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Arabian Journal for Science and Engineering

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04.12.2022 | Research Article-mechanical Engineering

Free Vibration Behaviors of Nanoplates Resting on Viscoelastic Medium

verfasst von: Bui Van Tuyen

Erschienen in: Arabian Journal for Science and Engineering | Ausgabe 9/2023

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Abstract

In this study, for the first time, the free vibrations of a nanoplate that is resting on a viscoelastic substrate are investigated while also taking into consideration the flexoelectricity effect that is derived from the classical plate theory. To properly find the natural frequency of the nanoplate, first, the equilibrium equation of the plate is established based on Hamilton’s principle. Then, based on the analytic solution form, the natural frequency of the nanoplate is determined. The presence of the viscoelastic component of the elastic foundation is the primary factor that contributes to the natural frequency expression of the nanostructure. This is because the presence of the viscoelastic component causes the natural frequency of the plate to vibrate in the general case with both real and imaginary components. The findings of the numerical calculation make it abundantly evident that the natural vibration frequency will have a variety of loss rates that are determined by the values of the viscous resistance characteristics of the foundation, as well as the temperature, size effect, and compression force. The validity of this study has been validated via the use of computational theory in conjunction with previously published research. This important work calculates the nanoplate structures based on flexoelectric and viscoelastic materials under different loads. This is necessary before they can be made and used in real life.

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Yudin, P.V.; Tagantsev, A.K.: Fundamentals of flexoelectricity in solids. Nanotechnology (2013). https://doi.org/10.1088/0957-4484/24/43/432001CrossRef

Nguyen, T.D.; Mao, S.; Yeh, Y.W.; Purohit, P.K.; McAlpine, M.C.: Nanoscale flexoelectricity. Adv. Mater. 25(7), 946–974 (2013). https://doi.org/10.1002/adma.201203852CrossRef

Wang, B.; Gu, Y.; Zhang, S.; Chen, L.Q.: Flexoelectricity in solids: Progress, challenges, and perspectives. Prog. Mater. Sci. (2019). https://doi.org/10.1016/j.pmatsci.2019.05.003CrossRef

Yan, Z.: Size-dependent bending and vibration behaviors of piezoelectric circular nanoplates. Smart Mater. Struct. (2016). https://doi.org/10.1088/0964-1726/25/3/035017CrossRef

Yang, W.; Liang, X.; Shen, S.: Electromechanical responses of piezoelectric nanoplates with flexoelectricity. Acta Mech. 226(9), 3097–3110 (2015). https://doi.org/10.1007/s00707-015-1373-8MathSciNetCrossRefMATH

Li, A.; Zhou, S.; Qi, L.: Size-dependent electromechanical coupling behaviors of circular micro-plate due to flexoelectricity. Appl. Phys. A Mater. Sci. Process 50, 5 (2016)

Wang, X.; Zhang, R.; Jiang, L.: A study of the flexoelectric effect on the electroelastic fields of a cantilevered piezoelectric nanoplate. Int. J. Appl. Mech. (2017). https://doi.org/10.1142/S1758825117500569CrossRef

He, L.; Lou, J.; Zhang, A.; Wu, H.; Du, J.; Wang, J.: On the coupling effects of piezoelectricity and flexoelectricity in piezoelectric nanostructures. AIP Adv. (2017). https://doi.org/10.1063/1.4994021CrossRef

Ebrahimi, F.; Barati, M.R.: Static stability analysis of embedded flexoelectric nanoplates considering surface effects. Appl. Phys. A Mater. Sci. Process (2017). https://doi.org/10.1007/s00339-017-1265-yCrossRef

10.

Ghobadi, A.; Beni, Y.T.; Golestanian, H.: Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field. Arch. Appl. Mech. 90(9), 2025–2070 (2020). https://doi.org/10.1007/s00419-020-01708-0CrossRef

11.

Amir, S.; BabaAkbar-Zarei, H.; Khorasani, M.: Flexoelectric vibration analysis of nanocomposite sandwich plates. Mech. Based Des. Struct. Mach. 48(2), 146–163 (2020). https://doi.org/10.1080/15397734.2019.1624175CrossRef

12.

