Browse > Article
http://dx.doi.org/10.12989/sem.2020.74.1.033

Free vibration and harmonic response of cracked frames using a single variable shear deformation theory  

Bozyigit, Baran (Department of Civil Engineering, Dokuz Eylul University)
Yesilce, Yusuf (Department of Civil Engineering, Dokuz Eylul University)
Wahab, Magd Abdel (Division of Computational Mechanics, Ton Duc Thang University)
Publication Information
Structural Engineering and Mechanics / v.74, no.1, 2020 , pp. 33-54 More about this Journal
Abstract
The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.
Keywords
cracked frame; free vibration; harmonic response; single variable shear deformation theory; transfer matrix method;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Elshamy, M., Crosby, W.A. and Elhadary, M. (2018), "Crack detection of cantilever beam by natural frequency tracking using experimental and finite element analysis", Alexandria Eng. J., 57(4), 3755-3766. https://doi.org/10.1016/j.aej.2018.10.002.   DOI
2 Gillich, G-R, Furdui, H, Abdel Wahab, M and Korka, Z-I (2019), "A robust damage detection method based on multi-modal analysis in variable temperature conditions", Mech. Syst. Signal Processing., 115, 361-379.   DOI
3 Greco, A. and Pau, A. (2012), "Damage identification in Euler frames", Comput. Struct., 92-93, 328-336. https://doi.org/10.1016/j.compstruc.2011.10.007.   DOI
4 Han, S.M., Benaroya, H. and Wei, T. (1999), "DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES", J. Sound Vib., 225(5), 935-988. https://doi.org/10.1006/jsvi.1999.2257.   DOI
5 Heyliger, P.R. and Reddy, J.N. (1988), "A higher order beam finite element for bending and vibration problems", J. Sound Vib., 126(2), 309-326. https://doi.org/10.1016/0022-460X(88)90244-1.   DOI
6 Khatir, S., Dekemele, K., Loccufier, M., Khatir, T. and Abdel Wahab, M. (2018), "Crack identification method in beam-like structures using changes in experimentally measured frequencies and Particle Swarm Optimization", Comptes Rendus Mécanique, 346(2), 110-120. https://doi.org/10.1016/j.crme.2017.11.008.   DOI
7 Khatir, S. and Abdel Wahab, M. (2019), "Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm", Eng. Fracture Mech., 205, 285-300. https://doi.org/10.1016/j.engfracmech.2018.09.032.   DOI
8 Khatir, S., Abdel Wahab, M., Boutchicha, D. and Khatir, T. (2019), "Structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis", J. Sound Vib., 448, 230-246. https://doi.org/10.1016/j.jsv.2019.02.017.   DOI
9 Khiem, N.T. and Lien, T.V. (2004), "Multi-crack detection for beam by the natural frequencies", J. Sound Vib., 273(1), 175-184. https://doi.org/10.1016/S0022-460X(03)00424-3   DOI
10 Khiem, N.T. and Lien, T.V. (2001), "A simplified method for natural frequency analysis of a multiple cracked beam", J. Sound Vib., 245(4), 737-751. https://doi.org/10.1006/jsvi.2001.3585   DOI
11 Kindova-Petrova, D. (2014), "Vibration-Based Methods for Detecting A Crack In A Simply Supported Beam", J. Theor. Appl. Mech., 44(4), 69-82. https://doi.org/10.2478/jtam-2014-0023.   DOI
12 Khiem, N.T. and Toan, L.K. (2014), "A novel method for crack detection in beam-like structures by measurements of natural frequencies", J. Sound Vib., 333(18), 4084-4103. https://doi.org/10.1016/j.jsv.2014.04.031.   DOI
13 Khnaijar, A. and Benamar, R. (2017), "A new model for beam crack detection and localization using a discrete model", Eng. Struct., 150, 221-230. https://doi.org/10.1016/j.engstruct.2017.07.034.   DOI
14 Kim, K., Kim, S., Sok, K., Pak, C. and Han, K. (2018), "A modeling method for vibration analysis of cracked beam with arbitrary boundary condition", J. Ocean Eng. Sci., 3(4), 367-381. https://doi.org/10.1016/j.joes.2018.11.003.   DOI
15 Labib, A., Kennedy, D. and Featherston, C. (2014), "Free vibration analysis of beams and frames with multiple cracks for damage detection", J. Sound Vib., 333(20), 4991-5003. https://doi.org/10.1016/j.jsv.2014.05.015.   DOI
16 Lee, J.W. and Lee, J.Y. (2017), "In-plane bending vibration analysis of a rotating beam with multiple edge cracks by using the transfer matrix method", Meccanica, 52(4), 1143-1157. 10.1007/s11012-016-0449-4.   DOI
