Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FG-SWCNTs based on a nonlocal strain gradient theory

  • Khazaei, Pegah (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2020.03.04
  • Accepted : 2020.06.01
  • Published : 2020.07.25
⟨ Previous Next ⟩

Abstract

This paper investigates the size dependent effect on the vibration analysis of a porous nanocomposite viscoelastic plate reinforced by functionally graded-single walled carbon nanotubes (FG-SWCNTs) by considering nonlocal strain gradient theory. Therefore, using energy method and Hamilton's principle, the equations of motion are derived. In this article, the effects of nonlocal parameter, aspect ratio, strain gradient parameter, volume fraction of carbon nanotubes (CNTs), damping coefficient, porosity coefficient, and temperature change on the natural frequency are perused. The innovation of this paper is to compare the effectiveness of each mentioned parameters individually on the free vibrations of this plate and to represent the appropriate value for each parameter to achieve an ideal nanocomposite plate that minimizes vibration. The results are verified with those referenced in the paper. The results illustrate that the effect of damping coefficient on the increase of natural frequency is significantly higher than the other parameters effect, and the effects of the strain gradient parameter and nonlocal parameter on the natural frequency increase are less than damping coefficient effect, respectively. Furthermore, the results indicate that the natural frequency decreases with a rise in the nonlocal parameter, aspect ratio and temperature change. Also, the natural frequency increases with a rise in the strain gradient parameter and CNTs volume fraction. This study can be used for optimizing the industrial and medical designs, such as automotive industry, aerospace engineering and water purification system, by considering ideal properties for the nanocomposite plate.

Keywords

Acknowledgement

The authors would like to thank the referees for their valuable comments. Also, they are thankful to the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work by Grant No. 891238/3.