Ghobadi, A.; Beni, Y.T.; Golestanian, H.: Size dependent thermo-electro-mechanical nonlinear bending analysis of flexoelectric nano-plate in the presence of magnetic field. Int. J. Mech. Sci. 152, 118–137 (2019). https://doi.org/10.1016/j.ijmecsci.2018.12.049CrossRef

13.

Ghobadi, A.; Tadi Beni, Y.; Golestanian, H. Size dependent nonlinear bending analysis of a flexoelectric functionally graded nano-plate under thermo-electro-mechanical loads. J. Solid Mech. 12(1), 33–56 (2020). [Online]. Available from: http://jsm.iau-arak.ac.ir/article_670598_33046179b9d8267e4f6111de3f7af938.pdf.

14.

Nguyen, T.C.N.: Static bending analysis of variable thickness microplates using the finite element method and modified couple stress theory. J. Sci. Tech. (2022). https://doi.org/10.56651/lqdtu.jst.v17.n03.351CrossRef

15.

Thai, L.M.; Luat, D.T.; Phung, V.B.; Van Minh, P.; Van Thom, D.: Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects. Arch. Appl. Mech. 92(1), 163–182 (2022). https://doi.org/10.1007/s00419-021-02048-3CrossRef

16.

Su, Y., et al.: Exceptional negative thermal expansion and viscoelastic properties of graphene oxide paper. Carbon N. Y. 50(8), 2804–2809 (2012). https://doi.org/10.1016/j.carbon.2012.02.045CrossRef

17.

Srivastava, I.; Yu, Z.-Z.; Koratkar, N.: Viscoelastic properties of graphene-polymer composites. Adv. Sci. Eng. Med. 4(1), 10–14 (2012). https://doi.org/10.1166/asem.2012.1127CrossRef

18.

Eichler, A.; Moser, J.; Chaste, J.; Zdrojek, M.; Wilson-Rae, I.; Bachtold, A.: Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. Nat. Nanotechnol. 6(6), 339–342 (2011). https://doi.org/10.1038/nnano.2011.71CrossRef

19.

Pouresmaeeli, S.; Ghavanloo, E.; Fazelzadeh, S.A.: Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium. Compos. Struct. 96, 405–410 (2013). https://doi.org/10.1016/j.compstruct.2012.08.051CrossRef

20.

Karličić, D.; Kozić, P.; Pavlović, R.: Free transverse vibration of nonlocal viscoelastic orthotropic multi-nanoplate system (MNPS) embedded in a viscoelastic medium. Compos. Struct. 115(1), 89–99 (2014). https://doi.org/10.1016/j.compstruct.2014.04.002CrossRef

21.

Karličić, D.; Cajić, M.; Murmu, T.; Adhikari, S.: Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems. Eur. J. Mech. A/Solids 49, 183–196 (2015). https://doi.org/10.1016/j.euromechsol.2014.07.005MathSciNetCrossRefMATH

22.

Hashemi, S.H.; Mehrabani, H.; Ahmadi-Savadkoohi, A.: Exact solution for free vibration of coupled double viscoelastic graphene sheets by viscoPasternak medium. Compos. Part B Eng. 78, 377–383 (2015). https://doi.org/10.1016/j.compositesb.2015.04.008CrossRef

23.

Wang, Y.; Li, F.M.; Wang, Y.Z.: Nonlinear vibration of double layered viscoelastic nanoplates based on nonlocal theory. Phys. E Low Dimens. Syst. Nanostruct. 67, 65–76 (2015). https://doi.org/10.1016/j.physe.2014.11.007CrossRef

24.

Akbaş, ŞD.: Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium. Smart Struct. Syst. 18(6), 1125–1143 (2016). https://doi.org/10.12989/sss.2016.18.6.1125CrossRef

25.

Akbaş, ŞD.: Forced vibration analysis of functionally graded sandwich deep beams. Coupled Syst. Mech. 8(3), 259–271 (2019). https://doi.org/10.12989/csm.2019.8.3.259CrossRef

26.

