Hybrid analytical–neural network modelling for damped vibrations of size-dependent functionally graded nanoplates on viscoelastic foundations
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OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Thermoelastic and Magnetoelastic Phenomena
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References (75)
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1. Abdelrahman, A.A., Esen, I., Tharwan, M.Y., Assie, A., Eltaher, M.A.: On vibrations of functionally graded carbon nanotube (FGCNT) nanoplates under moving load. Adv. Nano Res. 16, 395–412 (2024). https://doi.org/10.12989/anr.2024.16.4.39510.12989/anr.2024.16.4.395 ↗
2. Aksencer, T., Aydogdu, M.: Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory. Phys. E Low Dimens. Syst. Nanostruct. 43, 954–959 (2011). https://doi.org/10.1016/j.physe.2010.11.02410.1016/j.physe.2010.11.024 ↗
3. Amiri, A., Talebitooti, R., Aliakbari, F.: Size-dependent dynamics and instability of sandwich magnetorheological elastomer (MRE)-cored shells in presence of moving flow, based on modified first strain gradient theory. Thin Walled Struct. 181, 109800 (2022). https://doi.org/10.1016/j.tws.2022.10980010.1016/j.tws.2022.109800 ↗
4. Ansari, R., Shahabodini, A., Faghih Shojaei, M.: Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations. Phys. E Low Dimens. Syst. Nanostruct. 76, 70–81 (2016). https://doi.org/10.1016/j.physe.2015.09.04210.1016/j.physe.2015.09.042 ↗
5. Arefi, M., Zenkour, A.M.: Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation. Phys. B Condens. Matter 521, 188–197 (2017). https://doi.org/10.1016/j.physb.2017.06.06610.1016/j.physb.2017.06.066 ↗
6. Baghdali, I., Attia, A., Bourada, F., Bousahla, A.A., Tounsi, A., Heireche, H., Tounsi, A., Bourada, M., Yaylaci, M.: Analysis of the impact of the viscoelastic foundation on bending and vibration of FG porous nanoplates within integral higher-order shear deformation theory. Phys. Mesomech. 28, 245–262 (2025). https://doi.org/10.1134/S102995992460131310.1134/S1029959924601313 ↗
7. Benmessaoud, M., Nasreddine, M.M.: Optimization of MEMS capacitive accelerometer. Microsyst. Technol. 19, 713–720 (2013). https://doi.org/10.1007/s00542-013-1741-z10.1007/s00542-013-1741-z ↗
8. Daikh, A.A., Zenkour, A.M.: Bending of functionally graded sandwich nanoplates resting on Pasternak foundation under different boundary conditions. J. Appl. Comput. Mech. 6, 1245–1259 (2020). https://doi.org/10.22055/JACM.2020.33136.216610.22055/JACM.2020.33136.2166 ↗
9. Dell’Isola, F., Eremeyev, V.A., Korolenko, V.A., Solyaev, Y.O.: Deformation of an elastic second gradient spherical body under equatorial line density of dead forces. Eur. J. Mech. a. Solids 103, 105153 (2024). https://doi.org/10.1016/j.euromechsol.2023.10515310.1016/j.euromechsol.2023.105153 ↗
10. Eltaher, M.A., Khairy, A., Sadoun, A.M., Omar, F.A.: Static and buckling analysis of functionally graded Timoshenko nanobeams. Appl. Math. Comput. 229, 283–295 (2014). https://doi.org/10.1016/j.amc.2013.12.07210.1016/j.amc.2013.12.072 ↗
11. Eremeyev, V.A.: Ellipticity of gradient poroelasticity. Int. J. Eng. Sci. 190, 103885 (2023). https://doi.org/10.1016/j.ijengsci.2023.10388510.1016/j.ijengsci.2023.103885 ↗
12. Eremeyev, V.A., Naumenko, K.: Wave dispersion relations in peridynamics: influence of kernels and similarities to nonlocal elasticity theories. Int. J. Eng. Sci. 211, 104256 (2025). https://doi.org/10.1016/j.ijengsci.2025.10425610.1016/j.ijengsci.2025.104256 ↗
13. Eremeyev, V.A., Rosi, G., Naili, S.: On effective surface elastic moduli for microstructured strongly anisotropic coatings. Int. J. Eng. Sci. (2024). https://doi.org/10.1016/j.ijengsci.2024.10413510.1016/j.ijengsci.2024.104135 ↗
14. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972a). https://doi.org/10.1016/0020-7225(72)90070-510.1016/0020-7225(72)90070-5 ↗
15. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–435 (1972b). https://doi.org/10.1016/0020-7225(72)90050-X10.1016/0020-7225(72)90050-X ↗
16. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983). https://doi.org/10.1063/1.33280310.1063/1.332803 ↗
17. Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972). https://doi.org/10.1016/0020-7225(72)90039-010.1016/0020-7225(72)90039-0 ↗
18. Eyvazian, A., Zhang, C., Civalek, Ö., Khan, A., Sebaey, T.A., Farouk, N.: Wave propagation analysis of sandwich FGM nanoplate surrounded by viscoelastic foundation. Arch. Civ. Mech. Eng. (2022). https://doi.org/10.1007/s43452-022-00474-w10.1007/s43452-022-00474-w ↗
19. Fan, L., Sahmani, S., Safaei, B.: Couple stress-based dynamic stability analysis of functionally graded composite truncated conical microshells with magnetostrictive facesheets embedded within nonlinear viscoelastic foundations. Eng. Comput. 37, 1635–1655 (2021). https://doi.org/10.1007/s00366-020-01182-w10.1007/s00366-020-01182-w ↗
20. Fan, Y.-H., She, G.-L., Eltaher, M.A.: Nonlinear vibrations of two-directional functionally graded spinning annular plates with variable thickness. Thin Walled Struct. 216, 113627 (2025). https://doi.org/10.1016/j.tws.2025.11362710.1016/j.tws.2025.113627 ↗
21. Farzam, A., Hassani, B.: Size-dependent analysis of FG microplates with temperature-dependent material properties using modified strain gradient theory and isogeometric approach. Compos. Part B Eng. 161, 150–168 (2019). https://doi.org/10.1016/j.compositesb.2018.10.02810.1016/j.compositesb.2018.10.028 ↗
22. Ghayesh, M.H., Farajpour, A.: A review on the mechanics of functionally graded nanoscale and microscale structures. Int. J. Eng. Sci. 137, 8–36 (2019). https://doi.org/10.1016/j.ijengsci.2018.12.00110.1016/j.ijengsci.2018.12.001 ↗
23. Ghazwani, M.H., Alnujaie, A., Van Vinh, P.: Assessment of the porosity and general viscoelastic foundation effects on the damped vibration analysis of functionally graded plates. Mech. Based des. Struct. Mach. 0, 1–26 (2025). https://doi.org/10.1080/15397734.2025.247846410.1080/15397734.2025.2478464 ↗
24. Hai, T., Al-Masoudy, M.M., Alsulamy, S., El Ouni, M.H., Ayvazyan, A., Kumar, A.: Size-dependent free vibration analysis of honeycomb sandwich microplates integrated with piezoelectric actuators based on the modified strain gradient theory. Compos. Struct. 305, 116555 (2023). https://doi.org/10.1016/j.compstruct.2022.11655510.1016/j.compstruct.2022.116555 ↗
25. Hung, P.T., Phung-Van, P., Thai, C.H.: Small scale thermal analysis of piezoelectric–piezomagnetic FG microplates using modified strain gradient theory. Int. J. Mech. Mater. des. 19, 739–761 (2023). https://doi.org/10.1007/s10999-023-09651-y10.1007/s10999-023-09651-y ↗
26. Huu-Quoc, T., Van-Tham, V.: Electro-mechanical vibration characteristics of imperfect sandwich FG piezoelectric honeycomb nanoplates resting on Kerr foundation. Nano-Struct. Nano-Objects 39, 101229 (2024). https://doi.org/10.1016/j.nanoso.2024.10122910.1016/j.nanoso.2024.101229 ↗
27. Kadoli, R., Akhtar, K., Ganesan, N.: Static analysis of functionally graded beams using higher order shear deformation theory. Appl. Math. Model. 32, 2509–2525 (2008). https://doi.org/10.1016/j.apm.2007.09.01510.1016/j.apm.2007.09.015 ↗
28. Karamanli, A., Vo, T.P.: Size-dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory. Compos. Struct. 246, 112401 (2020). https://doi.org/10.1016/j.compstruct.2020.11240110.1016/j.compstruct.2020.112401 ↗
29. Karamanli, A., Vo, T.P., Civalek, O.: Finite element formulation of metal foam microbeams via modified strain gradient theory. Eng. Comput. 39, 751–772 (2023). https://doi.org/10.1007/s00366-022-01666-x10.1007/s00366-022-01666-x ↗
30. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003). https://doi.org/10.1016/S0022-5096(03)00053-X10.1016/S0022-5096(03)00053-X ↗
31. Li, C., Wang, P.Y., Luo, Q.Y., Li, S.: Free vibration of axially moving functionally graded nanoplates based on the nonlocal strain gradient theory. Int. J. Acoust. Vib. 25, 587–596 (2021). https://doi.org/10.20855/ijav.2020.25.4172510.20855/ijav.2020.25.41725 ↗
32. Li, Q., Wu, D., Gao, W., Tin-Loi, F., Liu, Z., Cheng, J.: Static bending and free vibration of organic solar cell resting on Winkler-Pasternak elastic foundation through the modified strain gradient theory. Eur. J. Mech. a. Solids 78, 103852 (2019). https://doi.org/10.1016/j.euromechsol.2019.10385210.1016/j.euromechsol.2019.103852 ↗
33. Li, Y.-P., She, G.-L.: Nonlinear dynamic response of porous graphene platelets reinforced plates subjected to moving load considering initial geometrical imperfection. J. Vib. Eng. Technol. 13, 17 (2025). https://doi.org/10.1007/s42417-024-01651-210.1007/s42417-024-01651-2 ↗
34. Liu, G., Wu, S., Shahsavari, D., Karami, B., Tounsi, A.: Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation. Eur. J. Mech. a. Solids (2022). https://doi.org/10.1016/j.euromechsol.2022.10464910.1016/j.euromechsol.2022.104649 ↗
35. Lurie, S., Belov, P.: Gradient effects in fracture mechanics for nano-structured materials. Eng. Fract. Mech. 130, 3–11 (2014). https://doi.org/10.1016/j.engfracmech.2014.07.03210.1016/j.engfracmech.2014.07.032 ↗
36. Lurie, S., Solyaev, Y.: Variant of strain gradient elasticity with simplified formulation of traction boundary value problems. ZAMM J. Appl. Math. Mech. / Zeitschrift Für Angewandte Mathematik und Mechanik 103, 1–14 (2023). https://doi.org/10.1002/zamm.20230032910.1002/zamm.202300329 ↗
37. Lurie, S.A., Kuznetsova, E.L., Rabinskii, L.N., Popova, E.I.: Refined gradient theory of scale-dependent superthin rods. Mech. Solids 50, 135–146 (2015). https://doi.org/10.3103/S002565441502003X10.3103/S002565441502003X ↗
38. Malikan, M.: On the plastic buckling of curved carbon nanotubes. Theor. Appl. Mech. Lett. 10, 46–56 (2020). https://doi.org/10.1016/j.taml.2020.01.00410.1016/j.taml.2020.01.004 ↗
39. Malikan, M., Eremeyev, V.A.: A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition. Compos. Struct. 249, 112486 (2020). https://doi.org/10.1016/j.compstruct.2020.11248610.1016/j.compstruct.2020.112486 ↗
40. Malikan, M., Eremeyev, V.A.: On time-dependent nonlinear dynamic response of micro-elastic solids. Int. J. Eng. Sci. 182, 103793 (2023). https://doi.org/10.1016/j.ijengsci.2022.10379310.1016/j.ijengsci.2022.103793 ↗
41. Malikan, M., Nguyen, V.B., Tornabene, F.: Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Eng. Sci. Technol. an Int. J. 21, 778–786 (2018). https://doi.org/10.1016/j.jestch.2018.06.00110.1016/j.jestch.2018.06.001 ↗
42. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S., Rabczuk, T.: Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput. Mater. Sci. 65, 74–80 (2012). https://doi.org/10.1016/j.commatsci.2012.06.03110.1016/j.commatsci.2012.06.031 ↗
43. Nguyen, N.T., Hui, D., Lee, J., Nguyen-Xuan, H.: An efficient computational approach for size-dependent analysis of functionally graded nanoplates. Comput. Methods Appl. Mech. Eng. 297, 191–218 (2015). https://doi.org/10.1016/j.cma.2015.07.02110.1016/j.cma.2015.07.021 ↗
44. Ozdemir, M.T., Das, T., Esen, I.: Effect of the hexachiral auxetic structure on the thermal buckling behaviour of the magneto electro elastic sandwich smart nano plate using nonlocal strain gradient elasticity. Int. J. Mech. Mater. des. (2025). https://doi.org/10.1007/s10999-025-09777-110.1007/s10999-025-09777-1 ↗
45. 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.2012.08.05110.1016/j.compstruct.2012.08.051 ↗