References

  1. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  2. Akbarzadeh Khorshidi, M. (2018), "The material length scale parameter used in couple stress theories is not a material constant", Int. J. Eng. Sci., 133, 15-25. https://doi.org/10.1016/j.ijengsci.2018.08.005.
  3. AkhavanAlavi, S.M, Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech. A/Solid., 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008
  4. Alibeigloo, A. (2013), "Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity", Compos. Struct., 95, 612-622. https://doi.org/10.1016/j.compstruct.2012.08.018.
  5. Amir, S., Soleimani-Javid, Z. and Arshid, E. (2019), "Size-dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT", Z. Angew. Math. Mech., 99(9), e201800334. https://doi.org/10.1002/zamm.201800334.
  6. Ansari, R., Faghih-Shojaei, M., Mohammadi, V., Gholami, R. and Rouhi, H. (2015), "Buckling and postbuckling of single-walled carbon nanotubes based on a nonlocal Timoshenko beam model", Z. Angew. Math. Mech., 95(9), 939-951. https://doi.org/10.1002/zamm.201300017.
  7. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part. B. Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057.
  8. Arefi, M., Pourjamshidian, M. and Ghorbanpour-Arani, A. (2018), "Free vibration analysis of a piezoelectric curved sandwich nanobeam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories", Eur. Phys. J. Plus., 133(5), 193. https://doi.org/10.1140/epjp/i2018-12015-1.
  9. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.
  10. Dinh Duc, N., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mech., 4(4), 245-259. https://dx.doi.org/10.22055/jacm.2018.23219.1151.
  11. Ebrahimi, F. and Barati, M.R. (2017), "Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams", Mech. Syst. Signal Pr., 93, 445-459. https://doi.org/10.1016/j.ymssp.2017.02.021.
  12. Ebrahimi, F. and Barati, M.R. (2018), "Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory", Compos. Struct., 185, 241-253. https://doi.org/10.1016/j.compstruct.2017.10.021.
  13. Ebrahimi, F. and Dabbagh, A. (2017), "Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory", Eur. Phys. J. Plus., 132(11), 449. https://doi.org/10.1140/epjp/i2017-11694-2.
  14. Ebrahimi, F. and Dabbagh, A. (2019), "An analytical solution for static stability of multi-scale hybrid nanocomposite plates", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-019-00840-y.
  15. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24(10), 820-829. https://doi.org/10.1080/15376494.2016.1196786.
  16. Ebrahimi, F. and Shafiei, N. (2017), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772. https://doi.org/10.1080/15376494.2016.1196781.
  17. Ebrahimi, F., Barati, M.R. and Civalek, O. (2019a), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-019-00742-z.
  18. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019b), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. Comput., 35(4), 1375-1389. https://doi.org/10.1007/s00366-018-0669-4.
  19. Ebrahimi, F., Nouraei, M. and Dabbagh, A. (2019c), "Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-019-00737-w.
  20. Gao, Y., Xiao, W.S. and Zhu, H. (2019), "Nonlinear vibration analysis of different types of functionally graded beams using nonlocal strain gradient theory and a two-step perturbation method", Eur. Phys. J. Plus., 134(1), 23. https://doi.org/10.1140/epjp/i2019-12446-0.
  21. Gholami, R. and Ansari, R. (2017), "A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports", Compos. Struct., 166, 202-218. https://doi.org/10.1016/j.compstruct.2017.01.045.
  22. Ghorbanpour-Arani, A. and Jalaei, M.H. (2017), "Investigation of the longitudinal magnetic field effect on dynamic response of viscoelastic graphene sheet based on sinusoidal shear deformation theory", Physica B, 506, 94-104. https://doi.org/10.1016/j.physb.2016.11.004.
  23. Ghorbanpour-Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016), "Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory", Compos. Part B. Eng., 95, 209-224. https://doi.org/10.1016/j.compositesb.2016.03.077.
  24. Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189.
  25. Jafarian Arani, A. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/CAC.2016.17.5.567.
  26. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concrete, 25(1), 37. https://doi.org/10.12989/cac.2020.25.1.03.
  27. Kim, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.
  28. Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028.
  29. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  30. Lu, L., Guo, X. and Zhao, J. (2019), "A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects", Appl. Math. Model., 68, 583-602. https://doi.org/10.1016/j.apm.2018.11.023.
  31. Malikan, M. (2020), "On the plastic buckling of curved carbon nanotubes", Theor. Appl. Mech. Lett., 10(1), 46-56. https://doi.org/10.1016/j.taml.2020.01.004.
  32. Malikan, M. and Eremeyev, V.A. (2020a), "On the dynamics of a visco-piezo-flexoelectric nanobeam", Symmetry, 12(4), 643. https://doi.org/10.3390/sym12040643.
  33. Malikan, M. and Eremeyev, V.A. (2020b), "Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method", Mater. Res. Express., 7(2), 025005. https://doi.org/10.1088/2053-1591/ab691c.
  34. Malikan, M. and Nguyen, V.B. (2018), "Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory", Physica E Low Dimens. Syst. Nanostruct., 102, 8-28. https://doi.org/10.1016/j.physe.2018.04.018.