Akbaş, ŞD.: Forced vibration analysis of cracked nanobeams. J. Braz. Soc. Mech. Sci. Eng. (2018). https://doi.org/10.1007/s40430-018-1315-1CrossRef

27.

Demir, C.; Oz, F.E.: Free vibration analysis of a functionally graded viscoelastic supported beam. JVC/J. Vib. Control 20(16), 2464–2486 (2014). https://doi.org/10.1177/1077546313479634MathSciNetCrossRef

28.

Ebrahimi, F.; Fardshad, R.E.; Mahesh, V.: Frequency response analysis of curved embedded magneto-electro-viscoelastic functionally graded nanobeams. Adv. Nano Res. 7(6), 391–403 (2019). https://doi.org/10.12989/anr.2019.7.6.391CrossRef

29.

Rahman, M.S.; Hasan, A.S.M.Z.; Yeasmin, I.A.: Modified multi-level residue harmonic balance method for solving nonlinear vibration problem of beam resting on nonlinear elastic foundation. J. Appl. Comput. Mech. 5(4), 627–638 (2019). https://doi.org/10.22055/JACM.2018.26729.1352CrossRef

30.

Tho, N.C.; Thanh, N.T.; Tho, T.D.; Van Minh, P.; Hoa, L.K.: Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection. J. Braz. Soc. Mech. Sci. Eng. (2021). https://doi.org/10.1007/s40430-021-03189-wCrossRef

31.

Civalek, Ö.; Avcar, M.: Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Eng. Comput. 38, 489–521 (2022). https://doi.org/10.1007/s00366-020-01168-8CrossRef

32.

Sobhani, E.; Avcar, M.: Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak foundations under arbitrary boundary conditions. Eng. Anal. Bound. Elem. 144, 145–164 (2022). https://doi.org/10.1016/j.enganabound.2022.08.018MathSciNetCrossRef

33.

Hadji, L.; Avcar, M.; Civalek, Ö.: An analytical solution for the free vibration of FG nanoplates. J. Braz. Soc. Mech. Sci. Eng. (2021). https://doi.org/10.1007/s40430-021-03134-xCrossRef

34.

Hadji, L.; Avcar, M.; Zouatnia, N.: Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation. Mater. Today Proc. 53, 153–160 (2022). https://doi.org/10.1016/j.matpr.2021.12.485CrossRef

35.

Sobhani, E.; Avcar, M.: The influence of various nanofiller materials (CNTs, GNPs, and GOPs) on the natural frequencies of nanocomposite cylindrical shells: A comparative study. Mater. Today Commun. (2022). https://doi.org/10.1016/j.mtcomm.2022.104547CrossRef

36.

Van Thom, D.; Duc, D.H.; Van Minh, P.; Tung, N.S.: Finite element modelling for free vibration response of cracked stiffened Fgm plates. Vietnam J. Sci. Technol. 58(1), 119 (2020). https://doi.org/10.15625/2525-2518/58/1/14278CrossRef

37.

Nguyen Thai, D.; Van Minh, P.; Phan Hoang, C.; Ta DucNguyen Thi CamNguyen Thi, T.N.D.: Bending of symmetric sandwich FGM beams with shear connectors. Math. Probl. Eng. (2021). https://doi.org/10.1155/2021/7596300MathSciNetCrossRefMATH

38.

Van Phung, M.; Nguyen, D.T.; Doan, L.T.; Van Nguyen, D.; Van Duong, T.: numerical investigation on static bending and free vibration responses of two-layer variable thickness plates with shear connectors. Iran. J. Sci. Technol. Trans. Mech. Eng. (2022). https://doi.org/10.1007/s40997-021-00459-9CrossRef

39.

Phung, V.M.: Static bending analysis of symmetrical three-layer Fgm beam with shear connectors under static load. J. Sci. Tech. 15(3), 68–78 (2020). https://doi.org/10.56651/lqdtu.jst.v15.n03.213CrossRef

40.

