Steel and Composite Structures

  • 제45권5호
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  • Pages.697-713
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  • 2022
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Study of the dynamic behavior of porous functionally graded suspension structural systems using finite elements method

  • Ayman E., Nabawy (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University) ;
  • Ayman M.M., Abdelhaleem (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University) ;
  • Soliman. S., Alieldin (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University) ;
  • Alaa A., Abdelrahman (Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University)
  • 투고 : 2022.03.07
  • 심사 : 2022.11.28
  • 발행 : 2022.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

In the context of the finite elements method, the dynamic behavior of porous functionally graded double wishbone vehicle suspension structural system incorporating joints flexibility constraints under road bump excitation is studied and analyzed. The functionally graded material properties distribution through the thickness direction is simulated by the power law including the porosity effect. To explore the porosity effects, both classical and adopted porosity models are considered based on even porosity distribution pattern. The dynamic equations of motion are derived based on the Hamiltonian principle. Closed forms of the inertia and material stiffness components are derived. Based on the plane frame isoparametric Timoshenko beam element, the dynamic finite elements equations are developed incorporating joint flexibilities constraints. The Newmark's implicit direct integration methodology is utilized to obtain the transient vibration time response under road bump excitation. The presented procedure is validated by comparing the computational model results with the available numerical solutions and an excellent agreement is observed. Obtained results show that the decrease of porosity percentage and material graduation tends to decrease the deflection as well as the resulting stresses of the control arms thus improving the dynamic performance and increasing the service lifetime of the control arms.

키워드

참고문헌

  1. Abdelrahman, A.A. and El-Shafei, A.G. (2021), "Modeling and analysis of the transient response of viscoelastic solids", Waves Random Complex Media, 31(6), 1990-2020. https://doi.org/10.1080/17455030.2020.1714790.
  2. Abdelrahman, A.A., Ashry, M., Alshorbagy, A.E. and Abdallah, W. S. (2021), "On the mechanical behavior of two directional symmetrical functionally graded beams under moving load", Int. J. Mech. Mater. Des., 17, 563-586. https://doi.org/10.1007/s10999-021-09547-9.
  3. Abdelrahman, A.A., Nabawy, A.E., Abdelhaleem, A.M., Alieldin, S.S. and Eltaher, M.A. (2020), "Nonlinear dynamics of viscoelastic flexible structural systems by finite element method", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01141-5.
  4. Akbas, S.D. (2017), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coup. Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.
  5. Akbas, S.D. (2017), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 579-589. https://doi.org/10.12989/scs.2017.24.5.57.
  6. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/jacm.2017.21540.1107.
  7. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811.
  8. Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous, thick beams under pulse load", Eng. Comput., 1-13. https://doi.org/10.1007/s00366-020-01070-3.
  9. Al Jahwari, F., Anwer, A.A. and Naguib, H.E. (2015), "Fabrication and microstructural characterization of functionally graded porous acrylonitrile butadiene styrene and the effect of cellular morphology on creep behavior", J. Polymer Sci. Part B: Polymer Phys., 53(11), 795-803. https://doi.org/10.1002/polb.23698.
  10. Alam, M.N. and Akhlaq, A. (2015), "Dynamic analysis and vibration control of a multi-body system using MSC Adams", Latin Amer. J. Solids Struct., 12, 1505-1524. http://dx.doi.org/10.1590/1679-78251598.
  11. Almitani, K.H., Eltaher, M.A., Abdelrahman, A.A. and Abd-ElMottaleb, H.E. (2021), "Finite element-based stress and vibration analysis of axially functionally graded rotating beams", Struct. Eng. Mech., 79(1), 23-33. https://doi.org/10.12989/sem.2021.79.1.023.
  12. Amidi, S. and Wang, J. (2018), "Three-parameter viscoelastic foundation model of adhesively bonded single-lap joints with functionally graded adherends", Eng. Struct., 170, 118-134. https://doi.org/10.1016/j.engstruct.2018.05.076.
