DOI QR코드

DOI QR Code

Superharmonic and subharmonic vibration resonances of rotating stiffened FGM truncated conical shells

  • Hamid Aris (Faculty of Mechanical Engineering, Shahrood University of Technology) ;
  • Habib Ahmadi (Faculty of Mechanical Engineering, Shahrood University of Technology)
  • 투고 : 2022.01.08
  • 심사 : 2023.01.30
  • 발행 : 2023.02.25

초록

In this work, superharmonic and subharmonic resonance of rotating stiffened FGM truncated conical shells exposed to harmonic excitation in a thermal environment is investigated. Utilizing classical shell theory considering Coriolis acceleration and the centrifugal force, the governing equations are extracted. Non-linear model is formulated employing the von Kármán non-linear relations. In this study, to model the stiffener effects the smeared stiffened technique is utilized. The non-linear partial differential equations are discretized into non-linear ordinary differential equations by applying Galerkin's method. The method of multiple scales is utilized to examine the non-linear superharmonic and subharmonic resonances behavior of the conical shells. In this regard, the effects of the rotating speed of the shell on the frequency response plot are investigated. Also, the effects of different semi-vertex angles, force amplitude, volume-fraction index, and temperature variations on the frequency-response graph are examined for different rotating speeds of the stiffened FGM truncated conical shells.