Dung, N.T.; Van Minh, P.; Hung, H.M.; Tien, D.M.: The third-order shear deformation theory for modeling the static bending and dynamic responses of piezoelectric bidirectional functionally graded plates. Adv. Mater. Sci. Eng. (2021). https://doi.org/10.1155/2021/5520240CrossRef

41.

Duc, N.D.; Trinh, T.D.; Van Do, T.; Doan, D.H.: On the buckling behavior of multi-cracked FGM plates. Lect. Notes Mech. Eng. Part F3, 29–45 (2018). https://doi.org/10.1007/978-981-10-7149-2_3CrossRef

42.

Bui, T.Q.; Doan, D.H.; Van Do, T.; Hirose, S.; Duc, N.D.: High frequency modes meshfree analysis of Reissner-Mindlin plates. J. Sci. Adv. Mater. Devices 1(3), 400–412 (2016). https://doi.org/10.1016/j.jsamd.2016.08.005CrossRef

43.

Doan, T.N., et al.: Analysis of stress concentration phenomenon of cylinder laminated shells using higher-order shear deformation Quasi-3D theory. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2019.111526CrossRef

44.

Dat, P.T.; Van Thom, D.; Luat, D.T.: Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory. Vietnam J. Mech. 38(2), 103–122 (2016). https://doi.org/10.15625/0866-7136/38/2/6730CrossRef

45.

Nguyen, H.N.; Tan, T.C.; Luat, D.T.; Phan, V.D.; Van Thom, D.; Van Minh, P.: Research on the buckling behavior of functionally graded plates with stiffeners based on the third-order shear deformation theory. Mater. (Basel) (2019). https://doi.org/10.3390/ma12081262CrossRef

46.

Van Do, T.; Hong Doan, D.; Chi Tho, N.; Dinh Duc, N.: Thermal buckling analysis of cracked functionally graded plates. Int. J. Struct. Stab. Dyn. (2022). https://doi.org/10.1142/S0219455422500894MathSciNetCrossRef

47.

Duong, V.Q.; Tran, N.D.; Luat, D.T.; Van Thom, D.: Static analysis and boundary effect of FG-CNTRC cylindrical shells with various boundary conditions using quasi-3D shear and normal deformations theory. Structures 44, 828–850 (2022). https://doi.org/10.1016/j.istruc.2022.08.039CrossRef

48.

Yu, T., et al.: On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis. Compos. Struct. 136, 684–695 (2016). https://doi.org/10.1016/j.compstruct.2015.11.002CrossRef

49.

Bui, T.Q., et al.: On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory. Compos. Part B Eng. 92, 218–241 (2016). https://doi.org/10.1016/j.compositesb.2016.02.048CrossRef

50.

Babu, B.; Patel, B.P.: A new computationally efficient finite element formulation for nanoplates using second-order strain gradient Kirchhoff’s plate theory. Compos. Part B Eng. 168, 302–311 (2019). https://doi.org/10.1016/j.compositesb.2018.12.066CrossRef

51.

Shu, L.; Wei, X.; Pang, T.; Yao, X.; Wang, C.: Symmetry of flexoelectric coefficients in crystalline medium. J. Appl. Phys. DOI 10(1063/1), 3662196 (2011)

52.

Gao, J.; Shen, Y.: Vibration and damping analysis of a composite plate with active and passive damping layer. Appl. Math. Mech. Engl. Ed. 20(10), 1075–1086 (1999). https://doi.org/10.1007/bf02460324CrossRefMATH

53.

Baferani, A.H.; Saidi, A.R.; Ehteshami, H.: Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Compos. Struct. 93(7), 1842–1853 (2011). https://doi.org/10.1016/j.compstruct.2011.01.020CrossRef

Titel: Free Vibration Behaviors of Nanoplates Resting on Viscoelastic Medium
verfasst von: Bui Van Tuyen
Publikationsdatum: 04.12.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Arabian Journal for Science and Engineering / Ausgabe 9/2023
Print ISSN: 2193-567X
Elektronische ISSN: 2191-4281
DOI: https://doi.org/10.1007/s13369-022-07500-2

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