DOI QR코드

DOI QR Code

Vibrations and stress analysis of rotating perforated beams by using finite elements method

  • Eltaher, M.A. (Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Abdelmoteleb, Hanaa E. (Department of Structural Engineering, Faculty of Engineering, Zagazig University) ;
  • Daikh, Ahmed Amin (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Abdelrahman, Alaa. A. (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University)
  • Received : 2021.03.05
  • Accepted : 2021.10.22
  • Published : 2021.11.25

Abstract

This paper presents a computational finite element model to study and analyze vibrations and stresses of regularly perforated rotated beams considering different perforation configurations, for the first time. Both regular circular and squared perforation configurations are considered. The geometry of the perforated beam is modelled using shell finite elements. The finite elements equations of motion are derived for a straight perforated cantilevered beam with a symmetrical cross section. The proposed computational procedure is checked by comparing the obtained results with the available results in the literature and an excellent agreement is observed. The free vibration response, as well as stress distributions throughout the beam, are investigated. The obtained results reveal that the perforation configuration, as well as the rotating speed, have remarkable effects on the dynamics and stress distributions of the rotating perforated beams.

Keywords

References

  1. Abdelrahman, A.A., Abd-El-Mottaleb H.E. and Eltaher, M.A. (2020b), "On bending of perforated beams incorporating the microstructure effect", Struct. Eng. Mech., 76(6), 765-779. https://doi.org/10.12989/sem.2020.76.6.765.
  2. Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendy, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  3. Abdelrahman, A.A., Mohamed, N.A. and Eltaher, M.A. (2020a), "Static bending of perforated nanobeams including surface energy and microstructure effects", Eng. with Comput., 1-21. https://doi.org/10.1007/s00366-020-01149-x.
  4. Aksencer, T. and Aydogdu, M. (2019), "Vibration of a rotating composite beam clamped-off the axis of rotation", Compos. Struct., 225, 111174. https://doi.org/10.1016/j.compstruct.2019.111174.
  5. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.
  6. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020a), "Influence of the perforation configuration on dynamic behaviors of multilayered beam structure", Structure, 28, 1413-1426. https://doi.org/10.1016/j.istruc.2020.09.055.
  7. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020b), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35(4), 555-566. https://doi.org/10.12989/scs.2020.35.4.555.
  8. Arab, S.B., Rodrigues, J.D., Bouaziz, S. and Haddar, M. (2017), "A finite element based on equivalent single layer theory for rotating composite shafts dynamic analysis", Compos. Struct., 178, 135-144. https://doi.org/10.1016/j.compstruct.2017.06.052.
  9. Azimi, M., Mirjavadi, S.S., Shafiei, N., Hamouda, A.M.S. and Davari, E. (2018), "Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution", Mech. Adv. Mater. Struct., 25(6), 467-480. https://doi.org/10.1080/15376494.2017.1285455.
  10. Berkani, A. (2018), "Stabilization of a viscoelastic rotating Euler-Bernoulli beam", Math. Method. Appl. Sci., 41(8), 2939-2960.https://doi.org/10.1002/mma.4793.
  11. Bhat, R.A. and Gupta, L.M. (2020), "Moment-gradient factor for perforated cellular steel beams under lateral torsional buckling", Arabian J. Sci. Eng., 1-17. https://doi.org/10.1007/s13369-020-04836-5.
  12. Boumediene, F., Bekhoucha, F. and Daya, E.M. (2019), "Modal analysis of rotating viscoelastic sandwich beams", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2019.1567887.
  13. Bourouina, H., Yahiaoui, R., Kerid, R., Ghoumid, K., Lajoie, I., Picaud, F. and Herlem, G. (2020), "The influence of hole networks on the adsorption-induced frequency shift of a perforated nanobeam using non-local elasticity theory", J. Phys. Chem. Solids, 136, 109201. https://doi.org/10.1016/j.jpcs.2019.109201.
  14. Bucalem, M.L. and Bathe, K.J. (2011), "The Mechanics of Solids and Structures-Hierarchical Modeling and The Finite Element Solution", Springer Science & Business Media, Cambridge, MA, USA.
  15. Carnegie, W. (1959), "Vibrations of rotating cantilever blading: theoretical approaches to the frequency problem based on energy methods", J. Mech. Eng. Sci., 1(3), 235-240. https://doi.org/10.1243/JMES_JOUR_1959_001_028_02.