키워드

참고문헌

  1. Ahmadi, H. (2019), "Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation", Eng. Comput., 35(4), 1491-1505. https://doi.org/10.1007/s00366-018-0679-2.
  2. Amabili, M. and Balasubramanian, P. (2020), "Nonlinear vibrations of truncated conical shells considering multiple internal resonances", Nonlin. Dyn., 100(1), 77-93. https://doi.org/10.1007/s11071-020-05507-8.
  3. Anh, V.T.T. and Duc, N.D. (2019), "Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells surrounded by an elastic medium in thermal environments", Acta Mechanica, 230(1), 157-178. https://doi.org/10.1007/s00707-018-2282-4.
  4. Aris, H. and Ahmadi, H. (2020), "Nonlinear vibration analysis of FGM truncated conical shells subjected to harmonic excitation in thermal environment", Mech. Res. Commun., 104, 103499. https://doi.org/10.1016/j.mechrescom.2020.103499.
  5. Aris, H. and Ahmadi, H. (2021), "Combination resonance analysis of imperfect functionally graded conical shell resting on nonlinear viscoelastic foundation in thermal environment under multi-excitation", J. Vib. Control, 28(15-16), 2121-2144. https://doi.org/10.1177/10775463211006527.
  6. Aris, H. and Ahmadi, H. (2021), "Nonlinear forced vibration and resonance analysis of rotating stiffened FGM truncated conical shells in a thermal environment", Mech. Bas. Des. Struct. Mach., 1-25. https://doi.org/10.1080/15397734.2021.1950011.
  7. Bakhtiari, M., Lakis, A.A. and Kerboua, Y. (2020), "Nonlinear vibration of truncated conical shells: Donnell, Sanders and Nemeth theories", Int. J. Nonlin. Sci. Numer. Simul., 21(1), 83-97. https://doi.org/10.1515/ijnsns-2018-0377.
  8. Chai, Q. and Wang, Y.Q. (2021), "A general approach for free vibration analysis of spinning joined conical-cylindrical shells with arbitrary boundary conditions", Thin Wall. Struct., 168, 108243. https://doi.org/10.1016/j.tws.2021.108243.
  9. Chai, Q. and Wang, Y.Q. (2022), "Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion", Eng. Struct., 252, 113718. https://doi.org/10.1016/j.engstruct.2021.113718.
  10. Chen, C. and Dai, L. (2009), "Nonlinear vibration and stability of a rotary truncated conical shell with intercoupling of high and low order modals", Commun. Nonlin. Sci. Numer. Simul., 14(1), 254-269. https://doi.org/10.1016/j.cnsns.2007.06.007.
  11. Civalek, O. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25(1), 127-130. https://doi.org/10.12989/sem.2007.25.1.127.
  12. Das, A. and Karmakar, A. (2018), "Free vibration characteristics of functionally graded pre-twisted conical shells under rotation", J. Inst. Eng. (India): Ser. C, 99(6), 681-692. https://doi.org/10.1007/s40032-017-0378-6.
  13. Das, A., Sarkar, S. and Karmakar, A. (2014), "Free vibration of pre-twisted functionally graded conical shells with rotational effect", Proceedings of ICTACEM 2014 International Conference on Theoretical, Applied, Computational and Experimental Mechanics, IIT Kharagpur, India, December.
  14. Dey, S., Bandopadhyay, T., Karmakar, A. and Kishimoto, K. (2011), "Free vibration of delaminated composite shallow conical shells", J. Solid Mech. Mater. Eng., 5(11), 610-626. https://doi.org/10.1299/jmmp.5.610.
  15. Dey, S., Sarkar, S., Das, A., Karmakar, A. and Adhikari, S. (2015), "Effect of twist and rotation on vibration of functionally graded conical shells", Int. J. Mech. Mater. Des., 11(4), 425-437. https://doi.org/10.1007/s10999-014-9266-x.
  16. Duc, N.D., Seung-Eock, K. and Chan, D.Q. (2018), "Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT", J. Therm. Stress., 41(3), 331-365. https://doi.org/10.1080/01495739.2017.1398623.
  17. Dung, D.V., Anh, L.T.N. and Hoa, L.K. (2018), "Analytical investigation on the free vibration behavior of rotating FGM truncated conical shells reinforced by orthogonal eccentric stiffeners", Mech. Adv. Mater. Struct., 25(1), 32-46. https://doi.org/10.1080/15376494.2016.1255807.
  18. Eyvazian, A., Musharavati, F., Tarlochan, F., Pasharavesh, A., Rajak, D.K., Husain, M.B. and Tran, T.N. (2020), "Free vibration of FG-GPLRC conical panel on elastic foundation", Struct. Eng. Mech., 75(1), 1-18. https://doi.org/10.12989/sem.2020.75.1.001.
  19. Fard, K.M. and Livani, M. (2015), "New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores", Struct. Eng. Mech., 55(4), 719-742. https://doi.org/10.12989/sem.2015.55.4.719.
  20. Fu, Y. and Chen, C. (2001), "Non-linear vibration of elastic truncated conical moderately thick shells in large overall motion", Int. J. Nonlin. Mech., 36(5), 763-771. https://doi.org/10.1016/S0020-7462(00)00042-1.
  21. Gao, K., Gao, W., Wu, B., Wu, D. and Song, C. (2018), "Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales", Thin Wall. Struct., 125, 281-293. https://doi.org/10.1016/j.tws.2017.12.039.
