Engineering Transactions, Online first
10.24423/EngTrans.3166.2024

Frequency-Based Crack Effect Study on Beams Under Free Vibration Using Finite Element Analysis

Ompriya SAHU
Siksha 'O' Anusandhan University
India

Priyadarshi DAS
Siksha 'O' Anusandhan University
India

Manoj Kumar MUNI
Indira Gandhi Institute of Technology
India

Nibedita PRADHAN
Siksha 'O' Anusandhan University
India

Bidyadhar BASA
Siksha 'O' Anusandhan University
India

Shishir Kumar SAHU
National Institute of Technology Rourkela
India

A numerical computation-based analysis of the free vibration analysis of uniform beams with rectangular cross-sections is presented in this work using finite element analysis. The approach involves dividing the beam into segments at the crack section, which is then modelled for simulation for eigenfrequencies on the ABAQUS platform. The numerical simulation results are in excellent agreement with the findings of previous research, confirming the efficacy and applicability of the developed beam model. A sequential comprehensive approach towards analysis of the effects of the position and depth of the cracks on the natural frequencies are addressed in numerical results. The research findings confirm that the simulation model is suitable for the vibration analysis of beams or beam-like elements with different cross-sections.

Keywords: free vibration; transverse cracks; finite element: beam; ABAQUS
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References

Moreno-García P., Araújo dos Santos J.V., Lopes H., A review and study on Ritz method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates, Archives of Computational Methods in Engineering, 25(3): 785–815, 2018, doi: 10.1007/s11831-017-9214-7.

Gayen D., Tiwari R., Chakraborty D., Static and dynamic analyses of cracked functionally graded structural components: a review, Composites Part B: Engineering, 173: 106982, 2019, doi: 10.1016/j.compositesb.2019.106982.

Sinha G.P., Kumar B., Review on vibration analysis of functionally graded material structural components with cracks, Journal of Vibration Engineering & Technologies, 9: 23–49, 2021, doi: 10.1007/s42417-020-00208-3.

Peng Z.K., Lang Z.Q., Chu F.L., Numerical analysis of cracked beams using nonlinear output frequency response functions, Computers & Structures, 86(17–18): 1809–1818, 2008, doi: 10.1016/j.compstruc.2008.01.011.

Matbuly M.S., Ragb O., Nassar M., Natural frequencies of a functionally graded cracked beam using the differential quadrature method, Applied Mathematics and Computation, 215(6): 2307–2316, 2009, doi: 10.1016/j.amc.2009.08.026.

Caddemi S., Morassi A., Multi-cracked Euler–Bernoulli beams: Mathematical modeling and exact solutions, International journal of solids and structures, 50(6): 944–956, 2013, doi: 10.1016/j.amc.2009.08.026.

Ostachowicz W.M.,Krawczuk M., Analysis of the effect of cracks on the natural frequencies of a cantilever beam, Journal of Sound and Vibration, 150(2): 191–201, 1991, doi: 10.1016/0022-460X(91)90615-Q.

Bakhtiari-Nejad F., Khorram A., Rezaeian M., Analytical estimation of natural frequencies and mode shapes of a beam having two cracks, International Journal of Mechanical Sciences, 78: 193–202, 2014, doi: 10.1016/j.ijmecsci.2013.10.007.

Chondros T.G., Dimarogonas A.D.,Yao J., Vibration of a beam with a breathing crack, Journal of Sound and Vibration, 239(1): 57–67, 2001, doi: 10.1006/jsvi.2000.3156.

Caddemi S., Caliò I., Exact closed-form solution for the vibration modes of the Euler–Bernoulli beam with multiple open cracks, Journal of Sound and Vibration, 327(3–5): 473–489, 2009, doi: 10.1016/j.jsv.2009.07.008.

Kisa M., Brandon J., The effects of closure of cracks on the dynamics of a cracked cantilever beam, Journal of sound and Vibration, 238(1): 1–18, 2000, doi: 10.1006/jsvi.2000.3099.

Altunışık A.C., Okur F.Y., Karaca S., Kahya V., Vibration-based damage detection in beam structures with multiple cracks: modal curvature vs. modal flexibility methods, Non-destructive Testing and Evaluation, 34(1): 33–53, 2019, doi: 10.1080/10589759.2018.1518445.

Alshorbagy A.E., Eltaher M.A., Mahmoud F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35(1): 412–425, 2011, doi: 10.1016/j.apm.2010.07.006.

Soltani M., Asgarian B., Mohri F., Elastic instability and free vibration analyses of tapered thin-walled beams by the power series method, Journal of Constructional Steel Research, 96: 106–126, 2014, doi: 10.1016/j.jcsr.2013.11.001.

Biswal A.R., Roy T., Behera R.K., Pradhan S.K., Parida P.K., Finite element based vibration analysis of a nonprismatic Timoshenko beam with transverse open crack, Procedia Engineering, 144: 226–233, 2016, doi: 10.1016/j.proeng.2016.05.028.