  16. Chen, Q. and Du, J. (2019), "A Fourier series solution for the transverse vibration of rotating beams with elastic boundary supports", Appl. Acoust., 155, 1-15. https://doi.org/10.1016/j.apacoust.2019.05.008.
  17. Chen, S. and Ren, F. (2017), "Vibration analysis of horizontal rotating beam in pipe", Int. J. Hydrogen Energy, 42(29), 18741-18746. https://doi.org/10.1016/j.ijhydene.2017.04.174.
  18. Chen, Z. and Qian, L. (2020), "Nonlinear dynamic characteristics analysis of planar flexible rotating beams with clearance joint", J. Braz. Soc. Mech. Sci. Eng., 42(333), 333. https://doi.org/10.1007/s40430-020-02388-1.
  19. Cheng, J., Xu, H. and Yan, A. (2006), "Frequency analysis of a rotating cantilever beam using assumed mode method with coupling effect", Mech. Based Des. Struct., 34(1), 25-47. https://doi.org/10.1080/15367730500501587.
  20. Chung, J. and Yoo, H.H. (2002), "Dynamic analysis of a rotating cantilever beam by using the finite element method", J. Sound Vib., 249(1), 147-164. https://doi.org/10.1006/jsvi.2001.3856.
  21. Chung, K.F. and Wang, A.J. (2004), "Verification to design of perforated composite beams using finite element method'. In Proc. Int. Conf. Steel and Composite Structures, Seoul, Korea September.
  22. Degtyarev, V.V. (2020), "Flexural strength of steel decks with square and rectangular holes: Numerical studies", J. Constr. Steel Res., 172, 106241. https://doi.org/10.1016/j.jcsr.2020.106241.
  23. Ebrahimi, F. and Haghi, P. (2018a), "Wave dispersion analysis of rotating heterogeneous nanobeams in thermal environment", Adv. Nano Res., 6(1), 21. https://doi.org/10.12989/anr.2018.6.1.021.
  24. Ebrahimi, F. and Haghi, P. (2018b), "Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment", Adv. Nano Res., 6(3), 201-217. https://doi.org/10.12989/anr.2018.6.3.201.
  25. Eltaher, M.A. and Abdelrahman, A.A. (2020), "Bending behavior of squared cutout nanobeams incorporating surface stress effects", Steel Compos.Struct., 36(2), 143-161. https://doi.org/10.12989/scs.2020.36.2.143.
  26. Eltaher, M.A. and Mohamed, N.A. (2020), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart Struct. Syst., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501.
  27. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.
  28. Eltaher, M.A., Omar, F.A., Abdalla, W.S., Kabeel, A.M. and Alshorbagy, A.E. (2020a), "Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects", Struct. Eng. Mech., 76(1), 141-151. https://doi.org/10.12989/sem.2020.76.1.141.
  29. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and Alshorbagy, A.E. (2020b), "Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts", Smart Struct. Syst., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219.
  30. Erfani, S. and Akrami, V. (2019), "A Nonlinear macro-model for numerical simulation of perforated steel beams", Int. J. Steel Struct., 19(5), 1605-1623. https://doi.org/10.1007/s13296-019-00239-x.
  31. Esen (2019), "Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load", Eur. J. Mech. - A/Solids, 78, 103841. https://doi.org/10.1016/j.euromechsol.2019.103841.
  32. Esen, I. (2018), "Finite element formulation and analysis of a functionally graded Timoshenko beam subjected to an accelerating mass including inertial effects of the mass", Latin Am. J. Solids Struct., 15(10). https://doi.org/10.1590/1679-78255102.
  33. Esen, I. (2020a), "Dynamics of size-dependant Timoshenko micro beams subjected to moving loads", Int. J. Mech. Sci., 175, 105501. https://doi.org/10.1016/j.ijmecsci.2020.105501.
  34. Esen, I. (2020b), "Response of a micro-capillary system exposed to a moving mass in magnetic field using nonlocal strain gradient theory", International Journal of Mechanical Sciences, 188, 105937. https://doi.org/10.1016/j.ijmecsci.2020.105937
  35. Fallahi, B. (2003), "Integration of dynamic equation of a rotating Timoshenko beam via Chebyshev polynomials", Int. J. Model. Simul., 23(3), 172-178. https://doi.org/10.1080/02286203.2003.11442269.
  36. Fan, W., Zhu, W.D. and Zhu, H. (2019), "Dynamic analysis of a rotating planar Timoshenko beam using an accurate global spatial discretization method", J. Sound Vib., 457, 261-279. https://doi.org/10.1016/j.jsv.2019.05.003.
