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Vibration analysis of double-bonded micro sandwich cylindrical shells under multi-physical loadings

  • Yazdani, Raziye (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2019.02.07
  • Accepted : 2019.09.29
  • Published : 2019.10.10

Abstract

In the present study, vibration analysis of double bonded micro sandwich cylindrical shells with saturated porous core and carbon/boron nitride nanotubes (CNT/BNNT) reinforced composite face sheets under multi-physical loadings based on Cooper-Naghdi theory is investigated. The material properties of the micro structure are assumed to be temperature dependent, and each of the micro-tubes is placed on the Pasternak elastic foundations, and mechanical, moisture, thermal, electrical, and magnetic forces are effective on the structural behavior. The distributions of porous materials in three distributions such as non-linear non-symmetric, nonlinear-symmetric, and uniform are considered. The relationship including electro-magneto-hydro-thermo-mechanical loadings based on modified couple stress theory is obtained and moreover the governing equations of motion using the energy method and the Hamilton's principle are derived. Also, Navier's type solution is also used to solve the governing equations of motion. The effects of various parameters such as material length scale parameter, temperature change, various distributions of nanotube, volume fraction of nanotubes, porosity and Skempton coefficients, and geometric parameters on the natural frequency of double bonded micro sandwich cylindrical shells are investigated. Increasing the porosity and the Skempton coefficients of the core in micro sandwich cylindrical shell lead to increase the natural frequency of the structure. Cylindrical shells and porous materials in the industry of filters and separators, heat exchangers and coolers are widely used and are generally accepted today.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Alashti, R.A. and Khorsand, M. (2012), "Three-dimensional dynamo-thermo-elastic of a functionally graded cylindrical shell with piezoelectric layers by DQ-FD coupled", Int. J. Press. Vessels Pip., 96, 49-67. https://doi.org/10.1016/j.ijpvp.2012.06.006
  2. Arani, A.G., Mohammadimehr, M., Saidi, A.R., Shogaei, S. and Arefmanesh, A. (2011), "Thermal buckling analysis of doublewalled carbon nanotubes considering the small-scale length effect", Proc. IMechE, PartC, Journal of Mechanical Engineering Science, 225, 248-256. https://doi.org/10.1177/09544062JMES1975
  3. Arani, A.G., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magnetothermo-electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5
  4. Arani, A.G., Haghparast, E., Maraghi, Z.K. and Amir, S. (2015), "Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields", Compos. Part B, 68, 136-145. https://doi.org/10.1016/j.compositesb.2014.08.036
  5. Arani, A.G., Arani, H.K. and Maraghi, Z.K. (2016), "Vibration analysis of sandwich composite micro-plate under electromagneto-mechanical loadings", Appl. Math. Model., 40, 10596-10615. https://doi.org/10.1016/j.apm.2016.07.033
  6. Bahadori, R. and Najafizadeh, M.M. (2015), "Free vibration of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler-Pasternak elastic foundation by first-order shear deformation theory and using Navier differential quadrature solution methods", Appl. Math. Model., 39, 4877-4894. https://doi.org/10.1016/j.apm.2015.04.012
  7. Barati, M.R. and Zenkour, A. (2017), "A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate", Compos. Struct., 168, 885-892. https://doi.org/10.1016/j.compstruct.2017.02.090
  8. Barati, M.R. and Zenkour, A.M. (2018), "Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions", J. Vib. Control, 24(10), 1910-1926. https://doi.org/10.1177/1077546316672788
  9. Barati, M.R., Sadr, M.H. and Zenkour, A.M. (2016), "Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation", Int. J. Mech. Sci., 117, 309-320. https://doi.org/10.1016/j.ijmecsci.2016.09.012
  10. Barati, M.R., Shahverdi, H. and Zenkour, A.M. (2017), "Electromechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory", Mech. Adv. Mater. Struct., 24(12), 987-998. https://doi.org/10.1080/15376494.2016.1196799
  11. Beni, Y.T., Mehralian, F. and Razavi, H. (2015), "Free vibration analysis of size-dependent shear deformation functionally graded cylindrical shell on the basis of modified couple stress theory", Compos. Struct., 120, 65-78. https://doi.org/10.1016/j.compstruct.2014.09.065
  12. Dey, T. and Ramachandra, L.S. (2016), "Non-linear vibration analysis of laminated composite circular cylindrical shells", Compos. Struct., 163, 89-100. https://doi.org/10.1016/j.compstruct.2016.12.018
  13. Do, Q.C., Pham, D.N., Vu, D.Q., Vu, T.T.A. and Nguyen, D.D. (2019), "Nonlinear buckling and post-buckling of functionally graded carbon nanotubes reinforced composite truncated conical shells subjected to axial load", Steel Compos. Struct., Int. J., 31(3), 243-259. https://doi.org/10.12989/scs.2019.31.3.243
  14. Duc, N.D. (2014), "Nonlinear static and dynamic stability of functionally graded plates and shells", Vietnam National University Press, Hanoi, Vietnam.
