Structural Engineering and Mechanics

  • 제86권3호
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  • Pages.361-371
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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

Nonlinear resonance of axially moving GPLRMF plates with different boundary conditions

  • Jin-Peng Song (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • 투고 : 2022.12.13
  • 심사 : 2023.03.27
  • 발행 : 2023.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

키워드

참고문헌

  1. Abolhassanpour, H. Ghasemi, F.A., Shahgholi, M. and Mohamadi, A. (2021), "Stability and vibration analysis of an axially moving thinwalled conical shell", J Vib Control, 28(13-14), 1655-1672. http://doi.org/10.1177/1077546321997600. 
  2. Abouelregal, A.E. and Sedighi, H.M. (2022), "Thermoelastic characteristics of moving viscoelastic nanobeams based on the nonlocal couple stress theory and dual-phase lag model", Phys Scripta, 97(11), 114003. http://doi.org/10.1088/1402-4896/ac97cc. 
  3. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. http://doi.org/10.1177/1077546320947302 . 
  4. Alnujaie, A., Akba, E.D., Eltaher, M. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. http://doi.org/10.12989/gae.2021.24.1.091. 
  5. Anvari, M., Mohammadimehr, M. and Amiri, A.(2020), "Vibration behavior of a micro cylindrical sandwich panel reinforced by graphene platelet", J. Vib. Control, 26(13-14), 1311-1343. http://doi.org/10.1177/1077546319892730. 
  6. Arani, A.G., Shahraki, M.E. and Haghparast, E. (2022), "Instability analysis of axially moving sandwich plates with a magnetorheological elastomer core and GNP-reinforced face sheets", J. Brazil. Soc. Mech. Sci. Eng., 44, 150. https://doi.org/10.1007/s40430-022-03446-6. 
  7. Babaei, H. (2022a), "Nonlinear analysis of size‑dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory", Eng. Struct., 38(Suppl 3), S1717-S1734. https://doi.org/10.1007/s00366-021-01317-7. 
  8. Babaei, H. (2022b), "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation", Appl. Math. Comput., 413, 126606. https://doi.org/10.1016/j.amc.2021.126606. 
  9. Baghbadorani, A.A. and Kiani,Y. (2021), "Free vibration analysis of functionally graded cylindrical shells reinforced with graphene platelets", Compos. Struct., 276, 114546. http://doi.org/10.1016/j.compstruct.2021.114546. 
  10. Barati, M.R. and Shahverdi, H. (2018), "A general nonlocal stressstrain gradient theory for forced vibration analysis of heterogeneous nanoporous plates", Eur. J. Mech. A-Solid., 67, 215-230. https://doi.org/10.1016/j.euromechsol.2017.09.001. 
  11. Chen, S.H. and Cheung, Y.K. (1996), "A modified lindstedtpoincare method for a strongly nonlinear system with quadratic and cubic nonlinearities", Shock Vib., 3(4), 279-285. https://doi.org/10.1155/1996/231241. 
  12. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus, 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0. 
  13. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641. 
  14. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://doi.org/10.12989/sem.2021.80.1.063. 
  15. Ding, H.X. and She, G.L. (2023), "Nonlinear resonance of axially moving graphene platelet reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civil Mech. Eng., 23, 97. http://doi.org/10.1007/s43452-023-00634-6. 
  16. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1. 
  17. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433. 
  18. Duan, J., Zhang, D. and Wang, W. (2019), "Flutter and divergence instability of axially-moving nanoplates resting on a viscoelastic foundation", Appl. Sci., 9, 1097. https://doi.org/10.3390/app9061097. 
  19. Eghbali, M. and Hosseini, S.A. (2022), "Influences of magnetic environment and two moving loads on lateral and axial displacement of sandwich graphene-reinforced copper-based composite beams with soft porous core", J. Vib. Control, 10775463221135030. https://doi.org/10.1177/10775463221135030. 
  20. Esmaeili, H.R., Kiani, Y. and Beni, Y.T. (2022a), "Vibration characteristics of composite doubly curved shells reinforced with graphene platelets with arbitrary edge supports", Acta Mechanica, 233(2), 665-683. http://doi.org/10.1007/s00707-021-03140-z 
  21. Esmaeili, H.R., Kiani, Y. and Beni, Y.T. (2022b), "Vibration characteristics of composite doubly curved shells reinforced with graphene platelets with arbitrary edge supports", Acta Mechanica, 233(2), 665-683. http://doi.org/10.1007/s00707-021-03140-z 