  13. Anirudh, B., Ganapathi, M., Anant, C. and Polit, O. (2019), "A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling", Compos. Struct., 222, 110899(1-13). https://doi.org/10.1016/j.compstruct.2019.110899.
  14. Arbind, A. and Reddy, J.N. (2013), "Nonlinear analysis of functionally graded microstructure-dependent beams", Compos. Struct., 98, 272-281. http://dx.doi.org/10.1016/j.compstruct.2012.10.003.
  15. Aria, A.I., Rabczuk, T. and Friswell, M.I. (2019), "A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams", Europ. J. Mech.-A/Solids, 77, 103767(1-34). https://doi.org/10.1016/j.euromechsol.2019.04.002.
  16. Attia, H.A. (2002), "Dynamic modelling of the double wishbone motor-vehicle suspension system", Europ. J. Mech. A/Solids, 21(1), 167-174. https://doi.org/10.1016/S0997-7538(01)01178-0.
  17. Attia, M.A. and Mohamed, S.A. (2020), "Thermal vibration characteristics of pre/post-buckled bi-directional functionally graded tapered microbeams based on modified couple stress Reddy beam theory", Eng. Comput., 1-27. https://doi.org/10.1007/s00366-020-01188-4.
  18. Attia, M.A. and Rahman, A.A.A. (2018), "On vibrations of functionally graded viscoelastic nanobeams with surface effects", Int. J. Eng. Sci., 127, 1-32. https://doi.org/10.1016/j.ijengsci.2018.02.005.
  19. Attia, M.A., Eltaher, M.A., Soliman, A., Abdelrahman, A.A. and Alshorbagy, A.E. (2018), "Thermoelastic crack analysis in functionally graded pipelines conveying natural gas by an FEM", Int. J. Appl. Mech., 10(04), 1850036. https://doi.org/10.1142/S1758825118500369.
  20. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.60.
  21. Babaei, M., Asemi, K. and Safarpour, P. (2019), "Buckling and static analyses of functionally graded saturated porous, thick beam resting on elastic foundation based on higher order beam theory", Iran. J. Mech. Eng. Transact. ISME, 20(1), 94-112.
  22. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  23. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aeros. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  24. Daouadji, T.H., Abderezak, R., Rabia, B. and Tounsi, A. (2021), "Renovation of steel beams using by imperfect functionally graded materials plate", Steel Compos. Struct., 41(6), 851-860. https://doi.org/10.12989/scs.2021.41.6.851.
  25. Dehbari, S. and Marzbanrad, J. (2018), "Kinematic and dynamic analysis for a new MacPherson strut suspension system", Mech. Mech. Eng., 22(4), 1223-1238. https://doi.org/10.2478/mme2018-0094.
  26. Dinh Duc, N., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mec., 4(4), 245-259. https://doi.org/10.22055/JACM.2018.23219.1151.
  27. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016, 1-20. http://dx.doi.org/10.1155/2016/9561504.
  28. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014), "Vibration of nonlinear graduation of nanoTimoshenko beam considering the neutral axis position", Appl. Mathem. Comput., 235, 512-529. http://dx.doi.org/10.1016/j.amc.2014.03.028.
  29. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. http://dx.doi.org/10.1016/j.compstruct.2012.11.039.
  30. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(3), 1-10. https://doi.org/10.1007/s40430-018-1065-0.
  31. Esen, I. (2019a), "Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass", Int. J. Mech. Sci., 153, 21-35. https://doi.org/10.1016/j.ijmecsci.2019.01.033.
  32. Esen, I. (2019b), "Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load", Europ. J. Mech.-A/Solids, 78, 103841(1-18). https://doi.org/10.1016/j.euromechsol.2019.103841.
  33. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17, 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  34. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38(4), 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  35. Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Europ. Phys. J. Plus, 136(4), 1-22.https://doi.org/10.1140/epjp/s13360-021-01419-7.
  36. Esen, I., Eltaher, M.A. and Abdelrahman, A.A. (2021), "Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass", Mech. Based Des. Struct. Machines, 1-25. https://doi.org/10.1080/15397734.2021.1904255.