46. Rai, S., Gupta, A.: Dynamic response of sandwich functionally graded nanoplate under thermal environments and elastic foundations using dynamic stiffness method. Sci. Rep. (2024). https://doi.org/10.1038/s41598-024-70210-210.1038/s41598-024-70210-2 ↗
47. Russo, C., Mocera, F., Somà, A.: MEMS sensors for sport engineer applications. IOP Conf. Ser. Mater. Sci. Eng. 1038, 12056 (2021). https://doi.org/10.1088/1757-899X/1038/1/01205610.1088/1757-899X/1038/1/012056 ↗
48. Sabahi, M.A., Saidi, A.R.: On nonlinear vibrations of Timoshenko FG porous micropipes in thermal environment: analysis and optimization. Int. J. Mech. Mater. des. 21, 799–821 (2025). https://doi.org/10.1007/s10999-025-09764-610.1007/s10999-025-09764-6 ↗
49. Shahraki, H., Riahi, H.T., Izadinia, M., Talaeitaba, S.B.: Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment. J. Thermoplast. Compos. Mater. 34, 68–101 (2021). https://doi.org/10.1177/089270571984317510.1177/0892705719843175 ↗
50. Shahraki, H., Tajmir Riahi, H., Izadinia, M., Talaeitaba, S.B.: Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory. J. Vib. Control 26, 277–305 (2020). https://doi.org/10.1177/107754631987897610.1177/1077546319878976 ↗
51. Shahsavari, D., Karami, B., Fahham, H.R., Li, L.: On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory. Acta Mech. 229, 4549–4573 (2018). https://doi.org/10.1007/s00707-018-2247-710.1007/s00707-018-2247-7 ↗
52. She, G.-L., Ma, Z.-S., Li, C., Eltaher, M.A.: Geometrically nonlinear transient response of graphene platelets reinforced metal foams arbitrary quadrilateral plates under blast load. Thin-Walled Struct. 210, 113018 (2025). https://doi.org/10.1016/j.tws.2025.11301810.1016/j.tws.2025.113018 ↗
53. Shi, G.: A new simple third-order shear deformation theory of plates. Int. J. Solids Struct. 44, 4399–4417 (2007). https://doi.org/10.1016/j.ijsolstr.2006.11.03110.1016/j.ijsolstr.2006.11.031 ↗
54. Sobhy, M.: A comprehensive study on FGM nanoplates embedded in an elastic medium. Compos. Struct. 134, 966–980 (2015). https://doi.org/10.1016/j.compstruct.2015.08.10210.1016/j.compstruct.2015.08.102 ↗
55. Sobhy, M.: Piezoelectric bending of GPL-reinforced annular and circular sandwich nanoplates with FG porous core integrated with sensor and actuator using DQM. Arch. Civ. Mech. Eng. (2021). https://doi.org/10.1007/s43452-021-00231-510.1007/s43452-021-00231-5 ↗
56. Stollberg, J., Gangwar, T., Weeger, O., Schillinger, D.: Multiscale topology optimization of functionally graded lattice structures based on physics-augmented neural network material models. Comput. Methods Appl. Mech. Eng. (2025). https://doi.org/10.1016/j.cma.2025.11780810.1016/j.cma.2025.117808 ↗
57. Tang, H., Nguyen, N.V., Lee, J.: 3D material optimization of functionally graded shells using incremental Kriging surrogates and adaptive infill strategies. Comput. Methods Appl. Mech. Eng. (2025). https://doi.org/10.1016/j.cma.2025.11819210.1016/j.cma.2025.118192 ↗
58. Thai, H.T., Kim, S.E.: A review of theories for the modeling and analysis of functionally graded plates and shells. Compos. Struct. 128, 70 (2015). https://doi.org/10.1016/j.compstruct.2015.03.01010.1016/j.compstruct.2015.03.010 ↗
59. Thang, P.T., Nguyen-Thoi, T., Lee, J.: Modeling and analysis of bi-directional functionally graded nanobeams based on nonlocal strain gradient theory. Appl. Math. Comput. 407, 126303 (2021). https://doi.org/10.1016/j.amc.2021.12630310.1016/j.amc.2021.126303 ↗
60. Van Vinh, P.: On the damped vibration analysis of functionally graded porous beams resting on viscoelastic medium using higher-order shear deformation theory. J. Vib. Eng. Technol. (2025a). https://doi.org/10.1007/s42417-025-01954-y10.1007/s42417-025-01954-y ↗
61. Van Vinh, P.: A novel modified nonlocal strain gradient theory for comprehensive analysis of functionally graded nanoplates. Acta Mech. 236, 173–204 (2025b). https://doi.org/10.1007/s00707-024-04131-610.1007/s00707-024-04131-6 ↗
