Analysis of out-of-plane free vibration of single damaged curved beam based on precise algorithm of structural mechanics
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College of Transportation Engineering, Dalian Maritime University, Dalian, China
Submission date: 2022-09-26
Final revision date: 2023-02-22
Acceptance date: 2023-03-04
Online publication date: 2023-04-27
Publication date: 2023-04-28
Corresponding author
Zhouyang Pan   

Colleage of Transportation Engineering, Dalian Maritime University, China
Journal of Theoretical and Applied Mechanics 2023;61(2):407-414
Based on a dynamic discrete model of an out-of-plane curved beam with a constant cur- vature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent sec- tion reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated.
Anifantis N., Dimarogonas A., 1983, Stability of columns with a single crack subjected to follower and vertical loads, International Journal of Solids and Structures, 19, 4, 281-291.
Caliò I., Greco A., D’Urso D., 2014, Free vibrations of spatial Timoshenko arches, Journal of Sound and Vibration, 333, 19, 4543-4561.
Caliò I., Greco A., D’Urso D., 2016, Structural models for the evaluation of eigen-properties in damaged spatial arches: a critical appraisal, Archive of Applied Mechanics, 86, 11, 1853-1867
Dessi D., Camerlengo G., 2015, Damage identification techniques via modal curvature analysis: Overview and comparison, Mechanical Systems and Signal Processing, 52-53, 181-205.
Dimarogonas A.D., 1996, Vibration of cracked structures: A state of the art review, Engineering Fracture Mechanics, 55, 5, 831-857.
Friswell M.I., Penny J.E.T., 2002, Crack modeling for structural health monitoring, Structural Health Monitoring, 1, 2, 139-148.
Howson W.P., Jemah A.K., 1999, Exact out-of-plane natural frequencies of curved Timoshenko beams, Journal of Engineering Mechanics, 125, 1, 19-25.
Hu J.S., Feng X., Zhou J., 2007, State-of-art of vibration analysis and crack identification of cracked beams, Journal of Vibration and Shock, 11, 146-152+189.
Ishaquddin M., Raveendranath P., Reddy J.N., 2016, Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams, Finite Elements in Analysis and Design, 110, 58-66.
Mao H., Yu G., Liu W., Xu T., 2020, Out-of-plane free vibration and forced harmonic response of a curved beam, Shock and Vibration.
Pau A., Greco A., Vestroni F., 2011, Numerical and experimental detection of concentrated damage in a parabolic arch by measured frequency variations, Journal of Vibration and Control, 17, 4, 605-614.
Petroski H.J., 1981, Simple static and dynamic-models for the cracked elastic beam, International Journal of Fracture, 17, 4, R71-R76.
Wang Y.L., Ju Y., Zhuang Z., Li C.F., 2018, Adaptive finite element analysis for damage detection of non-uniform Euler-Bernoulli beams with multiple cracks based on natural frequencies, Engineering Computations, 35, 3, 1203-1229.
Zare M., 2019, Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor, Mechanics of Advanced Materials and Structures, 27, 14, 1238-1245.
Zhao Y., Kang H., Feng R., et al., 2006, Research progress of curved beam, Progress in Mechanics, 2, 170-186.
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