  37. Fang, J., Zhou, D. and Dong, Y. (2018), "Three-dimensional vibration of rotating functionally graded beams", J. Vib. Control, 24(15), 3292-3306. https://doi.org/10.1177/1077546317703867.
  38. Feng, R., Zhan, H., Meng, S. and Zhu, J. (2018), "Experiments on H-shaped high-strength steel beams with perforated web", Eng. Struct., 177, 374-394. https://doi.org/10.1016/j.engstruct.2018.08.059.
  39. Feyzollahzadeh, M. and Bamdad, M. (2019), "Vibration analysis of rotating beam with variable cross section using Riccati transfer matrix method", Struct. Eng. Mech.,70(2), 199-207. https://doi.org/10.12989/sem.2019.70.2.199.
  40. Ghadiri, M. and Shafiei, N. (2016), "Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions", Acta Astronautica, 121, 221-240. https://doi.org/10.1016/j.actaastro.2016.01.003.
  41. Gohar, S., Afefy, H. M., Kassem, N.M. and Taher, S.E.D.F. (2017), "Flexural performance of self-compacted perforated concrete beams under repeated loading", Eng. Struct., 143, 441-454. https://doi.org/10.1016/j.engstruct.2017.04.031.
  42. Guha, K., Kumar, M., Agarwal, S. and Baishya, S. (2015), "A modified capacitance model of RF MEMS shunt switch incorporating fringing field effects of perforated beam", Solid-State Electron., 114, 35-42. https://doi.org/10.1016/j.sse.2015.07.008.
  43. Gunda, J.B. and Ganguli, R. (2008), "New rational interpolation functions for finite element analysis of rotating beams", Int. J. Mech. Sci., 50(3), 578-588. https://doi.org/10.1016/j.ijmecsci.2007.07.014.
  44. Guo, Y., Li, L. and Zhang, D. (2019), "Dynamic modeling and vibration analysis of rotating beams with active constrained layer damping treatment in temperature field", Compos. Struct., 226, 111217. https://doi.org/10.1016/j.compstruct.2019.111217.
  45. Han, H., Liu, L. and Cao, D. (2020), "Dynamic modeling for rotating composite Timoshenko beam and analysis on its bending-torsion coupled vibration", Appl. Math. Model., 78, 773-791. https://doi.org/10.1016/j.apm.2019.09.056.
  46. https://doi.org/10.1016/B978-008044017-0/50013-5
  47. https://doi.org/10.1016/j.ijmecsci.2020.105937
  48. https://doi.org/10.1016/j.tws.2020.107407
  49. Hu, Y., Zhao, Y., Wang, N. and Chen, X. (2020), "Dynamic analysis of varying speed rotating pretwisted structures using refined beam theories", Int. J. Solids. Struct., 185, 292-310. https://doi.org/10.1016/j.ijsolstr.2019.08.008.
  50. Huang, Y.M. and Yang, M.L. (2009), "Dynamic analysis of a rotating beam subjected to repeating axial and transverse forces for simulating a lathing process", Int. J. Mech. Sci., 51(3), 256-268. https://doi.org/10.1016/j.ijmecsci.2008.12.005.
  51. Huo, Y. and Wang, Z. (2016), "Dynamic analysis of a rotating double-tapered cantilever Timoshenko beam", Arch. Appl. Mech., 86(6), 1147-1161. https://doi.org/10.1007/s00419-015-1084-6.
  52. Jeong, K.H. and Amabili, M. (2006), "Bending vibration of perforated beams in contact with a liquid", J. Sound Vib., 298(1-2), 404-419. https://doi.org/10.1016/j.jsv.2006.05.029.
  53. Kim, H. and Chung, J. (2016), "Nonlinear modeling for dynamic analysis of a rotating cantilever beam", Nonlinear Dynam., 86(3), 1981-2002. https://doi.org/10.1007/s11071-016-3009-5.
  54. Kim, H., Yoo, H.H. and Chung, J. (2013), "Dynamic model for free vibration and response analysis of rotating beams", J. Sound Vib., 332(22), 5917-5928. https://doi.org/10.1016/j.jsv.2013.06.004.
  55. Ko, C.H. and Chung, K.F. (2002), "A review of recent developments on design of perforated beams", Adv. Steel Struct., (ICASS'02), 121-128.
  56. Li, L., Liao, W. H., Zhang, D. and Guo, Y. (2019), "Dynamic modeling and analysis of rotating beams with partially covered enhanced active constrained layer damping treatment", J. Sound Vibr., 455, 46-68. https://doi.org/10.1016/j.jsv.2019.04.026.
