Analysis of the Impact of the Viscoelastic Foundation on Bending and Vibration of FG Porous Nanoplates within Integral Higher-Order Shear Deformation Theory
Source abstract
Abstract
Abstract This work examines the bending and vibration responses of a functionally graded (FG) 2D nanostructure resting on the viscoelastic foundation. The FG structure properties vary gradually in the thickness direction. In this investigation, three porosity patterns are examined. The nonlocal equilibrium equations are derived by Hamilton’s principle using Eringen’s nonlocal elasticity theory, which incorporates the integral plate theory with a reduced number of unknowns. The results computed for the studied simply supported FG nanoplates are compared with those published in the open literature. Several parametric studies are performed to illustrate various influences of the plate geometry, material inhomogeneity, elastic damping coefficient, and nonlocal effect on the stresses, frequency, and central deflection of FG nanoplates.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Akbas, S.D., Wave Propagation of a Functionally Graded Beam in Thermal Environments, Steel Compos. Struct., 2015, vol. 19, no. 6, pp. 1421–1447. https://doi.org/10.12989/SCS.2015.19.6.142110.12989/SCS.2015.19.6.1421 ↗
2. Daouadji, T.H. and Hadji, L., Analytical Solution of Nonlinear Cylindrical Bending for Functionally Graded Plates, Geomech. Eng., 2015, vol. 9, no. 5, pp. 631–644. https://doi.org/10.12989/GAE.2015.9.5.63110.12989/GAE.2015.9.5.631 ↗
3. Mehar, K. and Panda, S.K., Nonlinear Static Behavior of FG-CNT Reinforced Composite Flat Panel under Thermomechanical Load, J. Aerospace Eng., 2017, vol. 30, no. 3, p. 04016100. https://doi.org/10.1061/(ASCE)AS.1943-5525.000070610.1061/(ASCE)AS.1943-5525.0000706 ↗
4. Mehar, K. and Panda, S.K., Numerical Investigation of Nonlinear Thermomechanical Deflection of Functionally Graded CNT Reinforced Doubly Curved Composite Shell Panel under Different Mechanical Loads, Compos. Struct., 2017, vol. 161, pp. 287–298. https://doi.org/10.1016/j.compstruct.2016.10.13510.1016/j.compstruct.2016.10.135 ↗
5. Mehar, K. and Panda, S.K., Thermoelastic Flexural Analysis of FG-CNT Doubly Curved Shell Panel, Aircraft Eng. Aerospace Technol., 2018, vol. 90, pp. 11–23. https://doi.org/10.1108/AEAT-11-2015-023710.1108/AEAT-11-2015-0237 ↗
6. Ahmed, R.A., Fenjan, R.M., and Faleh, N.M., Analyzing Post-Buckling Behavior of Continuously Graded FG Nanobeams with Geometrical Imperfections, Geomech. Eng., 2019, vol. 17, no. 2, pp. 175–180. https://doi.org/10.12989/gae.2019.17.2.17510.12989/gae.2019.17.2.175 ↗
7. Madenci, E., A Refined Functional and Mixed Formulation to Static Analyses of FGM Beams, Struct. Eng. Mech., 2019, vol. 69, no. 4, pp. 427–437. https://doi.org/10.12989/sem.2019.69.4.42710.12989/sem.2019.69.4.427 ↗
8. Avcar, M., Free Vibration of Imperfect Sigmoid and Power Law Functionally Graded Beams, Steel Compos. Struct., 2019, vol. 30, no. 6, pp. 603–615. https://doi.org/10.12989/SCS.2019.30.6.60310.12989/SCS.2019.30.6.603 ↗