  15. Duc, N.D., Cong, P.H., Anh, V.M., Quang, V.D., Tran, P., Tuan, N.D. and Thinh, N.H. (2015a), "Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment", Compos. Struct., 132, 597-609. https://doi.org/10.1016/j.compstruct.2015.05.072
  16. Duc, N.D., Tuan, N.D., Tran, P., Dao, N.T. and Dat, N.T. (2015b), "Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments", Int. J. Mech. Sci., 101-102, 338-348. https://doi.org/10.1016/j.ijmecsci.2015.08.018
  17. Duc, N.D., Bich, D.H. and Cong, P.H. (2016), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Thermal Stress., 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194
  18. Duc, N.D., Lee, J., Nguyen-Thoi, T. and Thang, P.T. (2017), "Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations", J. Aerosp. Sci. Technol., 68, 391-402. https://doi.org/10.1016/j.ast.2017.05.032
  19. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibrationof magneto-electro-elastic nanoplate", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039
  20. Frostig, Y., Birman, V. and Kardomateas, G.A. (2018), "Non-linear wrinkling of a sandwich panel with functionally graded core -Extended high-order approach", Int. J. Solids Struct., 148-149, 122-139. https://doi.org/10.1016/j.ijsolstr.2018.02.023
  21. Ghorbanpour Arani, A., Amir, S., Shajari, A.R., Mozdianfard, M.R., Khoddami Maraghi, Z. and Mohammadimehr, M. (2012a), "Electro-thermal non-local vibration analysis of embedded DWBNNTs", Proc. IMechE, PartC: Journal of Mechanical Engineering Science, 226, 1410-1422. https://doi.org/10.1177/0954406211422619
  22. Ghorbanpour Arani, A., Rabbani, H., Amir, S., Khoddami Maraghi, Z., Mohammadimehr, M. and Haghparast, E. (2012b), "Analysis of nonlinear vibrations for multi-walled carbon nanotubes embedded in an elastic medium", J. Solid Mech., 3(3), 258-270.
  23. Jabbari, M., Joubaneh, E.F., Khorshidvand, A.R. and Eslami, M.R. (2013), "Buckling analysis of porous circular plate with piezoelectric actuator layers under uniform radial compression", Int. J. Mech. Sci., 70, 50-56. https://doi.org/10.1016/j.ijmecsci.2013.01.031
  24. Ke, L.L., Liu, C. and Wang, Y.S. (2015), "Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions", Physica E, 66, 93-106. https://doi.org/10.1016/j.physe.2014.10.002
  25. Kheibari, F. and Beni, Y.T. (2016), "Size dependent electromechanical vibration of single-walled piezoelectricnanotubes using thin shell model", Mater. Des., 114, 572-583. https://doi.org/10.1016/j.matdes.2016.10.041
  26. Khoa, N.D., Thiem, H.T. and Duc, N.D. (2019), "Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 26(3), 248-259. https://doi.org/10.1080/15376494.2017.1341583
  27. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2015), "Vibration analysis of CNT-reinforced functionally graded rotating cylindrical panels using the element-free kp-Ritz method", Compos. Part B, 77, 291-303. https://doi.org/10.1016/j.compositesb.2015.03.045
  28. Liu, S., Yu, T. and Bui, T.Q. (2017a) "Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometricanalysis", Eur. J. Mech. - A/Solids, 66, 446-458. https://doi.org/10.1016/j.euromechsol.2017.08.008
  29. Liu, S., Yu, T., Bui, T.Q. and Xia, S. (2017b), "Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory", Compos. Struct., 172, 34-44. https://doi.org/10.1016/j.compstruct.2017.03.067
  30. Liu, S., Yu, T., Van Lich, L., Yin, S. and Bui, T.Q. (2018), "Size effect on cracked functional composite micro-plates by an XIGA-based effective approach", Meccanica, 53(10), 2637-2658. https://doi.org/10.1007/s11012-018-0848-9
  31. Liu, S., Yu, T., Van Lich, L., Yin, S. and Bui, T.Q. (2019), "Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis", Comput. Struct., 212, 173-187. https://doi.org/10.1016/j.compstruc.2018.10.009
  32. Loy, C.T., Lam, K.Y. and Shu, C. (1997), "Analysis of cylindrical shells using generalized differential quadrature", Shock Vib., 4, 193-198. https://doi.org/10.3233/SAV-1997-4305
  33. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Thermal Stress., 40, 899-916. https://doi.org/10.1080/01495739.2017.1318689
  34. Minh, P.P. and Duc, N.D. (2019), "The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory", Compos. Part B, 175, 107086. https://doi.org/10.1016/j.compositesb.2019.107086
  35. Mohammadimehr, M. and Mehrabi, M. (2017), "Stability and free vibration analysis of double-bonded micro composite sandwich cylindrical shells conveying fluid flow", Appl. Math Model, 47, 685-709. https://doi.org/10.1016/j.apm.2017.03.054
  36. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of singlewalled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37, 1-15.