  57. Li, L., Wu, J.Q., Zhu, W.D., Wang, L., Jing, L.W., Miao, G.H. and Li, Y.H. (2020), "A nonlinear dynamical model for rotating composite thin-walled beams subjected to hygrothermal effects", Compos. Struct., 112839. https://doi.org/10.1016/j.compstruct.2020.112839.
  58. Li, Y. and Li, M. (2020), "Dynamic analysis of rotating double-tapered cantilever Timoshenko nano-beam using the nonlocal strain gradient theory", Math. Method. Appl. Sci., 43(15), 9206-9222. https://doi.org/10.1002/mma.6616.
  59. Lin, B.C., Xie, T.F., Xu, M., Li, Y.H. and Yang, J. (2019), "Natural frequencies and dynamic responses of rotating composite nonuniform beams with an elastically root in hygrothermal environment", Compos. Struct., 209, 968-980. https://doi.org/10.1016/j.compstruct.2018.11.029.
  60. Luschi, L. and Pieri, F. (2012), "A simple analytical model for the resonance frequency of perforated beams", Procedia Eng., 47, 1093-1096. https://doi.org/10.1016/j.proeng.2012.09.341.
  61. Ma'en, S.S. and Butcher, E.A. (2012), "Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method", Int. J. Mech. Sci., 60(1), 1-11. https://doi.org/10.1016/j.ijmecsci.2012.03.008.
  62. Malik, M. and Das, D. (2020), "Free vibration analysis of rotating nano-beams for flap-wise, chord-wise and axial modes based on Eringen's nonlocal theory", Int. J. Mech. Sci., 105655. https://doi.org/10.1016/j.ijmecsci.2020.105655.
  63. Mohammadnejad, M. and Saffari, H. (2019), "Flapwise and non-local bending vibration of the rotating beams", Struct. Eng. Mech., 72(2), 229-244. https://doi.org/10.12989/sem.2019.72.2.229.
  64. Nadia, B., Martina, B., Bernuzzi, C. and Simoncelli, M. (2020), "Perforated TWCF steel beam-columns: European design alternatives", Steel Compos. Struct., 35(5), 701-715. http://doi.org/10.12989/scs.2020.35.5.701.
  65. Nawar, M.T., Arafa, I.T. and Elhosseiny, O. (2020), "Numerical investigation on effective spans ranges of perforated steel beams", Structures, 25, 398-410. https://doi.org/10.1016/j.istruc.2020.03.026.
  66. Nikolic, A. and Salinic, S. (2017), "Dynamics of the rotating cantilever beam", In IX International Conference "Heavy Machinery-HM. Zlatibor, 28 June - 1 July 2.
  67. Oh, Y. and Yoo, H.H. (2016), "Vibration analysis of rotating cantilever beams orienting inward", J. Mech. Sci. Technol., 30(9), 4177-4184. https://doi.org/10.1007/s12206-016-0829-7.
  68. Ondra, V. and Titurus, B. (2019), "Free vibration analysis of a rotating pre-twisted beam subjected to tendon-induced axial loading", J. Sound Vib., 461, 114912. https://doi.org/10.1016/j.jsv.2019.114912.
  69. Ozarpa, C. and Esen, I (2020), "Modelling the dynamics of a nanocapillary system with a moving mass using the non-local strain gradient theory", Math. Method. Appl. Sci., https://doi.org/10.1002/mma.6812.
  70. Rao, S.S. (2007), "Vibration of Continuous Systems", (Vol. 464), Wiley & Sons, Inc, New York.
  71. Ryigit, E., Zor, M. and Arman, Y. (2009), "Hole effects on lateral buckling of laminated cantilever beams", Compos. Part B: Engineering, 40(2), 174-179. https://doi.org/10.1016/j.compositesb.2008.07.005.
  72. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin-Walled Structures, 160, 107407. https://doi.org/10.1016/j.tws.2020.107407
  73. Sivakumar, N., Kanagasabapathy, H. and Srikanth, H. P. (2018), "Analysis of Perforated Piezoelectric Sandwich Smart Structure Cantilever Beam Using COMSOL", Mater. Today: Proceedings, 5(5), 12025-12034. https://doi.org/10.1016/j.matpr.2018.02.177.