9. Selmi, A., Exact Solution for Nonlinear Vibration of Clamped-Clamped Functionally Graded Buckled Beam, Smart Struct. Syst., 2020, vol. 26, no. 3, pp. 361–371. https://doi.org/10.12989/SSS.2020.26.3.36110.12989/SSS.2020.26.3.361 ↗
10. Vinyas, M., On Frequency Response of Porous Functionally Graded Magneto-Electro-Elastic Circular and Annular Plates with Different Electro-Magnetic Conditions Using HSDT, Compos. Struct., 2020, vol. 240, p. 112044. https://doi.org/10.1016/j.compstruct.2020.11204410.1016/j.compstruct.2020.112044 ↗
11. Hadji, L., Influence of the Distribution Shape of Porosity on the Bending of FGM Beam Using a New Higher Order Shear Deformation Model, Smart Struct. Syst., 2020, vol. 26, no. 2, pp. 253–262. https://doi.org/10.12989/sss.2020.26.2.25310.12989/sss.2020.26.2.253 ↗
12. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M., and Benachour, A., Impact of the Homogenization Models on the Thermoelastic Response of FG Plates on Variable Elastic Foundation, Geomech. Eng., 2020, vol. 22, no. 1, pp. 65–80. https://doi.org/10.12989/gae.2020.22.1.06510.12989/gae.2020.22.1.065 ↗
13. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S., and Benachour, A., 2D and Quasi 3D Computational Models for Thermoelastic Bending of FG Beams on Variable Elastic Foundation: Effect of the Micromechanical Models, Geomech. Eng., 2020, vol. 22, no. 4, pp. 361–374. https://doi.org/10.12989/gae.2020.22.4.36110.12989/gae.2020.22.4.361 ↗
14. Zhou, C., Zhan, Z., Zhang, J., Fang, Y., and Tahouneh, V., Vibration Analysis of FG Porous Rectangular Plates Reinforced by Graphene Platelets, Steel Compos. Struct. Int. J., 2020, vol. 34, no. 2, pp. 215–226. http://dx.doi.org/10.12989/scs.2020.34.2.215
15. Arefi, M. and Żur, K.K., Free Vibration Analysis of Functionally Graded Cylindrical Nanoshells Resting on Pasternak Foundation Based on Two-Dimensional Analysis, Steel Compos. Struct. Int. J., 2020, vol. 34, no. 4, pp. 615–623. http://dx.doi.org/10.12989/scs.2020.34.4.615
16. Nazemnezhad, R. and Shokrollahi, H., Free Axial Vibration of Cracked Axially Functionally Graded Nanoscale Rods Incorporating Surface Effect, Steel Compos. Struct. Int. J., 2020, vol. 35, no. 3, pp. 449–462. http://dx.doi.org/10.12989/scs.2020.35.3.449
17. She, G.L., Liu, H.B., and Karami, B., On Resonance Behavior of Porous FG Curved Nanobeams, Steel Compos. Struct., 2020, vol. 36, no. 2, pp. 179–186. http://dx.doi.org/10.12989/scs.2020.36.2.179
18. Yuan, Y., Zhao, K., Zhao, Y., and Kiani, K., Nonlocal-Integro-Vibro Analysis of Vertically Aligned Monolayered Nonuniform FGM Nanorods, Steel Compos. Struct., 2020, vol. 37, no. 5, pp. 551–569. http://dx.doi.org/10.12989/scs.2020.37.5.551
19. Noroozi, R., Barati, A., Kazemi, A., Norouzi, S., and Hadi, A., Torsional Vibration Analysis of Bi-Directional FG Nano-Cone with Arbitrary Cross-Section Based on Nonlocal Strain Gradient Elasticity, Adv. Nano Res., 2020, vol. 8, no. 1, pp. 13–24. http://dx.doi.org/10.12989/anr.2020.8.1.013
20. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A., and Hadi, A., Free Vibrations Analysis of Arbitrary Three-Dimensionally FGM Nanoplates, Adv. Nano Res., 2020, vol. 8, no. 2, pp. 115–134. http://dx.doi.org/10.12989/anr.2020.8.2.115