  37. Esen, I., Koc, M.A. and Cay, Y. (2018), "Finite element formulation and analysis of a functionally graded Timoshenko beam subjected to an accelerating mass including inertial effects of the mass", Latin Amer. J. Solids Struct., 15, 1-18. http://dx.doi.org/10.1590/1679-78255102.
  38. Fallah, M.S., Bhat, R. and Xie, W.F. (2010), "H∞ robust control of semi-active Macpherson suspension system: new applied design", Vehicle Syst. Dyn., 48(3), 339-360. https://doi.org/10.1080/00423110902807714.
  39. Fouda, N., El-Midany, T. and Sadoun, A.M. (2017), "Bending, buckling and vibration of a functionally graded porous beam using finite elements", J. Appl. Comput. Mech., 3(4), 274-282. https://doi.org/10.22055/JACM.2017.21924.1121.
  40. Ghayesh, M.H. (2019), "Mechanics of viscoelastic functionally graded microcantilevers", Europ. J. Mech. A/Solids, 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001.
  41. Gillespie, T.D. (1992), Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Inc, USA.
  42. Hurel, J., Mandow, A. and Garcia-Cerezo, A. (2013), "Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model", Vehicle Syst. Dyn., 51(9), 1422-1437. http://dx.doi.org/10.1080/00423114.2013.804937.
  43. Ikhsan, N., Ramli, R. and Alias, A. (2014), "Analysis of kinematic and compliance of passive suspension system using Adams car", J. Mech. Eng. Sci., 8, 1293-1301. http://dx.doi.org/10.15282/jmes.8.2015.4.0126.
  44. Kavitha, C., Shankar, S.A., Ashok, B., Ashok, S.D., Ahmed, H. and Kaisan, M.U. (2018), "Adaptive suspension strategy for a double wishbone suspension through camber and toe optimization", Eng. Sci. Technol., 21(1), 149-158. https://doi.org/10.1016/j.jestch.2018.02.003.
  45. Kim, S.S., Jung, H.K., Shim, J.S. and Kim, C.W. (2005), "Development of vehicle dynamics model for real-time electronic control unit evaluation system using kinematic and compliance test data", Int. J. Auto. Technol,, 6(6), 599-604.
  46. Kohnke, P.C. (1998), ANSYS Theory Reference: Release 5.5. ANSYS, Canonsburg, Pennsylvania.
  47. Liu, H., Liu, H. and Yang, J. (2018), "Vibration of FG magnetoelectro-viscoelastic porous nanobeams on visco-Pasternak foundation", Compos. Part B: Eng., 155, 244-256. https://doi.org/10.1016/j.compositesb.2018.08.042.
  48. Liu, Y.F. and Wang, Y.Q. (2019), "Thermo-electro-mechanical vibrations of porous functionally graded piezoelectric nanoshells", Nanomaterials, 9(2), 301(1-20). https://doi.org/10.3390/nano9020301.
  49. Masoudi, R., Uchida, T. and McPhee, J. (2015), "Reduction of multibody dynamic models in automotive systems using the proper orthogonal decomposition", J. Comput. Nonlinear Dyn., 10(3), 031007(1-8). https://doi.org/10.1115/1.4029390.
  50. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.41.
  51. Mota, A.F. and Loja, M.A.R. (2019), "Mechanical behavior of porous functionally graded nanocomposite materials", C, 5(2), 34(1-21). https://doi.org/10.3390/c5020034.
  52. Nabawy, A.E., Abdelrahman, A.A., Abdalla, W.S., Abdelhaleem, A. M. and Alieldin, S.S. (2019), "Analysis of the dynamic behavior of the double wishbone suspension system", Int. J. Appl. Mech., 11(5), 1950044(1-19). https://doi.org/10.1142/S1758825119500443.
  53. Nguyen, D.K. and Tran, T.T. (2018), "Free vibration of tapered BFGM beams using an efficient shear deformable finite element model", Steel Compos. Struct., 29(3), 363-377. https://doi.org/10.12989/scs.2018.29.3.363.