  22. Ghannad, M., Nejad, M.Z., Rahimi, G. and Sabouri, H. (2012), "Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials", Struct. Eng. Mech., 43(1), 105-126. https://doi.org/10.12989/sem.2012.43.1.105.
  23. Hua, L. (2000), "Frequency characteristics of a rotating truncated circular layered conical shell", Compos. Struct., 50(1), 59-68. https://doi.org/10.1016/S0263-8223(00)00080-5.
  24. Irie, T., Yamada, G. and Tanaka, K. (1984), "Natural frequencies of truncated conical shells", J. Sound Vib., 92(3), 447-453. https://doi.org/10.1016/0022-460x(84)90391-2.
  25. Kamaloo, A., Jabbari, M., Tooski, M.Y. and Javadi, M. (2019), "Nonlinear free vibrations analysis of delaminated composite conical shells", Int. J. Struct. Stab. Dyn., 20(01), 2050010. https://doi.org/10.1142/S0219455420500108.
  26. Kerboua, Y., Lakis, A. and Hmila, M. (2010), "Vibration analysis of truncated conical shells subjected to flowing fluid", Appl. Math. Model., 34(3), 791-809. https://doi.org/10.1016/j.apm.2009.06.028.
  27. Lam, K. and Hua, L. (1999), "On free vibration of a rotating truncated circular orthotropic conical shell", Compos. Part B: Eng., 30(2), 135-144. https://doi.org/10.1016/S1359-8368(98)00049-3.
  28. Li, F.M., Kishimoto, K. and Huang, W.H. (2009), "The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method", Mech. Res. Commun., 36(5), 595-602. https://doi.org/10.1016/j.mechrescom.2009.02.003.
  29. Li, H., Lam, K.Y. and Ng, T.Y. (2005), Rotating Shell Dynamics, Elsevier.
  30. Liew, K.M., Ng, T.Y. and Zhao, X. (2005), "Free vibration analysis of conical shells via the element-free kp-Ritz method", J. Sound Vib., 281(3-5), 627-645. https://doi.org/10.1016/j.jsv.2004.01.005.
  31. Malekzadeh, P. and Heydarpour, Y. (2013), "Free vibration analysis of rotating functionally graded truncated conical shells", Compos. Struct., 97, 176-188. https://doi.org/10.1016/j.compstruct.2012.09.047.
  32. Mehri, M., Asadi, H. and Wang, Q. (2016), "Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method", Comput. Meth. Appl. Mech. Eng., 303, 75-100. https://doi.org/10.1016/j.cma.2016.01.017.
  33. Moghaddam, S.M.F. and Ahmadi, H. (2020), "Active vibration control of truncated conical shell under harmonic excitation using piezoelectric actuator", Thin Wall. Struct., 151, 106642. https://doi.org/10.1016/j.tws.2020.106642.
  34. Najafov, A., Sofiyev, A. and Kuruoglu, N. (2014), "On the solution of nonlinear vibration of truncated conical shells covered by functionally graded coatings", Acta Mechanica, 225(2), 563-580. https://doi.org/10.1007/s00707-013-0980-5.
  35. Nayfeh, A.H. and Mook, D.T. (2008), Nonlinear Oscillations, John Wiley & Sons.
  36. Nejati, M., Asanjarani, A., Dimitri, R. and Tornabene, F. (2017), "Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes", Int. J. Mech. Sci., 130, 383-398. https://doi.org/10.1016/j.ijmecsci.2017.06.024.
  37. Nguyen, D.D., Tran, Q.Q. and Do, Q.C. (2018), "Nonlinear dynamic analysis and vibration of shear deformable piezoelectric-FGM truncated conical shell resting on elastic foundations inthermal environments", 2018 Theme Meeting on Multiscale Modelling of Materials for Sustainable Development (ACCMS), Hanoi, Vietnam, September.
  38. Nguyen, P.D., Quang, V.D., Anh, V.T.T. and Duc, N.D. (2019), "Nonlinear vibration of carbon nanotube reinforced composite truncated conical shells in thermal environment", Int. J. Struct. Stab. Dyn., 19(12), 1950158. https://doi.org/10.1142/S021945541950158X.
  39. Niu, Y., Wu, M., Yao, M. and Wu, Q. (2022), "Dynamic instability and internal resonance of rotating pretwisted composite airfoil blades", Chaos Solit. Fract., 165, 112835. https://doi.org/10.1016/j.chaos.2022.112835.
  40. Niu, Y., Yao, M. and Wu, Q. (2022), "Resonance in dangerous mode and chaotic dynamics of a rotating pre-twisted graphene reinforced composite blade with variable thickness", Compos. Struct., 288, 115422. https://doi.org/10.1016/j.compstruct.2022.115422.
  41. Raju, K.K. and Rao, G.V. (1976), "Large amplitude asymmetric vibrations of some thin shells of revolution", J. Sound Vib., 44(3), 327-333. https://doi.org/10.1016/0022-460X(76)90505-8.
  42. Reddy, J. and Chin, C. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165.
  43. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  44. Roh, J.H., Woo, J.H. and Lee, I. (2008), "Thermal post-buckling and vibration analysis of composite conical shell structures using layerwise theory", J. Therm. Stress., 32(1-2), 41-64. https://doi.org/10.1080/01495730802540031.
  45. Rougui, M., Moussaoui, F. and Benamar, R. (2007), "Geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells: A semi-analytical approach", Int. J. Nonlin. Mech., 42(9), 1102-1115. https://doi.org/10.1016/j.ijnonlinmec.2007.06.004.