21. Mirjavadi, S.S., Forsat, M., Nia, A.F., Badnava, S., and Hamouda, A.M.S., Nonlocal Strain Gradient Effects on Forced Vibrations of Porous FG Cylindrical Nanoshells, Adv. Nano Res., 2020, vol. 8, no. 2, pp. 149–156. http://dx.doi.org/10.12989/anr.2020.8.2.149
22. Nejadi, M.M. and Mohammadimehr, M., Buckling Analysis of Nano Composite Sandwich Euler–Bernoulli Beam Considering Porosity Distribution on Elastic Foundation Using DQM, Adv. Nano Res., 2020, vol. 8, no. 1, pp. 59–68. http://dx.doi.org/10.12989/anr.2020.8.1.059
23. Ahmed, R.A., Al-Maliki, A.F., and Faleh, N.M., Dynamic Characteristics of Multi-Phase Crystalline Porous Shells with Using Strain Gradient Elasticity, Adv. Nano Res, 2020, vol. 8, no. 2, pp. 157–167. http://dx.doi.org/10.12989/anr.2020.8.2.157
24. Yaylacı, M., Eyüboğlu, A., Adıyaman, G., Yaylacı, E.U., Öner, E., and Birinci, A., Assessment of Different Solution Methods for Receding Contact Problems in Functionally Graded Layered Mediums, Mech. Mater., 2021, vol. 154, p. 103730. https://doi.org/10.1016/j.mechmat.2020.10373010.1016/j.mechmat.2020.103730 ↗
25. Yaylaci, M., Yayli, M., Yaylaci, E.U., Olmez, H., and Birinci, A., Analyzing the Contact Problem of a Functionally Graded Layer Resting on an Elastic Half Plane with Theory of Elasticity, Finite Element Method and Multilayer Perceptron, Struct. Eng. Mech., 2021, vol. 78, no. 5, pp. 585–597. https://doi.org/10.12989/sem.2021.78.5.58510.12989/sem.2021.78.5.585 ↗
26. Yaylaci, M., Adiyaman, G., Oner, E., and Birinci, A., Investigation of Continuous and Discontinuous Contact Cases in the Contact Mechanics of Graded Materials Using Analytical Method and FEM, Comp. Concrete, 2021, vol. 27, no. 3, pp. 199–210. https://doi.org/10.12989/cac.2021.27.3.19910.12989/cac.2021.27.3.199 ↗
27. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A., and Mahmoud, S.R., A Novel Refined Plate Theory for Stability Analysis of Hybrid and Symmetric S-FGM Plates, Struct. Eng. Mech., 2018, vol. 68, no. 6, pp. 661–675. https://doi.org/10.12989/SEM.2018.68.6.66110.12989/SEM.2018.68.6.661 ↗
28. Craciunescu, C.M. and Wuttig, M., New Ferromagnetic and Functionally Grade Shape Memory Alloys, J. Optoelectron. Adv. Mater., 2003, vol. 5, no. 1, pp. 139–146. https://doi.org/10.1002/chin.20033923410.1002/chin.200339234 ↗
29. Fu, Y., Du, H., and Zhang, S., Functionally Graded TiN/TiNi Shape Memory Alloy Films, J. Mater. Lett., 2003, vol. 57, no. 20, pp. 2995–2999. https://doi.org/10.1016/S0167-577X(02)01419-210.1016/S0167-577X(02)01419-2 ↗
30. Fu, Y., Du, H., Huang, W., Zhang, S., and Hu, M., TiNi-Based Thin Films in MEMS Applications: A Review, Sens. Actuat. A. Phys., 2004, vol. 112, no. 2–3, pp. 395–408. https://doi.org/10.1016/j.sna.2004.02.01910.1016/j.sna.2004.02.019 ↗
31. Witvrouw, A. and Mehta, A., The Use of Functionally Graded Poly-SiGe Layers for MEMS Applications, Mater. Sci. Forum, 2005, vol. 492, pp. 255–260. https://doi.org/10.4028/www.scientific.net/MSF.492-493.25510.4028/www.scientific.net/MSF.492-493.255 ↗