  35. Malikan, M., Dimitri, R. and Tornabene, F. (2019), "Transient response of oscillated carbon nanotubes with an internal and external damping", Compos. Part B-Eng., 158, 198-205. https://doi.org/10.1016/j.compositesb.2018.09.092.
  36. Malikan, M., Krasheninnikov, M. and Eremeyev, V.A. (2020), "Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field", Int . J. Eng . Sci., 148, 103210. https://doi.org/10.1016/j.ijengsci.2019.103210 .
  37. Malikan, M., Nguyen, V.B. and Tornabene, F. (2018a), "Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory", Eng. Sci. Tech. Int. J., 21(4), 778-786. https://doi.org/10.1016/j.jestch.2018.06.001.
  38. Malikan, M., Nguyen, V.B. and Tornabene, F. (2018b), "Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory", Mater. Res. Express, 5(7), 075031. https://doi.org/10.1088/2053-1591/aad144.
  39. Malikan, M., Tornabene, F. and Dimitri, R. (2018c), "Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals", Mater. Res. Express, 5(9), 095006. https://doi.org/10.1088/2053-1591/aad4c3.
  40. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431.
  41. Mohammadimehr, M., Akhavan Alavi, SM., Okhravi, SV. and Edjtahed, SH. (2018b), "Free vibration analysis of micromagneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube-reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory", J. Intel. Mater. Syst. Struct., 29(5), 863-882. https://doi.org/10.1177/1045389X17721048.
  42. Mohammadimehr, M., Mohammadi-Najafabadi, M.M., Nasiri, H. and Rousta-Navi, B. (2016a), "Surface stress effects on the free vibration and bending analysis of the nonlocal single-layer graphene sheet embedded in an elastic medium using energy method', Proc. Inst. Mech. Eng. Part. N, 230(3), 148-160. https://doi.org/10.1177%2F1740349914559042. https://doi.org/10.1177/1740349914559042
  43. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016d), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method", Appl. Math. Mech., 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9.
  44. Mohammadimehr, M., Navi, B.R. and Ghorbanpour Arani, A. (2017b), "Dynamic stability of modified strain gradient theory sinusoidal viscoelastic piezoelectric polymeric functionally graded single-walled carbon nanotubes reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Struct., 24(16), 1325-1342. https://doi.org/10.1080/15376494.2016.1227507.
  45. Mohammadimehr, M., Rousta-Navi, B. and Ghorbanpour-Arani, A. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077.
  46. Mohammadimehr, M., Rousta-Navi, B. and Ghorbanpour-Arani, A. (2016c), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B. Eng., 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007.
  47. Mohammadimehr, M., Salemi, M. and Rousta-Navi, B. (2016b), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055.
  48. Mohammadimehr, M., Shabani-Nejad, E. 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., 65(4), 491-504. https://doi.org/10.12989/sem.2018.65.4.491.
  49. Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2017a), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622
  50. Moradi-Dastjerdi, R., Malek-Mohammadi, H. and Momeni-Khabisi, H. (2017), "Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates", Z. Angew. Math. Mech., 97(11), 1418-1435. https://doi.org/10.1002/zamm.201600209.
  51. Mousavi, M., Mohammadimehr, M. and Rostami, R. (2019), "Analytical solution for buckling analysis of micro sandwich hollow circular plate", Comput. Concrete, 24(3), 185-192. https://doi.org/10.12989/cac.2019.24.3.185.
  52. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  53. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125.
  54. Rezaei, A.S., Saidi, A.R., Abrishamdari, M. and Mohammadi, M.P. (2017), "Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach", Thin Wall. Struct., 120, 366-377. https://doi.org/10.1016/j.tws.2017.08.003.
  55. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018a), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus., 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5.
  56. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018b), "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.
  57. Tanzadeh, H. and Amoushahi, H. (2019), "Buckling and free vibration analysis of piezoelectric laminated composite plates using various plate deformation theories', Eur. J. Mech. A. Solid., 74, 242-256. https://doi.org/10.1016/j.euromechsol.2018.11.013.
  58. Thai, H.T. and Choi, D.H. (2013), "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Compos. Struct., 95, 142-153. https://doi.org/10.1016/j.compstruct.2012.08.023.
  59. Thai, H.T. and Kim, S.E. (2013), "A size-dependent functionally graded Reddy plate model based on a modified couple stress theory", Compos. Part. B. Eng., 45(1), 1636-1645. https://doi.org/10.1016/j.compositesb.2012.09.065.
  60. 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.
  61. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090.
  62. Zenkour, A.M. and Alghanmi, R.A. (2019), "Stress analysis of a functionally graded plate integrated with piezoelectric faces via a four-unknown shear deformation theory", Resul. Phys., 12, 268-277. https://doi.org/10.1016/j.rinp.2018.11.045.
  63. Zhang, D.P., Lei, Y. and Shen, Z.B. (2018), "Semi-analytical solution for vibration of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation", J. Appl. Comput. Mech., 4(3), 202-215. https://dx.doi.org/10.22055/jacm.2017.23096.1149.