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Nonlinear vibration analysis of fluid-conveying cantilever graphene platelet reinforced pipe

  • Bashar Mahmood Ali (Materials Sciences and Engineering PhD Program, Graduate School of Natural and Applied Sciences, Kastamonu University) ;
  • Mehmet AKKAS (Department of Mechanical Engineering, Faculty of Engineering and Architecture, Kastamonu University) ;
  • Aybaba HANCERLIOGULLARI (Kastamonu University, Faculty of Science Department of physics) ;
  • Nasrin Bohlooli (School of Civil Engineering, Urmia University)
  • Received : 2022.08.23
  • Accepted : 2023.12.27
  • Published : 2024.01.25
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Abstract

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

Keywords

References

  1. Abouelregal, A.E. and Marin, M. (2020), "The size-dependent thermoelastic vibrations of nanobeams subjected to harmonic excitation and rectified sine wave heating", Mathematics, 8 (7), 1128, https://doi.org/10.3390/math8071128.
  2. Ahmed Houari, M.S., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/scs.2018.28.1.013.
  3. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections', Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659.
  4. Arioui, O., Belakhdar, K., Kaci, A. and Tounsi, A. (2018), "Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials", Steel Compos. Struct., 27(6), 777-788. https://doi.org/10.12989/scs.2018.27.6.777.
  5. Bambaeechee, M. (2019), "Free vibration of AFG beams with elastic end restraints", Steel Compos. Struct., 33(3), 403-432. https://doi.org/10.12989/scs.2019.33.3.403.
  6. Barati, M.R. and Zenkour, A.M. (2019), "Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions", Mech. Adv. Mater. Struct., 26(18), 1580-1588. https://doi.org/10.1080/15376494.2018.1444235
  7. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  8. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Reviews, 49(1), 1-28. https://doi.org/10.1115/1.3101882
  9. Cao, J., Zhang, Z., Guo, Y. and Gong, T. (2019), "Inhomogeneous bonding state modeling for vibration analysis of explosive clad pipe", Steel Compos. Struct., 31(3), 233-242. https://doi.org/10.12989/scs.2019.31.3.233.
  10. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin Walled Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025.
  11. Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008.
  12. Chen, X. and Chen, X. (2016), "Effect of local wall thinning on ratcheting behavior of pressurized 900 elbow pipe under reversed bending using finite element analysis", Steel Compos. Struct., An 20(4), 931-950. https://doi.org/10.12989/scs.2016.20.4.931.
  13. Chen, X., Chen, X. and Li, Z. (2019), "Ratcheting boundary of pressurized pipe under reversed bending", Steel Compos. Struct., 32(3), 312-323. https://doi.org/10.12989/scs.2019.32.3.312.
  14. Dai, H.L. and Wang, L. (2015), "Dynamics and stability of magnetically actuated pipes conveying fluid", Int. J. Struct. Stab. Dyn., 16(6), https://doi.org/10.1142/S0219455415500261.
  15. Dai, J., Liu, Y., Liu, H., Miao, C. and Tong, G. (2019), "A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid", Int. J. Mech. Mater. Des., 15, 715-726, https://doi.org/10.1007/s10999-018-09439-5.
  16. Dong, Y., Li, X., Gao, K., Li, Y. and Yang, J. (2019), "Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment", Nonlinear Dyn., 99, 981-1000. https://doi.org/10.1007/s11071-019-05297-8.
  17. Eftekhari, M. and Hosseini, M. (2016), "On the stability of spinning functionally graded cantilevered pipes subjected to fluidthermomechanical loading", Int. J. Struct. Stab. Dyn., 16(9), https://doi.org/10.1142/S0219455415500625.
  18. Elishakoff, I. (2005), "Controversy associated with the socalled, follower forces, Critical overview", Appl. Mech. Rev., 58(2), 117-142. https://doi.org/10.1115/1.1849170.
  19. Elishakoff, I. and Impollonia, N. (2001), "Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid", J. Appl. Mech., 68(2), 206-212. https://doi.org/10.1115/1.1354206.
  20. Fakhar, M.H., Fakhar, A. and Tabatabaei, H. (2019), "Analysis of critical fluid velocity and heat transfer in temperature-dependent nanocomposite pipes conveying nanofluid subjected to heat generation, conduction, convection and magnetic field", Steel Compos. Struct., 30(3), 281-292. https://doi.org/10.12989/scs.2019.30.3.281.
  21. Hadji, L. and Bernard, F. (2020), "Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation", Adv. Mater. Res., 9(1), 63-98. https://doi.org/10.12989/amr.2020.9.1.063.
  22. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507.