  46. Shakouri, M. (2019), "Free vibration analysis of functionally graded rotating conical shells in thermal environment", Compos. Part B: Eng., 163, 574-584. https://doi.org/10.1016/j.compositesb.2019.01.007.
  47. Sheng, G. and Wang, X. (2017), "The non-linear vibrations of rotating functionally graded cylindrical shells", Nonlin. Dyn., 87(2), 1095-1109. https://doi.org/10.1007/s11071-016-3100-y.
  48. Singha, T.D., Rout, M., Bandyopadhyay, T. and Karmakar, A. (2020), "Free vibration analysis of rotating pretwisted composite sandwich conical shells with multiple debonding in hygrothermal environment", Eng. Struct., 204, 110058. https://doi.org/10.1016/j.engstruct.2019.110058.
  49. Sofiyev, A. (2012), "The non-linear vibration of FGM truncated conical shells", Compos. Struct., 94(7), 2237-2245. https://doi.org/10.1016/j.compstruct.2012.02.005.
  50. Sofiyev, A. (2014), "The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells", Compos. Part B: Eng., 61, 324-339. https://doi.org/10.1016/j.compositesb.2014.01.047.
  51. Sofiyev, A. (2019), "Review of research on the vibration and buckling of the FGM conical shells", Compos. Struct., 211, 301-317. https://doi.org/10.1016/j.compstruct.2018.12.047.
  52. Sofiyev, A. and Kuruoglu, N. (2015), "Large-amplitude vibration of the geometrically imperfect FGM truncated conical shell", J. Vib. Control, 21(1), 142-156. https://doi.org/10.1177/1077546313480998.
  53. Talebitooti, M. (2013), "Three-dimensional free vibration analysis of rotating laminated conical shells: Layerwise differential quadrature (LW-DQ) method", Arch. Appl. Mech., 83(5), 765-781. https://doi.org/10.1007/s00419-012-0716-3.
  54. Talebitooti, M. (2018), "Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends", Mech. Adv. Mater. Struct., 25(2), 155-165. https://doi.org/10.1080/15376494.2016.1255809.
  55. Talebitooti, M., Daneshjou, K. and Talebitooti, R. (2013), "Vibration and critical speed of orthogonally stiffened rotating FG cylindrical shell under thermo-mechanical loads using differential quadrature method", J. Therm. Stress., 36(2), 160-188. https://doi.org/10.1080/01495739.2013.764807.
  56. Tong, L. (1996), "Effect of axial load on free vibration of orthotropic truncated conical shells". J. Vib. Acoust., 118(2), 164-168. https://doi.org/10.1115/1.2889644.
  57. Torabi, J. and Ansari, R. (2018), "Thermally induced mechanical analysis of temperature-dependent FG-CNTRC conical shells", Struct. Eng. Mech., 68(3), 313-323. https://doi.org/10.12989/sem.2018.68.3.313.
  58. Ueda, T. (1979), "Non-linear free vibrations of conical shells", J. Sound Vib., 64(1), 85-95. https://doi.org/10.1016/0022-460X(79)90574-1.
  59. Vu, T.T.A. and Pham, D.N. (2018), "Investigation on nonlinear dynamic response and free vibration of FG-CNTs reinforced composite truncated conical shells in the thermal environment", 2018 Theme Meeting on Multiscale Modelling of Materials for Sustainable Development (ACCMS), Hanoi, Vietnam, September.
  60. Wang, Y., Ye, C. and Zu, J. (2018), "Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities", Appl. Math. Mech., 39(11), 1587-1604. https://doi.org/10.1007/s10483-018-2388-6.
  61. Wang, Y.Q. (2018), "Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state", Acta Astronautica, 143, 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004.
  62. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  63. Weingarten, V.I. (1965), "Free vibrations of ring-stiffened conical shells", AIAA J., 3(8), 1475-1481. https://doi.org/10.2514/3.3171.
  64. Wu, Q., Yao, M., Li, M., Cao, D. and Bai, B. (2021), "Nonlinear coupling vibrations of graphene composite laminated sheets impacted by particles", Appl. Math. Model., 93, 75-88. https://doi.org/10.1016/j.apm.2020.12.008.
  65. Xu, C., Xia, Z. and Chia, C. (1996), "Non-linear theory and vibration analysis of laminated truncated, thick, conical shells", Int. J. Nonlin. Mech., 31(2), 139-154. https://doi.org/10.1016/0020-7462(95)00051-8.
  66. Xu, H., Wang, Y.Q. and Zhang, Y. (2021), "Free vibration of functionally graded graphene platelet-reinforced porous beams with spinning movement via differential transformation method", Arch. Appl. Mech., 91(12), 4817-4834. https://doi.org/10.1007/s00419-021-02036-7.
  67. Yang, S., Zhang, W., Hao, Y. and Niu, Y. (2019), "Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances", Thin Wall. Struct., 142, 369-391. https://doi.org/10.1016/j.tws.2019.04.024.
  68. Ye, C. and Wang, Y.Q. (2021), "Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: Internal resonances", Nonlin. Dyn., 104(3), 2051-2069. https://doi.org/10.1007/s11071-021-06401-7.