62. Van Vinh, P., Sedighi, H.M., Civalek, Ö.: A comprehensive study on the critical damping characteristics of vibrating functionally graded sandwich plates with general visco-Winkler–Pasternak foundations. Arch. Civ. Mech. Eng. 25, 101 (2025). https://doi.org/10.1007/s43452-025-01145-210.1007/s43452-025-01145-2 ↗
63. Van Vinh, P., Tounsi, A., Belarbi, M.O.: On the nonlocal free vibration analysis of functionally graded porous doubly curved shallow nanoshells with variable nonlocal parameters. Eng. Comput. 39, 835–855 (2023). https://doi.org/10.1007/s00366-022-01687-610.1007/s00366-022-01687-6 ↗
64. Van Vinh, P., Zenkour, A.M.: Vibration analysis of functionally graded sandwich porous plates with arbitrary boundary conditions: a new general viscoelastic Winkler-Pasternak foundation approach. Eng. Comput. (2025). https://doi.org/10.1007/s00366-025-02106-210.1007/s00366-025-02106-2 ↗
65. Wang, A., Sahandabadi, S., Harrison, T., Spicer, D., Ahamed, M.J.: Modelling of air damping effect on the performance of encapsulated MEMS resonators. Microsyst. Technol. 28, 2529–2539 (2022). https://doi.org/10.1007/s00542-022-05385-710.1007/s00542-022-05385-7 ↗
66. Wang, T., Liu, G., Li, E., Xu, X.: Adaptive deep physics-informed neural network with dual-nested activation for solving complex partial differential equations. Comput. Methods Appl. Mech. Eng. (2025). https://doi.org/10.1016/j.cma.2025.11812510.1016/j.cma.2025.118125 ↗
67. Wu, C., Wan, B., Xu, Y., Al Maruf, D.S.A., Cheng, K., Lewin, W.T., Fang, J., Xin, H., Crook, J.M., Clark, J.R., Steven, G.P., Li, Q.: Dynamic optimisation for graded tissue scaffolds using machine learning techniques. Comput. Methods Appl. Mech. Eng. (2024). https://doi.org/10.1016/j.cma.2024.11691110.1016/j.cma.2024.116911 ↗
68. Xiang, W., Ni, H., Wu, Y., Liu, B.: New closed-form solutions for flexural vibration of microplates based on a modified strain gradient theory. Thin-Walled Struct. 185, 110558 (2023). https://doi.org/10.1016/j.tws.2023.11055810.1016/j.tws.2023.110558 ↗
69. Xie, B., Sahmani, S., Safaei, B., Xu, B.: Nonlinear secondary resonance of FG porous silicon nanobeams under periodic hard excitations based on surface elasticity theory. Eng. Comput. 37, 1611–1634 (2021). https://doi.org/10.1007/s00366-019-00931-w10.1007/s00366-019-00931-w ↗
70. Yang, S., Chen, W.: On hypotheses of composite laminated plates based on new modified couple stress theory. Compos. Struct. 133, 46–53 (2015). https://doi.org/10.1016/j.compstruct.2015.07.05010.1016/j.compstruct.2015.07.050 ↗
71. Yildirim, E., Esen, İ: Thermomechanical buckling of magneto-electro-elastic embedded smart sandwich nano plates. Int. J. Mech. Mater. des. 21, 701–736 (2025). https://doi.org/10.1007/s10999-025-09758-410.1007/s10999-025-09758-4 ↗
72. Zenkour, A.M.: A novel mixed nonlocal elasticity theory for thermoelastic vibration of nanoplates. Compos. Struct. 185, 821–833 (2018). https://doi.org/10.1016/j.compstruct.2017.10.08510.1016/j.compstruct.2017.10.085 ↗
73. Zhang, B., He, Y., Liu, D., Shen, L., Lei, J.: An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation. Appl. Math. Model. 39, 3814–3845 (2015). https://doi.org/10.1016/j.apm.2014.12.00110.1016/j.apm.2014.12.001 ↗
74. Zhao, B., She, G.-L.: Vibration analysis of graphene reinforced metal foam coupled plates under arbitrary boundary and coupled conditions. Eng. Struct. 343, 121143 (2025). https://doi.org/10.1016/j.engstruct.2025.12114310.1016/j.engstruct.2025.121143 ↗
75. Zhu, C., Yan, J., Wang, P., Li, C.: A nonlocal strain gradient approach for out-of-plane vibration of axially moving functionally graded nanoplates in a hygrothermal environment. Shock. Vib. (2021). https://doi.org/10.1155/2021/833212510.1155/2021/8332125 ↗