  23. Hellum, A.M., Mukherjee, R. and Hull, A.J. (2010), "Dynamics of pipes conveying fluid with turbulent and laminar velocity profiles", J. Fluids Struct., 26(5), 804-813. https://doi.org/10.1016/j.jfluidstructs.2010.05.001
  24. Ibrahim, R.A. (2010), "Overview of mechanics of pipes conveying fluids-Part I: fundamental studies", J. Pressure Vessel Technol., 132(3), 1-32. https://doi.org/10.1115/1.4001271
  25. Kamil Zur, K. and Jankowski, P. (2019), "Multiparametric analytical solution for the eigenvalue problem of FGM porous circular plates", Symmetry, 11(429), 1-24. https://doi.org/10.3390/sym11030429.
  26. Khoshroo, M. and Eftekhari, M. (2021), "Nonlinear behaviors of spinning pipes conveying fluid with pulsation", Int. J. Struct. Stab. Dyn., 21(4), https://doi.org/10.1142/S0219455421500504.
  27. Lai, B., Richard, J.Y. and Xiong, M. (2019), "Experimental and analytical investigation of composite columns made of high strength steel and high strength concrete", Steel Compos. Struct., 33(1), 67-79. https://doi.org/10.12989/scs.2019.33.1.067.
  28. Liang, F., Gao, A. and Yang, X.D. (2020), "Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans", Appl. Math. Model., 83, 454-469, https://doi.org/10.1016/j.apm.2020.03.011.
  29. Li, L., Li, X. and Hu, Y. (2018), "Nonlinear bending of a two-dimensionally functionally graded beam", Compos. Struct., 184, 1049-1061. https://doi.org/10.1016/j.compstruct.2017.10.087.
  30. Li, Q., Liu, W., Zhang, Z. and Yue, Z. (2018), "Parametric resonance of pipes with soft and hard segments conveying pulsating fluids", Int. J. Struct. Stab. Dyn., 18(10), https://doi.org/10.1142/S0219455418501195.
  31. Li, X., Zhou, X., Liu J. and Wang, X. (2019), "Shear behavior of short square tubed steel reinforced concrete columns with high-strength concrete", Steel Compos. Struct., 32(3), 411-422. https://doi.org/10.12989/scs.2019.32.3.411.
  32. Li, Z.Y., Wang, J.J. and Qiu, M.X. (2016), "Dynamic characteristics of fluid-conveying pipes with piecewise linear support", Int. J. Struct. Stab. Dyn., 16(6), https://doi.org/10.1142/S021945541550025X.
  33. Lin, J., Li, J., Guan, Y., Zhao, G., Naceur, H. and Coutellier, D. (2018), "Geometrically nonlinear bending analysis of functionally graded beam with variable thickness by a meshless method", Compos. Struct., 189, 239-246. https://doi.org/10.1016/j.compstruct.2018.01.063.
  34. Lopes, J.L., Paidoussis, M.P. and Semler, C. (2002), "Linear and nonlinear dynamics of cantilevered cylinders in axial flow-part II: the equations of motion", J. Fluids Struct., 16(6), 715-737. https://doi.org/10.1006/jfls.2002.0448
  35. Marin, M. and Florea, O. (2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", St. Univ. Ovidius Constanta, 22(1), 169-188. https://doi.org/ 10.2478/auom-2014-0014.
  36. Mechab, I., Meiche, N.E. and Bernard, F. (2016), "Free vibration analysis of higher-order shear elasticity nanocomposite beams with consideration of nonlocal elasticity and poisson effect", J. Nanomech. Micromech., 6(3), 1-13. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000110.
  37. 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.2017.25.4.415.
  38. Nayfeh, A.H. and Mook, D.T. (2008), Nonlinear Oscillations", John Wiley & Sons.
  39. 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.
  40. Nguyen, X.H., Le, D.D. and Nguyen, Q.H. (2019), "Static behavior of novel RCS through-column-type joint: Experimental and numerical study", Steel Compos. Struct., 32(1), 111-126. https://doi.org/10.12989/scs.2019.32.1.111.
  41. Nguyen, D.K., Nguyen, K.V., Gan, B.S. and Alexandrov, S. (2018), "Nonlinear bending of elastoplastic functionally graded ceramicmetal beams subjected to nonuniform distributed loads", Appl. Math. Comput., 333, 443-459, https://doi.org/10.1016/j.amc.2018.03.100.
  42. Ni, Q., Zhang, Z.L. and Wang, L. (2011), "Application of the differential transformation method to vibration analysis of pipes conveying fluid", Appl. Math. Comput., 217, 7028-7038. https://doi.org/10.1016/j.amc.2011.01.116
  43. Paidoussis, M.P. (1998), "Fluid-structure interactions: slender structures and axial flow", 1, Elsevier Academic Press, London, UK.
