Structural Engineering and Mechanics

  • 제87권2호
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  • Pages.191-200
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  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Study and analysis of a tapered shaft in composite materials with variable speed of rotation

  • Rachid Zahi (Laboratory of Mechanics of Structures and Solids (LMSS), University of Relizane) ;
  • Abderahmane Sahli (Department of Mechanical Engineering, University of Djillali Liabes Sidi Bel Abbes) ;
  • DjafarAit Kaci (Department of Mechanical Engineering, University of Djillali Liabes Sidi Bel Abbes) ;
  • Fouad Bourada (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Mofareh Hassan Ghazwani (Department of Mechanical Engineering, Faculty of Engineering, Jazan University)
  • 투고 : 2022.12.28
  • 심사 : 2023.06.19
  • 발행 : 2023.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a mechanical model of a "tapered composite shaft" rotating at a constant speed around its axis. The spatial equations of motion are solved using the Lagrange technique, and a finite element approach is employed to construct the model. Theoretical analysis is used to compute the kinetic and strain energies. A comparison is made between conventional finite element methods and hierarchical finite element methods, indicating that the former uses fewer elements and provides higher accuracy in determining natural frequencies. Numerical calculations are performed to determine the eigen frequencies and critical speeds of the rotating composite shaft. The critical speeds of composite shaft systems are compared with existing literature to validate the proposed model.

키워드

참고문헌

  1. Abouelregal, A.E., Sedighi, H.M. and Eremeyev, V.A. (2023), "Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model", Continuum Mech. Thermodyn., 35(1), 81-102. https://doi.org/10.1007/s00161-022-01170-z.
  2. Akbas, S.D. (2022), "Moving-load dynamic analysis of AFG beams under thermal effect", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  3. Alazzawy, W.I. (2009), "Analytical solution for buckling of laminated conical shells", Al-Nahrain J. Eng. Sci., 12(2), 129-146.
  4. Alimoradzadeh, M. and Akbas, S.D. (2022), "Nonlinear dynamic behavior of functionally graded beams resting on nonlinear viscoelastic foundation under moving mass in thermal environment", Struct. Eng. Mech., 81(6), 705-714. https://doi.org/10.12989/sem.2022.81.6.705.
  5. Al-Osta, M.A. (2022a), "An exponential-trigonometric quasi-3D HSDT for wave propagation in an exponentially graded plate with microstructural defects", Compos. Struct., 297, 115984. https://doi.org/10.1016/j.compstruct.2022.115984
  6. Al-Osta, M.A. (2022b), "Wave propagation investigation of a porous sandwich FG plate under hygrothermal environments via a new first-order shear deformation theory", Steel Compos. Struct., 43(1), 117-127. https://doi.org/10.12989/scs.2022.43.1.117.
  7. 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.2019.30.6.603.
  8. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  9. Baghani, M., Jafari-Talookolaei, R.A. and Salarieh, H. (2011), "Large amplitudes free vibrations and post-buckling analysis of unsymmetrically laminated composite beams on nonlinear elastic foundation", Appl. Math. Model., 35(1), 130-138. https://doi.org/10.1016/j.apm.2010.05.012.
  10. Balci, M., Nalbant, M.O., Kara, E. and Gundogdu, O. (2014), "Free vibration analysis of a laminated composite beam with various boundary conditions", Int. J. Autom. Mech. Eng., 9, 1734, http://doi.org/10.15282/ijame.9.2013.22.0144.
  11. Bochkareva, S.A. and Lekomtsev, S.V. (2022), "Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells", Struct. Eng. Mech., 81(6), 769-780. https://doi.org/10.12989/sem.2022.81.6.769.
  12. Brunelle, E.J. (2012), "Stress redistribution and instability of rotating beams and disks", AIAA J., 9(4), 758-759. https://doi.org/10.2514/3.6270.
  13. Chinnapandi, L.B.M., Pitchaimani, J. and Eltaher, M.A. (2022), "Vibro-acoustics of functionally graded porous beams subjected to thermo-mechanical loads", Steel Compos. Struct., 44(6), 829-843. https://doi.org/10.12989/scs.2022.44.6.829.