17 Lee, J.W. and Lee, J.Y. (2017), "A transfer matrix method capable of determining the exact solutions of a twisted Bernoulli-Euler beam with multiple edge cracks", Appl. Math. Model., 41, 474-493 https://doi.org/10.1016/j.apm.2016.09.013.   DOI
18 Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74(1), 81-87. https://doi.org/10.1016/0022-460X(81)90493-4.   DOI
19 Loya, J.A., Rubio, L. and Fernandez-Saez, J. (2006), "Natural frequencies for bending vibrations of Timoshenko cracked beams", J. Sound Vib., 290(3), 640-653. https://doi.org/10.1016/j.jsv.2005.04.005.   DOI
20 Moezi, S.A., Zakeri, E. and Zare, A. (2018), "Structural single and multiple crack detection in cantilever beams using a hybrid Cuckoo-Nelder-Mead optimization method", Mech. Syst. Signal Pr., 99, 805-831. https://doi.org/10.1016/j.ymssp.2017.07.013.   DOI
21 Nguyen-Thanh, N., Valizadeh, N., Nguyen, M.N., Nguyen-Xuan, H., Zhuang, X., Areias, P., Zi, G., Bazilevs, Y., De Lorenzis, L. and Rabczuk, T. (2015), "An extended isogeometric thin shell analysis based on Kirchhoff-Love theory", Comput. Method Appl. M., 284, 265-291. https://doi.org/10.1016/j.cma.2014.08.025.   DOI
22 Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P.A., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Method Appl. M., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002.   DOI
23 Nguyen, N.-T., Hui, D., Lee, J. and Nguyen-Xuan, H. (2015), "An efficient computational approach for size-dependent analysis of functionally graded nanoplates", Comput. Method Appl. M., 297, 191-218. https://doi.org/10.1016/j.cma.2015.07.021.   DOI
24 Nguyen, T.N., Ngo, T.D. and Nguyen-Xuan, H. (2017), "A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation", Comput. Method Appl. M., 326, 376-401. https://doi.org/10.1016/j.cma.2017.07.024.   DOI
25 Nguyen, T.N., Thai, C.H. and Nguyen-Xuan, H. (2016), "On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach", Int. J. Mech. Sci., 110, 242-255. https://doi.org/10.1016/j.ijmecsci.2016.01.012.   DOI
26 Rabczuk, T., Areias, P.M.A. and Belytschko, T. (2007), "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Meth. Eng., 72(5), 524-548. https://doi.org/10.1002/nme.2013.   DOI
27 Nikolakopoulos, P.G., Katsareas, D.E. and Papadopoulos, C.A. (1997), "Crack identification in frame structures", Comput. Struct., 64(1), 389-406. https://doi.org/10.1016/S0045-7949(96)00120-4.   DOI
28 Ntakpe, J.L., Gillich, G.R., Muntean, F., Praisach, Z.I. and Lorenz, P. (2014), "Vibration-Based Crack Detection in L-Frames", Appl. Mech. Mater., 658, 261-268 10.4028/www.scientific.net/AMM.658.261.   DOI
29 Ostachowicz, W.M. and Krawczuk, M. (1991), "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", J. Sound Vib., 150(2), 191-201. https://doi.org/10.1016/0022-460X(91)90615-Q.   DOI
30 Rabczuk, T., Gracie, R., Song, J.-H. and Belytschko, T. (2010), "Immersed particle method for fluid-structure interaction", Int. J. Numer. Meth. Eng., 81(1), 48-71. https://doi.org/10.1002/nme.2670.   DOI
31 Satpute, D., Baviskar, P., Gandhi, P., Chavanke, M. and Aher, T. (2017), "Crack Detection in Cantilever Shaft Beam Using Natural Frequency", Mater. Today-Proc., 4(2), 1366-1374. https://doi.org/10.1016/j.matpr.2017.01.158.   DOI
32 Shahverdi, H., Navardi, MM (2017), "Free vibration analysis of cracked thin plates using generalized differential quadrature element method", Struct. Eng. Mech., 62(3), 345-355.   DOI
33 Shimpi, R.P., Shetty, R.A. and Guha, A. (2017), "A simple single variable shear deformation theory for a rectangular beam", P. I. Mech. Eng. C-J. Mec., 231(24), 4576-4591. https://doi.org/10.1177/0954406216670682.   DOI
34 Tan, G.J., Shan, J.H., Wu, C.L. and Wang, W.S. (2017), "Free vibration analysis of cracked Timoshenko beams carrying spring-mass systems", Struct. Eng. Mech., 63(4), 551-565.   DOI
35 Areias, P., Rabczuk, T. and Msekh, M.A. (2016), "Phase-field analysis of finite-strain plates and shells including element subdivision", Comput. Method Appl. M., 312, 322-350 https://doi.org/10.1016/j.cma.2016.01.020.   DOI