32. Lee, Z., Ophus, C., Fischer, L.M., Nelson-Fitzpatrick, N., Westra, K.L., Evoy, S., Radmilovic, V., Dahmen, U., and Mitlin, D., Metallic NEMS Components Fabricated from Nanocomposite Al–Mo Films, J. Nanotechnol., 2006, vol. 17, no. 12, pp. 3063–3070. https://doi.org/10.1088/0957-4484/17/12/04210.1088/0957-4484/17/12/042 ↗
33. Fleck, N., Muller, G., Ashby, M., and Hutchinson, J., Strain Gradient Plasticity: Theory and Experiment, Acta Metall. Mater., 1994, vol. 42, pp. 475–487. https://doi.org/10.1016/0956-7151(94)90502-910.1016/0956-7151(94)90502-9 ↗
34. Ma, Q. and Clarke, D.R., Size Dependent Hardness of Silver Single Crystals, J. Mater. Res., 1995, vol. 10, pp. 853–863. https://doi.org/10.1557/JMR.1995.085310.1557/JMR.1995.0853 ↗
35. Chong, A., Yang, F., Lam, D., and Tong, P., Torsion and Bending of Micron-Scaled Structures, J. Mater. Res., 2001, vol. 16, pp. 1052–1058. https://doi.org/10.1557/JMR.2001.014610.1557/JMR.2001.0146 ↗
36. Yang, F., Chong, A.C.M., Lam, D.C.C., and Tong, P., Couple Stress Based Strain Gradient Theory for Elasticity, Int. J. Solids Struct., 2002, vol. 39, pp. 2731–2743. https://doi.org/10.1016/S0020-7683(02)00152-X10.1016/S0020-7683(02)00152-X ↗
37. Attia, M.A., On the Mechanics of Functionally Graded Nanobeams with the Account of Surface Elasticity, Int. J. Eng. Sci., 2017, vol. 115, pp. 73–101. https://doi.org/10.1016/j.ijengsci.2017.03.01110.1016/j.ijengsci.2017.03.011 ↗
38. Fenjan, R.M., Faleh, N.M., and Ahmed, R.A., Geometrical Imperfection and Thermal Effects on Nonlinear Stability of Microbeams Made of Graphene-Reinforced Nano-Composites, Adv. Nano Res., 2020, vol. 9, no. 3, pp. 147–156. https://doi.org/10.12989/ANR.2020.9.3.14710.12989/ANR.2020.9.3.147 ↗
39. Aifantis, E.C., Strain Gradient Interpretation of Size Effects, Int. J. Fract., 1999, vol. 95, pp. 1–4. https://doi.org/10.1007/978-94-011-4659-3_1610.1007/978-94-011-4659-3_16 ↗
40. Sadeghi, H., Baghani, M., and Naghdabadi, R., Strain Gradient Elasticity Solution for Functionally Graded Micro-Cylinders, Int. J. Eng. Sci., 2012, vol. 50, no. 1, pp. 22–30. https://doi.org/10.1016/j.ijengsci.2011.09.00610.1016/j.ijengsci.2011.09.006 ↗
41. Karami, B. and Karami, S., Buckling Analysis of Nanoplate-Type Temperature-Dependent Heterogeneous Materials, Adv. Nano Res., 2019, vol. 7, no. 1, pp. 51–61. https://doi.org/10.12989/ANR.2019.7.1.05110.12989/ANR.2019.7.1.051 ↗
42. Fenjan, R.M., Faleh, N.M., and Ridha, A.A., Strain Gradient Based Static Stability Analysis of Composite Crystalline Shell Structures Having Porosities, Steel Compos. Struct. Int. J., 2020, vol. 36, no. 6, pp. 631–642. http://dx.doi.org/10.12989/scs.2020.36.6.631
43. Gurtin, M.E., Weissmuller, J., and Larche, F., The General Theory of Curved Deformable Interfaces in Solids at Equilibrium, Philos. Mag. A, 1998, vol. 78, no. 5, pp. 1093–1109. https://doi.org/10.1080/0141861980823997710.1080/01418619808239977 ↗
44. Eringen, A.C. and Edelen, D.G.B., On Nonlocal Elasticity, Int. J. Eng. Sci., 1972, vol. 10, pp. 233–248. https://doi.org/10.1016/0020-7225(72)90039-010.1016/0020-7225(72)90039-0 ↗
45. Eringen, A.C., Theory of Micropolar Plates, Z. Angew. Math. Phys., 1967, vol. 18, pp. 12–30. https://doi.org/10.1007/BF0159389110.1007/BF01593891 ↗