  14. Cho, J.R. (2022a), "Nonlinear bending analysis of functionally graded CNT-reinforced composite plates", Steel Compos. Struct., 42(1), 23-32. https://doi.org/10.12989/scs.2022.42.1.023.
  15. Cho, J.R. (2022b), "Thermal buckling analysis of metal-ceramic functionally graded plates by natural element method", Struct. Eng. Mech., 84(6), 723-731. https://doi.org/10.12989/sem.2022.84.6.723.
  16. Choi, S.H., Heo, I., Kim, J.H., Jeong, H., Lee, J.Y. and Kim, K.S. (2022), "Flexural behavior of post-tensioned precast concrete girder at negative moment region", Comput. Concrete, 30(1),75-84. https://doi.org/10.12989/cac.2022.30.1.075.
  17. Civalek, O . and Demir, C . (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 35(5), 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004.
  18. Cuong-Le, T., Ferreira, A.J.M. and Abdel Wahab, M. (2019b), "A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis", Thin Wall. Struct., 145, 106427. https://doi.org/10.1016/j.tws.2019.106427.
  19. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Wahab, M.A. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condens. Matter, 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  20. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condensed Matter, 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  21. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and Nguyen-Xuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnol., 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  22. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and Nguyen-Xuan, H. (2021a), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnol., 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  23. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  24. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and AbdelWahab, M. (2021b), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  25. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38(2022), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  26. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and AbdelWahab, M. (2022c), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38 (1), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  27. Cuong-Le, T., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019a), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  28. Ding, F., Ding, H., He, C., Wang, L. and Lyu, F. (2022), "Method for flexural stiffness of steel-concrete composite beams based on stiffness combination coefficients", Comput. Concrete, 29(3), 127-144. https://doi.org/10.12989/cac.2022.29.3.127.
  29. Du, M., Liu, J., Ye, W., Yang, F. and Lin, G. (2022), "A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams", Struct. Eng. Mech., 81(2), 179-194. https://doi.org/10.12989/sem.2022.81.2.179.
  30. Fan, L., Kong, D., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Optimization dynamic responses of laminated multiphase shell in thermo-electro-mechanical conditions", Adv. Nano Res., 13(1), 29-45. https://doi.org/10.12989/anr.2022.13.1.029.
  31. Gursky, V., Krot, P., Korendiy, V. and Zimroz, R. (2022), "Dynamic analysis of an enhanced multi-frequency inertial exciter for industrial vibrating machines", Mach., 10(2), 130, https://doi.org/10.3390/machines10020130.
  32. Hagos, R.W., Choi, G., Sung, H. and Chang, S. (2022), "Substructuring-based dynamic reduction method for vibration analysis of periodic composite structures", Compos. Mater. Eng., 4(1), 43-62 https://doi.org/10.12989/cme.2022.4.1.043.
  33. Hajianmaleki, M. and Qatu, M.S. (2013), "Vibrations of straight and curved composite beams: A review", Compos. Struct., 100, 218-232. https://doi.org/10.1016/j.compstruct.2013.01.001.
  34. Huang, X., Shan, H., Chu, W. and Chen, Y. (2022), "Computational and mathematical simulation for the size-dependent dynamic behavior of the high-order FG nanotubes, including the porosity under the thermal effects", Adv. Nano Res., 12(1), 101-115. https://doi.org/10.12989/anr.2022.12.1.101.
  35. Ibraheem-Majeed, W., Al-Samarraie, S.A. and AL-SAIOR, M. M. (2013), "Vibration control analysis of a smart flexible cantilever beam using smart material", J. Eng., 19(1). 82-95.
  36. Jweeg, M.J. and Ibraheem-Majeed, W. (2009), "Free vibration analysis solution for laminated truncated conical shells using high orde theory", Proceedings of the 6 th Science Conference of the College of Engineering, University of Baghdad, 3, 208-225.
  37. Jweeg, M.J., Alnomani, S.N. and Mohammad, S.K. (2020), "Dynamic analysis of a rotating stepped shaft with and without defects", IOP Conf. Ser.: Mater. Sci. Eng., 671(1), 012004. https://doi.org/10.1088/1757-899X/671/1/012004.