36 MATLAB (2014), MATLAB R2014b, The MathWorks Inc., MI, U.S.A.
37 Anagnostides, G. (1986), "Frame response to a harmonic excitation, taking into account the effects of shear deformation and rotary inertia", Comput. Struct., 24(2), 295-304. https://doi.org/10.1016/0045-7949(86)90287-7.   DOI
38 Areias, P. and Rabczuk, T. (2013), "Finite strain fracture of plates and shells with configurational forces and edge rotations", Int. J. Numer. Meth. Eng., 94(12), 1099-1122. https://doi.org/10.1002/nme.4477.   DOI
39 Attar, M., Karrech, A. and Regenauer-Lieb, K. (2014), "Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model", J. Sound Vib., 333(11), 2359-2377. https://doi.org/10.1016/j.jsv.2013.11.013   DOI
40 Attar, M. (2012), "A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions", Int. J. Mech. Sci., 57(1), 19-33. https://doi.org/10.1016/j.ijmecsci.2012.01.010.   DOI
41 SAP2000 (2013), SAP2000 V 16.0.0, Integrated Solution for Structural Analysis & Design, Computers & Structures Inc., U.S.A.
42 Thalapil, J. and Maiti, S.K. (2014), "Detection of longitudinal cracks in long and short beams using changes in natural frequencies", Int. J. Mech. Sci., 83, 38-47. https://doi.org/10.1016/j.ijmecsci.2014.03.022.   DOI
43 Tiachacht, S., Bouazzouni, A., Khatir, S., Abdel Wahab, M., Behtani, A. and Capozucca, R. (2018), "Damage assessment in structures using combination of a modified Cornwell indicator and genetic algorithm", Eng. Struct., 177, 421-430.   DOI
44 Umar, S., Bakhary, N. and Abidin, A.R.Z. (2018), "Response surface methodology for damage detection using frequency and mode shape", Measurement, 115, 258-268. https://doi.org/10.1016/j.measurement.2017.10.047.   DOI
45 Rao, S.S. (1995), Mechanical Vibrations, Edison-Wesley Publishing Company, U.S.A.
46 Brasiliano, A., Doz, G.N. and de Brito, J.L.V. (2004), "Damage identification in continuous beams and frame structures using the Residual Error Method in the Movement Equation", Nucl. Eng. Des., 227(1), 1-17. https://doi.org/10.1016/j.nucengdes.2003.07.006   DOI
47 Barad, K.H., Sharma, D.S. and Vyas, V. (2013), "Crack Detection in Cantilever Beam by Frequency based Method", Procedia Eng., 51, 770-775. https://doi.org/10.1016/j.proeng.2013.01.110   DOI
48 Bickford, W.B. (1982), "Consistent higher order beam theory", Developments in Theoretical and Applied Mechanics, Springer, Germany.
49 Bozyigit, B. and Yesilce, Y. (2018), "Natural frequencies and harmonic responses of multi-story frames using single variable shear deformation theory", Mech. Res. Commun., 92, 28-36. https://doi.org/10.1016/j.mechrescom.2018.06.007   DOI
50 Caddemi, S. and Calio, I. (2013), "The exact explicit dynamic stiffness matrix of multi-cracked Euler-Bernoulli beam and applications to damaged frame structures", J. Sound Vib., 332(12), 3049-3063. https://doi.org/10.1016/j.jsv.2013.01.003   DOI
51 Dastjerdi, S. and Abbasi, M. (2019), "A vibration analysis of a cracked micro-cantilever in an atomic force microscope by using transfer matrix method", Ultramicroscopy, 196, 33-39 https://doi.org/10.1016/j.ultramic.2018.09.014   DOI
52 Carden, E.P. and Fanning, P. (2004), "Vibration Based Condition Monitoring: A Review", Struct. Health Monit., 3(4), 355-377. https://doi.org/10.1177/1475921704047500.   DOI
53 Chondros, T.G., Dimarogonas, A.D. and Yao, J. (1998), "A CONTINUOUS CRACKED BEAM VIBRATION THEORY", J. Sound Vib., 215(1), 17-34. https://doi.org/10.1006/jsvi.1998.1640.   DOI
54 Cunedioglu, Y (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech.,, 56(6), 1003-1020.   DOI