46. Eringen, A.C., On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, J. Appl. Phys., 1983, vol. 54, pp. 4703–4710. https://doi.org/10.1063/1.33280310.1063/1.332803 ↗
47. Eringen, A.C., Nonlocal Continuum Field Theories, New York: Springer, 2002. https://doi.org/10.1115/1.155343410.1115/1.1553434 ↗
48. Reddy, J.N., Nonlocal Theories for Bending, Buckling and Vibration of Beams, Int. J. Eng. Sci., 2007, vol. 45, no. 2, pp. 288–307. https://doi.org/10.1016/j.ijengsci.2007.04.00410.1016/j.ijengsci.2007.04.004 ↗
49. Ece, M.C. and Aydogdu, M., Nonlocal Elasticity Effect on Vibration of In-Plane Loaded Double-Walled Carbon Nano-Tubes, Acta Mech., 2007, vol. 190, no. 1–4, pp. 185–195. https://doi.org/10.1007/s00707-006-0417-510.1007/s00707-006-0417-5 ↗
50. Reddy, J.N. and Pang, S.D., Nonlocal Continuum Theories of Beams for The Analysis of Carbon Nanotubes, J. Appl. Phys., 2008, vol. 103, no. 2, p. 023511. https://doi.org/10.1063/1.283343110.1063/1.2833431 ↗
51. Aghababaei, R. and Reddy, J.N., Nonlocal Third-Order Shear Deformation Plate Theory with Application to Bending and Vibration of Plates, J. Sound Vib., 2009, vol. 326, no. 1, pp. 277–289. https://doi.org/10.1016/j.jsv.2009.04.04410.1016/j.jsv.2009.04.044 ↗
52. Samaei, A.T. and Mirsayar, M.M., Buckling Analysis of Multi-Walled Carbon Nanotubes with Consideration of Small Scale Effects, J. Comput. Theor. Nanosci., 2011, vol. 8, no. 11, pp. 2214–2219. https://doi.org/10.1166/jctn.2011.194610.1166/jctn.2011.1946 ↗
53. Hashemi, S.H. and Samaei, A.T., Buckling Analysis of Micro/Nanoscale Plates via Nonlocal Elasticity Theory, Physica E, 2011, vol. 43, no. 7, pp. 1400–1404. https://doi.org/10.1016/j.physe.2011.03.01210.1016/j.physe.2011.03.012 ↗
54. Ke, L.L, Wang, Y.S, Yang, J., and Kitipornchai, S., Free Vibration of Size-Dependent Magneto-Electro-Elastic Nanoplates Based on the Nonlocal Theory, Acta Mech. Sin., 2014, vol. 30, no. 4, pp. 516–525. https://doi.org/10.1007/s10409-014-0072-310.1007/s10409-014-0072-3 ↗
55. Mehar, K. and Panda, S.K., Multiscale Modeling Approach for Thermal Buckling Analysis of Nanocomposite Curved Structure, Adv. Nano Res., 2019, vol. 7, no. 3, pp. 181–190. https://doi.org/10.12989/ANR.2019.7.3.18110.12989/ANR.2019.7.3.181 ↗
56. Shahsavari, D., Karami, B., and Janghorban, M., Size-Dependent Vibration Analysis of Laminated Composite Plates, Adv. Nano Res., 2019, vol. 7, no. 5, pp. 337–349. https://doi.org/10.12989/ANR.2019.7.5.33710.12989/ANR.2019.7.5.337 ↗
57. Almitani, K.H., Abdelrahman, A.A., and Eltaher, M.A., Stability of Perforated Nanobeams Incorporating Surface Energy Effects, Steel Compos. Struct. Int. J., 2020, vol. 35, no. 4, pp. 555–566. http://dx.doi.org/10.12989/scs.2020.35.4.555
58. Ebrahimi, F., Hosseini, S.H.S., and Singhal, A., A Comprehensive Review on the Modeling of Smart Piezoelectric Nanostructures, Struct. Eng. Mech., 2020, vol. 74, no. 5, pp. 611–633. http://dx.doi.org/10.12989/sem.2020.74.5.611
59. Karami, B., Gheisari, P., Nazemosadat, S.M.R., Akbari, P., Shahsavari, D., and Naghizadeh, M., Elastic Wave Characteristics of Graphene Nanoplatelets Reinforced Composite Nanoplates, Struct. Eng. Mech. Int. J., 2020, vol. 74, no. 6, pp. 809–819. http://dx.doi.org/10.12989/sem.2020.74.6.809