  22. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541. 
  23. Gan, L.L., Xu, J.Q. and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Structural Engineering and Mechanics, 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645. 
  24. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051. 
  25. Hamidi, B.A., Hosseini, S.A., Hayati, H. and Hassannejad, R. (2020), "Forced axial vibration of micro and nanobeam under axial harmonic moving and constant distributed forces via nonlocal strain gradient theory", Mech. Bas. Des. Struct. Mach., 50(5), 1491-1505. http://doi.org/10.1080/15397734.2020.1744003. 
  26. Hao, Y. and Gao, M.L. (2019), "Traverse vibration of axially moving laminated sma beam considering random perturbation", Shock Vib, 2019, Article ID 6341289. http://doi.org/10.1155/2019/6341289. 
  27. Hao, Y., Dai, H.L., Qiao, N., Zhou, K. and Wang, L. (2020), "Dynamics and stability analysis of an axially moving beam in axial flow", J Mech Mater Struct, 15(1), 37-60. http://doi.org/10.2140/jomms.2020.15.37. 
  28. Hao, Y., Gao, M. and Gong, J.J. (2022), "Parametric random vibration analysis of an axially moving laminated shape memory alloy beam based on monte carlo simulation", Mater., 15(2), 562. http://doi.org/10.3390/ma15020562. 
  29. Jalaei, M.H. and Civalek, Ӧ. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013. 
  30. Li, H., Lang, T. and Liu, Y. (2019), "Nonlinear vibrations and stability of an axially moving plate immersed in fluid", Acta Mechanica Solida Sinica, 32, 737-753. https://doi.org/10.1007/s10338-019-00111-9. 
  31. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B. (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel. Compos, Struct., 46(5) 649-658. https://doi.org/10.12989/scs.2023.46.5.649. 
  32. Liu, Y. (2022), "Nonlinear dynamic analysis of an axially moving composite laminated cantilever beam", J. Vib. Eng. Technol., 1-13. http://doi.org/10.1007/s42417-022-00750-2. 
  33. Lotfan, S., Anamagh, M.R. and Bediz, B. (2021), "A general higher-order model for vibration analysis of axially moving doubly-curved panels/shells", Thin Wall Struct., 146, 107813. http://doi.org/10.1016/j.tws.2021.107813. 
  34. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021. 
  35. Lu, S.F., Xue, N., Zhang, W., Song, X.J. and Ma, W.S. (2021), "Dynamic stability of axially moving graphene reinforced laminated composite plate under constant and varied velocities", Thin Wall. Struct., 167, 108176. https://doi.org/10.1016/j.tws.2021.108176. 
  36. Ma, R. and Jin, Q. (2022), "Stability of functionally graded graphene-reinforced composite laminated thick plates in thermal environment", Acta Mechanica, 233, 3977-3996. https://doi.org/10.1007/s00707-022-03300-9. 
  37. Malikan, M. and Eremeyev, V.A. (2020), "A new hyperbolicpolynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition", Compos. Struct., 249, 112486. https://doi.org/10.1016/j.compstruct.2020.112486. 
  38. Malikan, M., Wiczenbach, T. and Eremeyev, V. A. (2021), "Thermal buckling of functionally graded piezomagnetic microand nanobeams presenting the flexomagnetic effect", Continuum Mech. Thermodyn., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8. 
  39. Marynowski, K. (2020), "Fractional rheological model of a metal alloy in the study vibrations of an axially moving aluminum beam in thermal environment", Int. J. Mech. Sci., 174, 105458. http://doi.org/10.1016/j.ijmecsci.2020.105458. 
  40. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math., 10, 583. https://doi.org/10.3390/math10040583. 
  41. Mohamadi, A., Shahgholi, M. and Ghasemi, F.A. (2021), "Nonlinear dynamic and bifurcations analysis of an axially moving circular cylindrical nanocomposite shell", Int. J. Mech. Mater. Des., 18(1), 125-154. http://doi.org/10.1007/s10999-021-09571-9. 
  42. Mostafa, E. and Mehran, K. (2019), "Numerical investigation into dynamic behaviors of axially moving functionally graded porous sandwich nanoplates reinforced with graphene platelets", Mater. Res. Expr., 6(10), 1050b7. https://doi.org/10.1088/2053-1591/ab407b. 
  43. Pieber, M., Ntarladima, K., Winkler, R. and Gerstmayr, J. (2022), "A hybrid arbitrary lagrangian eulerian formulation for the investigation of the stability of pipes conveying fluid and axially moving beams", J. Comput. Nonlin. Dyn., 17(5), 051006. http://doi.org/10.1115/1.4053505. 