  37. Mohammadimehr, M. and Shahedi, S. (2016), "Nonlinear magneto-electro-mechanical vibration analysis of double-bonded sandwich Timoshenko microbeams based on MSGT using GDQM", Steel Compos. Struct., Int. J., 21(1), 1-36. https://doi.org/10.12989/scs.2016.21.1.001
  38. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2011), "Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory", Proc. IMechE, Part C: Journal of Mechanical Engineering Science, 225(2), 498-506. https://doi.org/10.1177/2041298310392861
  39. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2016a), "Modified strain gradient Reddy rectangular plate model for biaxialbuckling and bending analysis of double-coupled piezoelectricpolymeric nanocomposite reinforced by FGSWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007
  40. Mohammadimehr, M., Salemi, M. and Navi, B.R. (2016b), "Bending buckling and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temprature-dependent material properties under hydro-thermomechanical loadings using DQM", Compos. Struct., 138, 361-380.https://doi.org/10.1016/j.compstruct.2015.11.055
  41. Mohammadimehr, M., Nejad, E.S. and Mehrabi, M. (2018a), "Buckling and vibration analyses of MGSGT double-bonded micro composite sandwich SSDT plates reinforced by CNTs and BNNTs with isotropic foam & flexible transversely orthotropic cores", Struct. Eng. Mech., Int. J., 65(4), 491-504. https://doi.org/10.12989/sem.2018.65.4.491
  42. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Akhavan Alavi, S.M., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018b), "Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., Int. J., 29(3), 405-422 https://doi.org/10.12989/scs.2018.29.3.405
  43. Mohammadimehr, M., Mehrabi, M., Hadizadeh, H. and Hadizadeh, H. (2018c), "Surface and size dependent effects on static, buckling, and vibration of micro composite beam under thermo-magnetic fields based on strain gradient theory", Steel Compos. Struct., Int. J., 26(4), 513-531. https://doi.org/10.12989/scs.2018.26.4.513
  44. Murmu, T., McCarthy, M.A. and Adhikari, S. (2012), "Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach", J. Sound Vib., 331, 5069-5086. https://doi.org/10.1016/j.jsv.2012.06.005
  45. Nguyen, D.D. (2016), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric Sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 1-28. https://doi.org/10.1177/1099636216653266
  46. Nguyen, D.K., Vu, M.A. and Nguyen, D.D. (2019b), "Nonlinear dynamic response and vibration of functionally graded nanocomposite cylindrical panel reinforced by carbon nanotubes in thermal environment", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636219847191
  47. Pourasghar, A. and Chen, Z. (2016), "Thermoelastic response of CNT reinforced cylindrical panel resting on elastic foundation using theory of elasticity", Compos. Part B: Eng., 99, 436-444. https://doi.org/10.1016/j.compositesb.2016.06.028
  48. Razavi, H., Babadi, A.F. and Beni, Y.T. (2016), "Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309. https://doi.org/10.1016/j.compstruct.2016.10.056
  49. Shen, H.S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments", Compos. Part B, 136, 177-186. https://doi.org/10.1016/j.compositesb.2017.10.032
  50. Sobhy, M. and Zenkour, A.M. (2018), "Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate", Compos. Part B: Eng., 154, 492-506. https://doi.org/10.1016/j.compositesb.2018.09.011
  51. Song, Z.G., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments", Int. J. Mech. Sci., 115, 339-347. https://doi.org/10.1016/j.ijmecsci.2016.06.020
  52. Van Do, T., Nguyen, D.K., Duc, N.D., Doan, D.H. and Bui, T.Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin-Wall. Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022
  53. Vuong, P.M. and Duc, N.D. (2018), "Nonlinear response and buckling analysis of eccentrically stiffened FGM toroidal shell segments in thermal environment", J. Aerosp. Sci. Technol., 79, 383-398. https://doi.org/10.1016/j.ast.2018.05.058
  54. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aero. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003
  55. Yang, J., Xiong, J., Ma, L., Zhang, G., Wang, X. and Wu, L. (2014), "Study on vibration damping of composite sandwich cylindrical shell with pyramidal truss-like cores", Compos. Struct., 117, 362-372. https://doi.org/10.1016/j.compstruct.2014.06.042
  56. Yu, T., Zhang, J., Hu, H. and Bui, T.Q. (2019a), "A novel sizedependent quasi-3D isogeometric beam model for twodirectional FG microbeams analysis", Compos. Struct., 211, 76-88. https://doi.org/10.1016/j.compstruct.2018.12.014
  57. Yu, T., Hu, H., Zhang, J. and Bui, T.Q. (2019b), "Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory", Thin-Wall. Struct., 138, 1-14. https://doi.org/10.1016/j.tws.2018.12.006
  58. Yuan, Z. and Kardomateas, G.A. (2018), "Nonlinear dynamic response of sandwich wide panels", Int. J. Solids Struct., 148-149, 110-121. https://doi.org/10.1016/j.ijsolstr.2017.09.028
  59. Zeighampour, H. and Beni, Y.T. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47. https://doi.org/10.1016/j.ijengsci.2014.01.004
  60. Zenkour, A.M. (2015), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  61. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147