Canales F.G., Mantari J.L., Free vibration of thick isotropic and laminated beams with arbitrary boundary conditions via unified formulation and Ritz method, Applied Mathematical Modelling, 61: 693–708, 2018, doi: 10.1016/j.apm.2018.05.005.

Lee J.W., Lee J.Y., Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122: 1–17, 2017, doi: 10.1016/j.ijmecsci.2017.01.011.

Corrêa R.M., Arndt M., Machado R.D., Free in-plane vibration analysis of curved beams by the generalized/extended finite element method, European Journal of Mechanics – A/Solids, 88: 104244, 2021, doi: 10.1016/j.euromechsol.2021.104244.

Yang H., Daneshkhah E., Augello R., Xu X., Carrera E., Numerical vibration correlation technique for thin-walled composite beams under compression based on accurate refined finite element, Composite Structures, 280: 114861, 2022, doi: 10.1016/j.compstruct.2021.114861.

Darpe A.K., Gupta K., Chawla A., Coupled bending, longitudinal and torsional vibrations of a cracked rotor, Journal of Sound and Vibration, 269(1–2): 33–60, 2004, doi: 10.1016/S0022-460X(03)00003-8.

Sekhar A.S., Multiple cracks effects and identification, Mechanical Systems and Signal Processing, 22(4): 845–878, 2008, doi: 10.1016/j.ymssp.2007.11.008.

Jassim Z.A., Ali N.N., Mustapha F., Abdul Jalil N.A., A review on the vibration analysis for a damage occurrence of a cantilever beam, Engineering Failure Analysis, 31: 442–461, 2013, doi: 10.1016/j.engfailanal.2013.02.016.

Jain A.K., Rastogi V., Agrawal A.K., Experimental investigation of vibration analysis of multi-crack rotor shaft, Procedia Engineering, 144: 1451–1458, 2016, doi: 10.1016/j.proeng.2016.05.177.

Senthilkumar M., Manikanta Reddy S., Sreekanth T.G., Dynamic Study and Detection of Edge Crack in Composite Laminates Using Vibration Parameters, Transactions of the Indian Institute of Metals, 75(2): 361–370, 2022, doi: 10.1007/s12666-021-02419-y.

Sahu S.K., Das P., Experimental and numerical studies on vibration of laminated composite beam with transverse multiple cracks, Mechanical Systems and Signal Processing, 135: 106398, 2020, doi: 10.1016/j.ymssp.2019.106398.

Prokudin O.A., Solyaev Y.O., Babaytsev A.V., Artemyev A.V., Korobkov M.A., Dynamic characteristics of three-layer beams with load-bearing layers made of alumino-glass plastic, PNRPU Mechanics Bulletin, 2020(4): 260–270, 2020, doi: 10.15593/perm.mech/2020.4.22.

Krysko A.V., Awrejcewicz J., Saltykova O.A., Zhigalov M.V., Krysko V.A., Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects, Communications in Nonlinear Science and Numerical Simulation, 19(8): 2568–2589, 2014, doi: 10.1016/j.cnsns.2013.12.013.

Lewandowski R., Wielentejczyk P., Litewka P., Dynamic characteristics of multi-layered, viscoelastic beams using the refined zig-zag theory, Composite Structures, 259: 113212, 2021, doi: 10.1016/j.compstruct.2020.113212.

Tada H., Paris P.C., Irwin G.R., The Stress Analysis of Cracks. Handbook, 3rd ed., Del Research Corporation, ASME Press, USA, 1973.

Krawczuk M., Ostachowicz W.M., Modelling and vibration analysis of a cantilever composite beam with a transverse open crack, Journal of Sound and Vibration, 183(1): 69–89, 1995, doi: 10.1006/jsvi.1995.0239.

Kisa M., Free vibration analysis of a cantilever composite beam with multiple cracks, Composites Science and Technology, 64(9): 1391–1402, 2004, doi: 10.1016/j.compscitech.2003.11.002.

Nikpur K., Dimarogonas A., Local compliance of composite cracked bodies, Composites Science and Technology, 32(3): 209–223, 1988, doi: 10.1016/0266-3538(88)90021-8.

Yardimoglu B., A novel finite element model for vibration analysis of rotating tapered Timoshenko beam of equal strength, Finite Element in Analysis and Design, 46(10): 838–842, 2010, doi: 10.1016/j.finel.2010.05.003.

Krawczuk M., Palacz M., Ostachowicz W., The dynamic analysis of a cracked Timoshenko beam by the spectral element method, Journal of Sound and Vibration, 264(5): 1139–1153, 2003, doi: 10.1016/S0022-460X(02)01387-1.




DOI: 10.24423/EngTrans.3166.2024