Steel and Composite Structures

  • 제31권5호
  • /
  • Pages.489-502
  • /
  • 2019
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free and forced analysis of perforated beams

  • Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Kabeel, Abdallah M. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Abdraboh, Azza M. (Physics Department, Faculty of Science, Banha University) ;
  • Hendi, Asmaa A. (Physics Department, Faculty of Science, University of Jeddah)
  • 투고 : 2019.01.28
  • 심사 : 2019.03.26
  • 발행 : 2019.06.10
⟨ 이전 논문 다음 논문 ⟩

초록

This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

키워드

참고문헌

  1. Abdelbari, S., Amar, L.H.H., Kaci, A. and Tounsi, A. (2018), "Single variable shear deformation model for bending analysis of thick beams", Struct. Eng. Mech., Int. J., 67(3), 291-300. http://dx.doi.org/10.12989/sem.2018.67.3.291
  2. Adhikary, S.D., Li, B. and Fujikake, K. (2012), "Dynamic behavior of reinforced concrete beams under varying rates of concentrated loading", Int. J. Impact Eng., 47, 24-38. https://doi.org/10.1016/j.ijimpeng.2012.02.001
  3. Bebiano, R., Calcada, R., Camotim, D. and Silvestre, N. (2017), "Dynamic analysis of high-speed railway bridge decks using generalised beam theory", Thin-Wall. Struct.res, 114, 22-31. https://doi.org/10.1016/j.tws.2017.01.027
  4. Berggren, S.A., Lukkassen, D., Meidell, A. and Simula, L. (2003), "Some methods for calculating stiffness properties of periodic structures", Applica. Math., 48(2), 97-110. https://doi.org/10.1023/A:1026090026531
  5. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. http://dx.doi.org/10.12989/scs.2015.19.3.521
  6. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. http://dx.doi.org/10.12989/scs.2015.18.2.409
  7. Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Bedia, E.A.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., Int. J., 15(5), 467-479. http://dx.doi.org/10.12989/scs.2013.15.5.467
  8. Cortes, C., Osorno, M., Uribe, D., Steeb, H., Ruiz-Salguero, O., Barandiaran, I. and Florez, J. (2019), "Geometry simplification of open-cell porous materials for elastic deformation FEA", Eng. Comput., 35, 257-276. https://doi.org/10.1007/s00366-018-0597-3
  9. De Pasquale, G., Veijola, T. and Soma, A. (2009), "Modelling and validation of air damping in perforated gold and silicon MEMS plates", J. Micromech. Microeng., 20(1), 015010. https://doi.org/10.1088/0960-1317/20/1/015010
  10. Driz, H., Benchohra, M., Bakora, A., Benachour, A., Tounsi, A. and Bedia, E.A.A. (2018), "A new and simple HSDT for isotropic and functionally graded sandwich plates", Steel Compos. Struct., Int. J., 26(4), 387-405. http://dx.doi.org/10.12989/scs.2018.26.4.387
  11. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  12. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  13. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014a), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Computat., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028
  14. Eltaher, M.A., Hamed, M.A., Sadoun, A.M. and Mansour, A. (2014b), "Mechanical analysis of higher order gradient nanobeams", Appl. Math. Computat., 229, 260-272. https://doi.org/10.1016/j.amc.2013.12.076
  15. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., Int. J., 4(1), 51-64. 10.12989/anr.2016.4.1.051
  16. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018a), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6
  17. Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018b), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsyst. Technol., 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3
  18. Ghayesh, M.H., Farokhi, H., Gholipour, A. and Tavallaeinejad, M. (2017), "Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 120, 51-62. https://doi.org/10.1016/j.ijengsci.2017.03.010
  19. Greco, A., Pluchino, A., Caddemi, S., Calio, I. and Cannizzaro, P. (2019), "On profile reconstruction of Euler-Bernoulli beams by means of an energy based genetic algorithm", Eng. Comput.
  20. 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 Electronics, 114, 35-42. https://doi.org/10.1016/j.sse.2015.07.008
  21. Guha, K., Laskar, N.M., Gogoi, H.J., Borah, A.K., Baishnab, K.L. and Baishya, S. (2017), "Novel analytical model for optimizing the pull-in voltage in a flexured MEMS switch incorporating beam perforation effect", Solid-State Electronics, 137, 85-94. https://doi.org/10.1016/j.sse.2017.08.007
  22. Guha, K., Laskar, N.M., Gogoi, H.J., Baishnab, K.L. and Rao, K.S. (2018), "A new analytical model for switching time of a perforated MEMS switch", Microsyst. Technol., 1-10.
  23. Gul, U., Aydogdu, M. and Karacam, F. (2019), "Dynamics of a functionally graded Timoshenko beam considering new spectrums", Compos. Struct., 207, 273-291. https://doi.org/10.1016/j.compstruct.2018.09.021
  24. 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
  25. Heidari, A., Keikha, R., Haghighi, M.S. and Hosseinabadi, H. (2018), "Numerical study for vibration response of concrete beams reinforced by nanoparticles", Struct. Eng. Mech., Int. J., 67(3), 311-316. https://doi.org/10.12989/sem.2018.67.3.311
  26. Hopcroft, M.A., Nix, W.D. and Kenny, T.W. (2010), "What is the Young's modulus of silicon?", J. Microelectromech. Syst., 19, 229-238. https://doi.org/10.1109/JMEMS.2009.2039697
  27. Inman, D.J. (2014), Engineering Vibration, (4th ed.), Pearson, Pearson Education.