  38. Kargarnovin, M.H., Ahmadian, M.T., Jafari-Talookolaei, R.A. and Abedi, M. (2013), "Semi-analytical solution for the free vibration analysis of generally laminated composite Timoshenko beams with single delamination", Compos. Part B: Eng., 45(1), 587-600. https://doi.org/10.1016/j.compositesb.2012.05.007.
  39. Khatir, S., Tiachacht, S., Cuong-Le, T, Quoc Bui, T. and Abdel Wahab, M. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator.", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  40. Khatir, S., Tiachacht, S., Cuong-Le, T., Ghandourah, E., Mirjalili, S. and Abdel Wahab, M. (2021), "An improved Artificial Neural Network using arithmetic optimization algorithm for damage assessment in FGM composite plates", Compos. Struct., 273, 114287. https://doi.org/10.1016/j.compstruct.2021.114.
  41. Kim, D.B. (2019), "An approach for composing predictive models from disparate knowledge sources in smart manufacturing environments", J. Intel. Manuf., 30(4), 1999-2012. https://doi.org/10.1007/s10845-017-1366-7.
  42. Kim, W., Argento, A. and Scott, R.A. (1999), "Free vibration of a rotating tapered composite Timoshenko shaft", J. Sound Vib., 226(1), 125-147. https://doi.org/10.1006/jsvi.1999.2289.
  43. Kumar, H.S.N. and Kattimani, S. (2022), "Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities", Struct. Eng. Mech., 82(4), 477-490. https://doi.org/10.12989/sem.2022.82.4.477.
  44. Lazarus, A., Prabel, B. and Combescure, D. (2010), "A 3D finite element model for the vibration analysis of asymmetric rotating machines", J. Sound Vib., 329(18), 3780-3797. https://doi.org/10.1016/j.jsv.2010.03.029.
  45. Lee, W.J., Xia, K., Denton, N.L., Ribeiro, B. and Sutherland, J.W. (2021), "Development of a speed invariant deep learning model with application to condition monitoring of rotating machinery", J. Intel. Manuf., 32(2), 393-406. https://doi.org/10.1007/s10845-020-01578-x.
  46. Liu, Y., Wang, X., Liu, L., Wu, B. and Yang, Q. (2022), "On the forced vibration of high-order functionally graded nanotubes under the rotation via intelligent modelling", Adv. Nano Res., 13(1), 47-61. https://doi.org/10.12989/anr.2022.13.1.047.
  47. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of FGM beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  48. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097.
  49. Man, Y. (2022), "On the dynamic stability of a composite beam via modified high-order theory", Comput. Concrete, 30(2), 151-164. https://doi.org/10.12989/cac.2022.30.2.151.
  50. Mehdi, H., Upadhyay, R., Mehra, R. and Singhal, A. (2014), "Modal analysis of composite beam reinforced by aluminium-synthetic fibers with and without multiple cracks using ansys", Int. J. Mech. Eng. (IJME), 4(2), 70-80.
  51. Motaghian, S.E., Mofid, M. and Alanjari, P. (2011), "Exact solution to free vibration of beams partially supported by an elastic foundation", Scientia Iranica, 18(4), 861-866. https://doi.org/10.1016/j.scient.2011.07.013.
  52. Mula, S.N., Leite, A.M.S. and Loja, M.A.R. (2022), "Analytical and numerical study of failure in composite plates", Compos. Mater. Eng., 4(1), 23-41. https://doi.org/10.12989/cme.2022.4.1.023.
  53. Osman, M.Y. and Elmardi Suleiman, O.M. (2017), "Free vibration analysis of laminated composite beams using finite element method", Int. J. Eng. Res. Adv. Technol. (IJERAT), 3(2), 5-22. https://doi.org/10.7324/IJERAT.2017.3138.
  54. Pavlenko, I.V., Simonovskiy, V.I. and Demianenko, M.M. (2017), "Dynamic analysis of centrifugal machines rotors supported on ball bearings by combined application of 3D and beam finite element models", IOP Conf. Ser.: Mater. Sci. Eng., 233(1), 012053. https://doi.org/10.1088/1757-899X/233/1/0120532019.
  55. Polat, A. and Kaya, Y. (2022), "Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method", Comput. Concrete, 29(4), 247-253. https://doi.org/10.12989/cac.2022.29.4.247.