  44. Paidoussis, M.P. and Li, G.L. (1993), "Pipes conveying fluid: a dynamical model problem", J. Fluids Struct., 7(2), 137-204. https://doi.org/10.1006/jfls.1993.1011
  45. Paidoussis, M.P. (2008), "The canonical problem of the fluidconveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics", J. Sound. Vib., 310(3), 462-492. https://doi.org/10.1016/j.jsv.2007.03.065.
  46. Parthasarathy, J., Starly, B. and Raman, S. (2011), "A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications", J. Manufact. Process., 13(2), 160-170, https://doi.org/10.1016/j.jmapro.2011.01.004.
  47. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  48. Pigolotti, L., Mannini, C. and Bartoli, G. (2017), "Destabilizing effect of damping on the post-critical flutter oscillations of flat plates", Meccanica, 52(13), 3149-3164, https://doi.org/10.1007/s11012-016-0604-y.
  49. Rafiee, R., Fakoor, M. and Hesamsadat, H. (2015), "The influence of production inconsistencies on the functional failure of GRP pipes", Steel Compos. Struct., 19(6), 1369-1379. https://doi.org/10.12989/scs.2015.19.6.1369.
  50. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano, 3(12), 3884-3890. https://doi.org/10.1021/nn9010472
  51. Rossikhin, Y.A. and Shitikova, M.V. (2012), "On fallacies in the decision between the Caputo and Riemann-Liouville fractional derivatives for the analysis of the dynamic response of a nonlinear viscoelastic oscillator", Mech. Res. Commun., 45, 22-27. https://doi.org/10.1016/j.mechrescom.2012.07.001
  52. Rumeng, L. and Wang, Lifeng (2016), "Thermal vibration of a doublelayered graphene sheet with initial stress at low temperature", Chinese Science Bull., 62(4), 245-253. https://doi.org/10.1360/N972016-00927.
  53. Saffari, P.R., Fakhraie, M. and Roudbari, M.A. (2020), "Nonlinear vibration of fluid conveying cantilever nanotube resting on viscopasternak foundation using non-local strain gradient theory", Micro Nano Lett., 15(3), 183-188. https://doi.org/10.1186/s11671-020-03415-9
  54. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082.
  55. Shafiei, H. and Setoodeh, A.R. (2017), "Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation", Steel Compos. Struct., 24(1), 65-77. https://doi.org/10.12989/scs.2017.24.1.065.
  56. Sharma, K. and Marin, M. (2013), "Effect of distinct conductive a thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space", Sci. Bull. Series A Appl. Mathem. Phys., 75(2), 121-132.
  57. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623, https://doi.org/10.1016/j.compstruct.2018.07.063.
  58. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  59. Shu, C. and Wang, C. (1999), "Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates", Eng. Struct., 21(2), 125-134. https://doi.org/10.1016/S0141-0296(97)00155-7
  60. Sugiyama, Y., Kumagai, Y., Kishi, T. and Kawagoe, H. (1986), "Studies on stability of pipes conveying fluid (the effect of a lumped mass and damping)", Bull JSME, 29(249), 929-934, https://doi.org/10.1299/jsme1958.29.929.
  61. Sugiyama, Y., Tanaka, Y., Kishi, T. and Kawagoe, H. (1985), "Effect of a spring support on the stability of pipes conveying fluid", J. Sound Vib., 100(2), 257-270, https://doi.org/10.1016/0022-460X(85)90419-5.
  62. Sun, X., Yan, H. and Dai, H. (2020), "Stability and dynamic evolution of sliding fluid-transporting pipes in three-dimensional sense", Int. J. Struct. Stab. Dyn., 20(3), https://doi.org/10.1142/S0219455420500364.
  63. Tahouneh, V., Naei, M.H. and Mosavi Mashhadi, M. (2019), "Using IGA and trimming approaches for vibrational analysis of L-shape graphene sheets via nonlocal elasticity theory", Steel Compos. Struct., 33(5), 717-727. https://doi.org/10.12989/scs.2019.33.5.717.
  64. Tahouneh, V., Naei, M.H. and Mosavi Mashhadi, M. (2020), "Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches", Steel Compos. Struct., 34(2), 261-277. https://doi.org/10.12989/scs.2020.34.2.261.
  65. Tahouneh, V., Mosavi Mashhadi, M. and Naei, M.H. (2016), "Finite element and micromechanical modeling for investigating effective material properties of polymer-matrix nanocomposites with microfiber, reinforced by CNT arrays", IJASE, 8(3), 297-306, http://doi.org/10.1007/s40091-016-0132-y.