  28. 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
  29. Katariya, P.V. and Panda, S.K. (2018), "Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings", Eng. Comput., 1-18.
  30. Kerid, R., Bourouina, H., Yahiaoui, R., Bounekhla, M. and Aissat, A. (2019), "Magnetic field effect on nonlocal resonance frequencies of structure-based filter with periodic square holes network", Physica E: Low-dimensional Syst. Nanostruct., 105, 83-89. https://doi.org/10.1016/j.physe.2018.05.021
  31. Kim, J.H., Jeon, J.H., Park, J.S., Seo, H.D., Ahn, H.J. and Lee, J.M. (2015), "Effect of reinforcement on buckling and ultimate strength of perforated plates", Int. J. Mech. Sci., 92, 194-205. https://doi.org/10.1016/j.ijmecsci.2014.12.016
  32. Kim, T., Park, I. and Lee, U. (2017), "Forced vibration of a Timoshenko beam subjected to stationary and moving loads using the modal analysis method", Shock Vib.
  33. Lee, Y.Y. (2016), "The effect of leakage on the sound absorption of a nonlinear perforated panel backed by a cavity", Int. J. Mech. Sci., 107, 242-252. https://doi.org/10.1016/j.ijmecsci.2016.01.019
  34. 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
  35. Luschi, L. and Pieri, F. (2014), "An analytical model for the determination of resonance frequencies of perforated beams" J. Micromech. Microeng., 24(5), 055004. https://doi.org/10.1088/0960-1317/24/5/055004
  36. Luschi, L. and Pieri, F. (2016), "An analytical model for the resonance frequency of square perforated Lame-mode resonators", Sensors Actuators B: Chem., 222, 1233-1239. https://doi.org/10.1016/j.snb.2015.07.085
  37. Nikkhoo, A., Rofooei, F.R. and Shadnam, M.R. (2007), "Dynamic behavior and modal control of beams under moving mass", J. Sound Vib., 306(3-5), 712-724. https://doi.org/10.1016/j.jsv.2007.06.008
  38. Pedersen, M., Olthuis, W. and Bergveld, P. (1996), "On the mechanical behaviour of thin perforated plates and their application in silicon condenser microphones", Sensors Actuators A: Phys., 54(1-3), 499-504. https://doi.org/10.1016/S0924-4247(95)01189-7
  39. Rajasekaran, S. (2018), "Analysis of axially functionally graded nano-tapered Timoshenko beams by element-based Bernstein pseudospectral collocation (EBBPC)", Eng. Comput., 34(3), 543-563. https://doi.org/10.1007/s00366-017-0557-3
  40. Rao, S.S. (2007), Vibration of Continuous Systems, John Wiley & Sons.
  41. Rouhi, H., Ebrahimi, F., Ansari, R. and Torabi, J. (2019), "Nonlinear free and forced vibration analysis of Timoshenko nanobeams based on Mindlin's second strain gradient theory", Eur. J. Mech.-A/Solids, 73, 268-281. https://doi.org/10.1016/j.euromechsol.2018.09.005
  42. Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", Int. J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004
  43. She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357. https://doi.org/10.1016/j.apm.2017.03.014
  44. She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H.B. (2018a), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., Int. J., 66(6), 729-736.
  45. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018b), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  46. Sinir, S., Cevik, M. and Sinir, B.G. (2018), "Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section", Compos. Part B: Eng., 148, 123-131. https://doi.org/10.1016/j.compositesb.2018.04.061
  47. Song, Y., Kim, T. and Lee, U. (2016), "Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis", Int. J. Mech. Sci., 113, 162-174. https://doi.org/10.1016/j.ijmecsci.2016.04.020
  48. Tekili, S., Khadri, Y., Merzoug, B., Daya, E.M. and Daouadji, A. (2017), "Free and Forced Vibration of Beams Strengthened by Composite Coats Subjected to Moving Loads", Mech. Compos. Mater., 52(6), 789-798. https://doi.org/10.1007/s11029-017-9630-7
  49. Thai, S., Thai, H.T., Vo, T.P. and Patel, V.I. (2018), "A simple shear deformation theory for nonlocal beams", Compos. Struct., 183, 262-270. https://doi.org/10.1016/j.compstruct.2017.03.022
  50. Tu, W.H., Chu, W.C., Lee, C.K., Chang, P.Z. and Hu, Y.C. (2013), "Effects of etching holes on complementary metal oxide semiconductor-microelectromechanical systems capacitive structure", J. Intel. Mater. Syst. Struct., 24(3), 310-317. https://doi.org/10.1177/1045389X12449917

피인용 문헌

  1. Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads vol.34, pp.1, 2019, https://doi.org/10.12989/scs.2020.34.1.075
  2. Buckling and stability analysis of sandwich beams subjected to varying axial loads vol.34, pp.2, 2019, https://doi.org/10.12989/scs.2020.34.2.241
  3. Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory vol.25, pp.3, 2020, https://doi.org/10.12989/cac.2020.25.3.225
  4. On bending analysis of perforated microbeams including the microstructure effects vol.76, pp.6, 2020, https://doi.org/10.12989/sem.2020.76.6.765
  5. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2019, https://doi.org/10.12989/gae.2021.24.1.091
  6. Vibration of multilayered functionally graded deep beams under thermal load vol.24, pp.6, 2019, https://doi.org/10.12989/gae.2021.24.6.545
  7. Transient response of functionally graded non-uniform cylindrical helical rods vol.40, pp.4, 2021, https://doi.org/10.12989/scs.2021.40.4.571
  8. Experimental studies on vibration serviceability of composite steel-bar truss slab with steel girder under human activities vol.40, pp.5, 2019, https://doi.org/10.12989/scs.2021.40.5.663