  54. Nguyen, L.B., Thai, C.H., Zenkour, A.M. and Nguyen-Xuan, H. (2019), "An isogeometric Bezier finite element method for vibration analysis of functionally graded piezoelectric material porous plates", Int. J. Mech. Sci., 157, 165-183. https://doi.org/10.1016/j.ijmecsci.2019.04.017.
  55. Onate, E. (2013), Structural Analysis with the Finite Element Method, Linear Statics: Beams, Plates, and Shells, Springer Science & Business Media, Germany.
  56. Rahman, A.A., Nabawy, A.E., Abdelhaleem, A.M. and Alieldin, S.S. (2019), "Dynamic finite element analysis of flexible double wishbone suspension systems with different damping mechanisms", Europ. J. Comput. Mech., 28(6), 573-604. https://doi.org/10.13052/ejcm2642-2085.2862.
  57. Ramirez, C.M., Tomas-Rodriguez, M. and Evangelou, S.A. (2018), "Dynamic analysis of double wishbone front suspension systems on sport motorcycles", Nonlinear Dyn., 91(6), 2347-2368. https://doi.org/10.1007/s11071-017-4017-9.
  58. Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59(11), 2382-2399. http://dx.doi.org/10.1016/j.jmps.2011.06.008.
  59. Reddy, K.V., Kodati, M., Chatra, K. and Bandyopadhyay, S. (2016), "A comprehensive kinematic analysis of the double wishbone and MacPherson strut suspension systems", Mech. Machine Theory, 105, 441-470. http://dx.doi.org/10.1016/j.mechmachtheory.2016.06.001.
  60. She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009.
  61. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. http://dx.doi.org/10.1016/j.compstruct.2012.10.038.
  62. Tanik, E. and Parlaktas, V. (2015), "On the analysis of double wishbone suspension", J. Adv. Mech. Des. Syst. Manufact., 9(3), JAMDSM0037(1-10). http://dx.doi.org/10.1299/jamdsm.2015jamdsm0037.
  63. Wang, Y.Q., Wan, Y.H. and Zhang, Y.F. (2017), "Vibrations of longitudinally traveling functionally graded material plates with porosities", Europ. J. Mech.-A/Solids, 66, 55-68. https://doi.org/10.1016/j.euromechsol.2017.06.006.
  64. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aeros. Sci. Technol., 32(1), 111-120. http://dx.doi.org/10.1016/j.ast.2013.12.002.
  65. Wideberg, J., Bordons, C., Luque, P., Mantaras, D.A., Marcos, D. and Kanchwala, H. (2014), "Development and experimental validation of a dynamic model for electric vehicle within hub motors", Procedia-Social Behavioral Sci., 160, 84-91. http://dx.doi.org/10.1016/j.sbspro.2014.12.119.
  66. Xie, B., Sahmani, S., Safaei, B. and Xu, B. (2021), "Nonlinear secondary resonance of FG porous silicon nanobeams under periodic hard excitations based on surface elasticity theory", Eng. Comput., 37(2), 1611-1634. https://doi.org/10.1007/s00366-019-00931-w.
  67. Yu, H., Zhao, C. and Zheng, H. (2017), "A higher-order variable cross-section viscoelastic beam element via ANCF for kinematic and dynamic analyses of two-link flexible manipulators", Int. J. Appl. Mech., 9(8), 1750116(1-22). http://dx.doi.org/10.1142/S1758825117501162.
  68. Zhang, B., Zhang, J., Yi, J., Zhang, N. and Jin, Q. (2016), "Modal and dynamic analysis of a vehicle with kinetic dynamic suspension system", Shock Vib., 2016, 1-18. http://dx.doi.org/10.1155/2016/5239837.
  69. Zhou, G., Wang, Y. and Du, H. (2020), "A generalized method for three-dimensional dynamic analysis of a full-vehicle model", Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 234(10-11), 2485-2499. https://doi.org/10.1177/0954407020916942.