60. Eltaher, M.A. and Abdelrahman, A.A., Bending Behavior of Squared Cutout Nanobeams Incorporating Surface Stress Effects, Steel Compos. Struct. Int. J., 2020, vol. 36, no. 2, pp. 143–161. http://dx.doi.org/10.12989/scs.2020.36.2.143
61. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M., and Bensattalah, T., Porosity-Dependent Free Vibration Analysis of FG Nanobeam Using Non-Local Shear Deformation and Energy Principle, Adv. Nano Res., 2020, vol. 8, no. 1, pp. 37–47. https://doi.org/10.12989/anr.2020.8.1.03710.12989/anr.2020.8.1.037 ↗
62. Bouhadra, A., Menasria, A., and Rachedi, M.A., Boundary Conditions Effect for Buckling Analysis of Porous Functionally Graded Nanobeam, Adv. Nano Res., 2021, vol. 10, no. 4, pp. 313–325. https://doi.org/10.12989/ANR.2021.10.4.31310.12989/ANR.2021.10.4.313 ↗
63. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S., and Rabczuk, T., Size-Dependent Free Flexural Vibration Behavior of Functionally Graded Nanoplates, Comput. Mater. Sci., 2012, vol. 65, pp. 74–80. https://doi.org/10.1016/j.commatsci.2012.06.03110.1016/j.commatsci.2012.06.031 ↗
64. Eltaher, M.A., Emam, S.A., and Mahmoud, F.F., Free Vibration Analysis of Functionally Graded Size-Dependent Nanobeams, Appl. Math. Comput., 2012, vol. 218, no. 14, pp. 7406–7420. https://doi.org/10.1016/j.amc.2011.12.09010.1016/j.amc.2011.12.090 ↗
65. Hashemi, S.H., Bedroud, M., and Nazemnezhad, R., An Exact Analytical Solution for Free Vibration of Functionally Graded Circular/Annular Mindlin Nanoplates via Nonlocal Elasticity, Compos. Struct., 2013, vol. 103, pp. 108–118. https://doi.org/10.1016/j.compstruct.2013.02.02210.1016/j.compstruct.2013.02.022 ↗
66. Nazemnezhad, R. and Hashemi, S.H., Nonlocal Nonlinear Free Vibration of Functionally Graded Nanobeams, Comp. Struct., 2014, vol. 110, pp. 192–199. https://doi.org/10.1016/j.compstruct.2013.12.00610.1016/j.compstruct.2013.12.006 ↗
67. Hashemi, S.H., Nazemnezhad, R., and Bedroud, M., Surface Effects on Nonlinear Free Vibration of Functionally Graded Nanobeams Using Nonlocal Elasticity, Appl. Math. Model., 2014, vol. 38, no. 14, pp. 3538–3553. https://doi.org/10.1016/j.apm.2013.11.06810.1016/j.apm.2013.11.068 ↗
68. Hashemi, S.H., Nahas, I., Fakher, M., and Nazemnezhad, R., Surface Effects on Free Vibration of Piezoelectric Functionally Graded Nanobeams Using Nonlocal Elasticity, Acta Mech., 2014, vol. 225, no. 6, pp. 1555–1564. https://doi.org/10.1007/s00707-013-1014-z10.1007/s00707-013-1014-z ↗
69. Amara, K., Tounsi, A., Mechab, I., and Adda-Bedia, E.A., Nonlocal Elasticity Effect on Column Buckling of Multiwalled Carbon Nanotubes under Temperature Field, Appl. Math. Model., 2010, vol. 34, pp. 3933–3942. https://doi.org/10.1016/j.apm.2010.03.02910.1016/j.apm.2010.03.029 ↗
70. Behshad, A., Shokravi, M., Alavijeh, A.S., and Karami, H., Elastic Wave Propagation Analysis in Sandwich Nanoplate Assuming Size Effects, Steel Compos. Struct., 2023, vol. 47, no. 1, pp. 71–77. https://doi.org/10.12989/SCS.2023.47.1.07110.12989/SCS.2023.47.1.071 ↗
