids and Structures, 2014,51(5):1020-1029.
[20] Caddemi S, Caliò I, Marletta M. The non-linear dynamic response of the Euler-Bernoulli beam with an arbitrary number of switching cracks[J]. International Journal of Non-Linear Mechanics, 2010,45(7):714-726.
[21] Carroll J, Efstathiou C, Lambros J, et al. Investigation of fatigue crack closure using multiscale image correlation experiments[J]. Engineering Fracture Mechanics, 2009,76(15):2384-2398.
[22] 汪德江, 杨骁. 基于裂纹诱导弦挠度的 Timoshenko 梁裂纹无损检测[J]. 工程力学, 2016,33(12):186-195.
[23] Caddemi S, Calio I. Exact closed-form solution for the vibration modes of the Euler--Bernoulli beam with multiple open cracks[J]. Journal of Sound and Vibration, 2009,327(3):473-489.
[24] 张英世, 胡伟平, 王燮山. 文克尔地基上纵横弯曲变截面梁主振型函数之正交性[J]. 振动与冲击, 2000,19(1):75-76.
[25] Rezaee M, Hassannejad R, et al. Free vibration analysis of simply supported beam with breathing crack using perturbation method[J]. Acta Mechanica Solida Sinica, 2010,23(5):459-470.
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