  44. Qiao, Y. and Yao, G. (2022), "Stability and nonlinear vibration of an axially moving plate interacting with magnetic field and subsonic airflow in a narrow gap", Nonlin. Dyn., 110, 3187-3208. https://doi.org/10.1007/s11071-022-07805-9. 
  45. Raj, S.K., Sahoo, B., Nayak, A.R. and Panda, L.N. (2022), "Parametrically excited axially accelerating viscoelastic beam subjected to time-varying axial speed, longitudinally varying axial tension and internal resonance", Int. J. Nonlin. Mech., 147, 104217. http://doi.org/10.1016/j.ijnonlinmec.2022.104213. 
  46. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2021), "Semi-analytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells", Thin Wall. Struct., 159, 107272. https://doi.org/10.1016/j.tws.2020.107272. 
  47. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323. 
  48. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mechanica Sinica, 39, 522392. https://doi.org/10.1007/s10409-022-22392-x. 
  49. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615. 
  50. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225. 
  51. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407. 
  52. Song, M.T., Sritawat, K. and Yang, J. (2017), "Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Struct., 159, 579-588. https://doi.org/10.1016/j.compstruct.2016.09.070. 
  53. Vahidi, H., Shahgholi, M., Hanzaki, A.R. and Mohamadi, A. (2022), "Nonlinear vibration, stability, and bifurcation of rotating axially moving conical shells", Acta Mechanica, 233(8), 3175-3196. http://doi.org/10.1007/s00707-022-03255-x. 
  54. Wang, Y.Q., Wu, H., Yang, F.L. and Wang, Q. (2021), "An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid", Appl. Math. Mech., 42(2), 291-308. http://doi.org/10.1007/s10483-021-2701-5. 
  55. Wang, Y.Q., Ye, C. and Zu, J.W. (2018), "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. 
  56. 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, 4817-4834. https://doi.org/10.1007/s00419-021-02036-7. 
  57. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329. 
  58. Yang, F.L., Wang, Y.Q. and Liu, Y.F. (2022), "Low-velocity impact response of axially moving functionally graded graphene platelet reinforced metal foam plates", Aerosp. Sci. Technol., 123, 107496. https://doi.org/10.1016/j.ast.2022.107496. 
  59. Yao, G. and Zhang, Y.M. (2016a), "Dynamics and stability of an axially moving plate interacting with surrounding airflow", Meccanica, 51, 2111-2119. https://doi.org/10.1007/s11012-016-0365-7. 
  60. Yao, G., Xie, Z.B., Zhu, L.S. and Zhang, Y.M. (2021), "Nonlinear vibrations of an axially moving plate in aero-thermal environment", Nonlin. Dyn., 105, 2921-2933. https://doi.org/10.1007/s11071-021-06807-3. 
  61. Yao, G., Zhang, Y.M. and Li, C.Y. (2016b), "Stability analysis and vibration characteristics of an axially moving plate in aero- thermal environment", Acta Mechanica, 227, 3517-3527.https://doi.org/10.1007/s00707-016-1674-6. 
  62. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos, Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397. 
  63. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlin. Dyn., 111(7), 6317-6334.https://doi.org/10.1007/s11071-022-08186-9. 
  64. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2023.2180556. 
  65. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042.https://doi.org/10.1080/01495739.2022.2125137. 
  66. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133. 
  67. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887. 
  68. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615. 
  69. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293. 
  70. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797. 
  71. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b),"Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://10.12989/anr.2022.13.5.465. 
  72. Zhao, X., Wang, C.F., Zhu, W.D., Li, Y.H. and Wan, X.S. (2021), "Coupled thermoelastic nonlocal forced vibration of an axially moving micro/nano-beam", Int. J. Mech. Sci., 206, 106600.http://doi.org/10.1016/j.ijmecsci.2021.106600. 
  73. Zhou, Y.F. and Wang, Z.M. (2019), "Dynamic instability of axially moving viscoelastic plate", Eur J Mech A-Solid, 73, 1-10. https://doi.org/10.1016/j.euromechsol.2018.06.009. 
  74. Zhu, C.X., Yan, J.W., Wang, P.Y. and Li, C. (2021), "A nonlocal strain gradient approach for out-of-plane vibration of axially moving functionally graded nanoplates in a hygrothermal environment", Shock Vib., 2021, Article ID 8332125. https://doi.org/10.1155/2021/8332125.