  56. Qin, Y., Li, C., Cao, F. and Chen, H. (2020), "A fault dynamic model of high-speed angular contact ball bearings", Mech. Mach. Theory, 143, 103627. https://doi.org/10.1016/j.mechmachtheory.2019.103627.
  57. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2022), "Vibrational behavior of exponentially graded joined conical-conical shells", Steel Compos. Struct., 43(5), 603-623. https://doi.org/10.12989/scs.2022.43.5.603.
  58. Sayyad, A.S. and Ghugal, Y.M. (2017), "Bending, buckling and free vibration of laminated composite and sandwich beams, A critical review of literature", Compos. Struct., 171, 486-504. https://doi.org/10.1016/j.compstruct.2017.03.053.
  59. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam". Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/sss.2020.26.3.361.
  60. Squarcella, N., Firrone, C.M., Allara, M. and Gola, M. (2014), "The importance of the material properties on the burst speed of turbine disks for aeronautical applications", Int. J. Mech. Sci., 84, 73-83. https://doi.org/10.1016/j.ijmecsci.2014.04.007.
  61. Tran, M.T. and Cuong-Le, T. (2022), "A nonlocal IGA numerical solution for free vibration and buckling analysis of porous sigmoid functionally graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  62. Tran, T.M. and Cuong-Le, T. (2022), "A nonlocal iga numerical solution for free vibration and buckling analysis of Porous Sigmoid Functionally Graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  63. Wieczorek, A.N., Konieczny, L., Burdzik, R., Wojnar, G., Filipowicz, K. and Kuczaj, M. (2022), "A complex vibration analysis of a drive system equipped with an innovative prototype of a flexible torsion clutch as an element of pre-implementation testing", Sensor., 22(6), 2183. https://doi.org/10.3390/s22062183.
  64. Wu, X. and Fang, T. (2022), "Intelligent computer modeling of large amplitude behavior of FG inhomogeneous nanotubes", Adv. Nano Res., 12(6), 617-627. https://doi.org/10.12989/anr.2022.12.6.617
  65. Yahea, H.T. and Ibraheem-Majeed, W. (2021), "Free vibration of laminated composite plates in thermal environment using a simple four variable plate theory", Compos. Mater. Eng., 3(3), 179-199. https://doi.org/10.12989/cme.2021.3.3.179.
  66. Yang, Y., Zheng, H., Yin, J., Xu, M. and Chen, Y. (2020), "Refined composite multivariate multiscale symbolic dynamic entropy and its application to fault diagnosis of rotating machine", Measure., 151, 107233. https://doi.org/10.1016/j.measurement.2019.107233.
  67. Yaylaci, M., Abanoz, M., Yaylaci, E.U., Olmez, H., Sekban, D.M. and Birinci, A. (2022), "The contact problem of the functionally graded layer resting on rigid foundation pressed via rigid punch", Steel Compos. Struct., 43(5), 661-672. https://doi.org/10.12989/scs.2022.43.5.661.
  68. Yildirim, S. and Tutuncu, N. (2018), "On the inertio-elastic instability of variable-thickness functionally-graded disks", Mech. Res. Commun., 91, 1-6. https://doi.org/10.1016/j.mechrescom.2018.04.011.
  69. Yildirim, S. and Tutuncu, N. (2019), "Effect of magneto-thermal loads on the rotational instability of heterogeneous rotors", AIAA J., 57(5), 2069-2074. https://doi.org/10.2514/1.J058124.
  70. Zahi, R., Refassi, K. and Habib, A. (2018), "Dynamic calculation of a tapered shaft rotor made of composite material", Adv. Aircraft Spacecraft Sci., 5(1), 51-71. https://doi.org/10.12989/aas.2018.5.1.051.
  71. Zenzen, R., Khatir, S., Belaidi, I., Cuong-Le, T. and Abdel Wahab, M. (2020), "A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures", Compos. Struct., 248, 112497. https://doi.org/10.1016/j.compstruct.2020.112497.
  72. Zhu, F.Y., Lim, H.J., Choi, H. and Yun, G.J. (2022), "A hierarchical micromechanics model for nonlinear behavior with damage of SMC composites with wavy fiber", Compos. Mater. Eng., 4(1), 1-21. https://doi.org/10.12989/cme.2022.4.1.001.