  74. Theocaris, P.S. (1988), "A simple solution for a perforated beam in bending and traction", Acta mechanica, 71(1-4), 21-38. https://doi.org/10.1007/BF01173935
  75. Tsavdaridis, K. D. and D'Mello, C. (2011), "FE Modelling Techniques for Web-Post Buckling Response", Proceedings of the 6th European Conference on Steel and Composite Structures, Budapest, Hungary, August.
  76. Tsavdaridis, K.D. and D Mello, C. (2009), "Finite element investigation of perforated steel beams with different web opening configurations", Proceedings of the 6th ICASS'09/IJSSD, International Conference on Advances in Steel Structures and Progress in Structural Stability and Dynamics, Hong Kong, China, 16-18 December.
  77. Tsavdaridis, K.D. and D'Mello, C. (2012), "Optimisation of novel elliptically-based web opening shapes of perforated steel beams", J. Constr. Steel Res., 76, 39-53. https://doi.org/10.1016/j.jcsr.2012.03.026.
  78. Tsavdaridis, K.D., D'Mello, C. and Huo, B.Y. (2013), "Experimental and computational study of the vertical shear behaviour of partially encased perforated steel beams", Eng. Struct., 56, 805-822. https://doi.org/10.1016/j.engstruct.2013.04.025.
  79. Tsavdaridis, K.D., Faghih, F. and Nikitas, N. (2014), "Assessment of perforated steel beam-to-column connections subjected to cyclic loading", J. Earthq. Eng., 18(8), 1302-1325. https://doi.org/10.1080/13632469.2014.935834.
  80. Tsavdaridis, K.D., Kingman, J.J. and Toropov, V.V. (2015), "Application of structural topology optimisation to perforated steel beams", Computers & structures, 158, 108-123. https://doi.org/10.1016/j.compstruc.2015.05.004.
  81. Wang, A.J. and Chung, K.F. (2008), "Advanced finite element modelling of perforated composite beams with flexible shear connectors", Eng. Struct., 30(10), 2724-2738. https://doi.org/10.1016/j.engstruct.2008.03.001.
  82. Wozniak, J. and Firkowski, M. (2019), "Optimal decay ratio of damped slowly rotating Timoshenko beams", ZAMM-J. Appl. Math. Mech., 99(10), e201800222. https://doi.org/10.1002/zamm.201800222.
  83. Yachin, V.V. and Zinenko, T.L. (2016), "3-D Gaussian beam scattering from a gyromagnetic perforated layer: Quasi-static approach", Opt. Commun., 380, 425-433. https://doi.org/10.1016/j.optcom.2016.06.032.
  84. Yang, J.L. and Yu, T.X. (2001), "Dynamic plastic behavior of a free-rotating hinged beam striking a cantilever beam", Mech. Struct. Mach., 29(3), 391-409. https://doi.org/10.1081/SME100105657.
  85. Yang, X., Wang, S., Zhang, W., Qin, Z. and Yang, T. (2017), "Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method", Appl. Math. Mech., 38(10), 1425-1438. https://doi.org/10.1007/s10483-017-2249-6.
  86. Yang, X.D., Wang, S. W., Zhang, W., Yang, T.Z. and Lim, C.W. (2018), "Model formulation and modal analysis of a rotating elastic uniform Timoshenko beam with setting angle", Eur. J. Mech. -A/Solids, 72, 209-222. https://doi.org/10.1016/j.euromechsol.2018.05.014.
  87. Yu, Y.S. and Liu, X.Y. (2020), "Finite element analyses on energy dissipation capacity of upper flange welded-lower flange bolted beam-column connection with slotted holes", J. Asian Architect. Build. Eng., 1-12. https://doi.org/10.1080/13467581.2020.1749639.
  88. Zaher, O.F., Yossef, N.M., El-Boghdadi, M.H. and Dabaon, M.A. (2018), "Structural behaviour of arched steel beams with cellular openings", J. Constr. Steel Res., 148, 756-767. https://doi.org/10.1016/j.jcsr.2018.06.029.
  89. Zeng, J., Zhao, C., Ma, H. and Wen, B. (2020), "Dynamic modeling and coupling characteristics of rotating inclined beams with twisted-shape sections", Front. Mech. Eng., 15(3): 374-389. https://doi.org/10.1007/s11465-019-0580-8.
  90. Zhao, C., Zeng, J., Ma, H., Ni, K. and Wen, B. (2020), "Dynamic Analysis of Cracked Rotating Blade Using Cracked Beam Element", Results in Phys., 19, 103360. https://doi.org/10.1016/j.rinp.2020.103360.