  66. Tahouneh, V. (2018), "Vibrational analysis of sandwich sectorial plates with functionally graded sheets reinforced by aggregated carbon nanotube", J. Sandw. Struct. Mater., 22(5), 1496-1541, https://doi.org/10.1177/1099636218785972.
  67. Tahouneh, V., Naei, M.H. and Mashhadi, M.M. (2018), "The effects of temperature and vacancy defect on the severity of the SLGS becoming anisotropic", Steel Compos. Struct., 29(5), 647-657, https://doi.org/10.12989/scs.2018.29.5.647.
  68. Tahouneh, V. (2018), "Vibration analysis of sandwich sectorial plates considering FG wavy CNT-reinforced face sheets", Steel Compos. Struct., 28(5), 541-557, https://doi.org/10.12989/scs.2018.28.5.541.
  69. Tang, Y., Yang, T. and Fang, B. (2018), "Fractional dynamics of fluidconveying pipes made of polymer-like materials", Acta Mech. Solida Sin., 31(2), 243-258. 2018. https://doi.org/10.1007/s10338-018-0007-9
  70. Tornabene, F., Bacciocchi, M., Fantuzzi, N. and Reddy, J.N. (2018), "Multiscale approach for three-phase CNT/polymer/fiber laminated nanocomposite structures", Polymer Compos., https://doi.org/10.1002/pc.24520.
  71. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater., 21(1), 320-365. https://doi.org/10.1177/1099636217693623.
  72. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2019), "Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis", Eng. Anal. Bound. Elem., 100, 24-47. https://doi.org/10.1016/j.enganabound.2017.07.029.
  73. Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E. (2015), "Strong formulation finite element method based on differential quadrature: A survey", Appl. Mech. Rev., 67(2), 1-55. https://doi.org/10.1115/1.4028859.
  74. Wang, L. and Hu, H. (2014a), "Thermal vibration of single-walled carbon nanotubes with quantum effects", Proc. R. Soc. A., 470. http://dx.doi.org/10.1098/rspa.2014.0087.
  75. Wang, L. and Hu, H. (2014b), "Thermal vibration of a rectangular single-layered graphene sheet with quantum effects", J. Appl. Phy., 115(23), https://doi.org/10.1063/1.4885015.
  76. Wang, L. and Hu, H. (2015), "Thermal vibration of a circular single-layered graphene sheet with simply supported or clamped boundary" J. Sound Vib., 349, 206-215. https://doi.org/10.1016/j.jsv.2015.03.045.
  77. Wang, Q. (2002), "On buckling of column structures with a pair of piezoelectric layers", Eng. Struct., 24, 199-205. https://doi.org/10.1016/S0141-0296(01)00088-8
  78. Wang, L. and Ni, Q. (2008), "Large-amplitude free vibrations of fluid-conveying pipes on a pasternak foundation", Int. J. Struct. Stab. Dyn., 8(4), 615-626, https://doi.org/10.1142/S0219455408002843.
  79. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM", Steel Compos. Struct., 17(5), 753-776. https://doi.org/10.12989/scs.2014.17.5.753.
  80. Yang, T., Tang, Y., Li, Q. and Yang, X.D. (2018), "Nonlinear bending, buckling and vibration of bi-directional functionally graded nanobeams", Compos. Struct., 204, 313-319. https://doi.org/10.1016/j.compstruct.2018.07.045.
  81. Zhang, L., Bhatti, M.M., Michaelides, E.E., Marin, M. and Ellahi, R. (2022), "Hybrid nanofluid flow towards an elastic surface with tantalum and nickel nanoparticles, under the influence of an induced magnetic field", Eur. Phys. J. Spec. Top., 231(3), 521-533, https://doi.org/10.1140/epjs/s11734-021-00409-1.
  82. Zahrai, S.M., Mirghaderi, S.R. and Saleh, A. (2017), "Increasing plastic hinge length using two pipes in a proposed web reduced beam section, an experimental and numerical study", Steel Compos. Struct., 23(4), 421-433. https://doi.org/10.12989/scs.2017.23.4.421.
  83. Zhou, X.W., Dai, H.L. and Wang, L. (2018), "Dynamics of axially functionally graded cantilevered pipes conveying fluid", Compos. Struct., 190, 112-118, https://doi.org/10.1016/j.compstruct.2018.01.097.
  84. Zhou, Z.G., Wu, L.Z. and Du, S.Y. (2006), "Non-local theory solution for a Mode I crack in piezoelectric materials", Eur. J. Mech. A/Solids, 25(5), 793-807. https://doi.org/10.1016/j.euromechsol.2005.10.003.