71. Arshadi, K. and Arefi, M., Free Vibration Analysis of Sandwich Cylindrical Panel Composed of Graphene Nanoplatelets Reinforcement Core Integrated with Piezoelectric Face-Sheets, Steel Compos. Struct., 2024, vol. 50, no. 1, pp. 63–75. https://doi.org/10.12989/SCS.2024.50.1.06310.12989/SCS.2024.50.1.063 ↗
72. Wang, H. and Guo, J., Nonlocal Bending, Vibration and Buckling of One-Dimensional Hexagonal Quasicrystal Layered Nanoplates with Imperfect Interfaces, Struct. Eng. Mech., 2024, vol. 89, no. 6, pp. 557–570. https://doi.org/10.12989/SEM.2024.89.6.55710.12989/SEM.2024.89.6.557 ↗
73. Esen, I., Alazwari, M.A., Almitani, K.H., Eltaher, M.A., and Abdelrahman, A., Dynamic Vibration Response of Functionally Graded Porous Nanoplates in Thermal and Magnetic Fields under Moving Load, Adv. Nano Res., 2023, vol. 14, no. 5, pp. 475–493. https://doi.org/10.12989/ANR.2023.14.5.47510.12989/ANR.2023.14.5.475 ↗
74. Zhao, J.-L., She, G.-L., Wu, F., Yuan, S.-J., Bai, R.-Q., Pu, H.-Y., Wang, S., and Luo, J., Guided Waves of Porous FG Nanoplates with Four Edges Clamped, Adv. Nano Res., 2022, vol. 13, no. 5, pp. 465–474. https://doi.org/10.12989/ANR.2022.13.5.46510.12989/ANR.2022.13.5.465 ↗
75. Liu, C., Yu, J., Zhang, B., Zhang, X., and Wang, X., Propagating and Evanescent Waves in a Functionally Graded Nanoplate Based on Nonlocal Theory, Adv. Nano Res., 2023, vol. 14, no. 5, pp. 463–474. https://doi.org/10.12989/ANR.2023.14.5.46310.12989/ANR.2023.14.5.463 ↗
76. Zhu, J., Lai, Z., Yin, Z., Jeon, J., and Lee, S., Fabrication of ZrO2-NiCr Functionally Graded Material by Powder Metallurgy, Mater. Chem. Phys., 2001, vol. 68, no. 1–3, pp. 130–135. https://doi.org/10.1016/S0254-0584(00)00355-210.1016/S0254-0584(00)00355-2 ↗
77. Li, J.F., Takagi, K., Ono, M., Pan, W., Watanabe, R., Almajid, A., and Taya, M., Fabrication and Evaluation of Porous Piezoelectric Ceramics and Porosity-Graded Piezoelectric Actuators, J. Am. Ceram. Soc., 2003, vol. 86, pp. 1094–1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x10.1111/j.1151-2916.2003.tb03430.x ↗
78. Aqida, S., Ghazali, M., and Hashim, J., Effects of Porosity on Mechanical Properties of Metal Matrix Composite: An Overview, J. Teknol., 2004, vol. 40, no. 1, pp. 17–32. https://doi.org/10.11113/jt.v40.39510.11113/jt.v40.395 ↗
79. Benferhat, R., Hassaine Daouadji, T., Hadji, L., and Said Mansour, M., Static Analysis of the FGM Plate with Porosities, Steel Compos. Struct., 2016, vol. 21, no. 1, pp. 123–136. https://doi.org/10.12989/scs.2016.21.1.12310.12989/scs.2016.21.1.123 ↗
80. Benferhat, R., Daouadji, T.H., Mansour, M.S., and Hadji, L., Effect of Porosity on the Bending and Free Vibration Response of Functionally Graded Plates Resting on Winkler–Pasternak Foundations, Earthq. Struct., 2016, vol. 10, no. 6, pp. 1429–1449. https://doi.org/10.12989/eas.2016.10.6.142910.12989/eas.2016.10.6.1429 ↗
81. Akbaş, Ş.D., Forced Vibration Analysis of Functionally Graded Porous Deep Beams, Compos. Struct., 2018, vol. 186, pp. 293–302. https://doi.org/10.1016/j.compstruct.2017.12.01310.1016/j.compstruct.2017.12.013 ↗
82. Abdelbari, S., Attia, A., Bourada, F., Bousahla, A.A., Tounsi, A., and Ghazwani, M.H., Investigation of Dynamic Characteristics of Imperfect FG Beams on the Winkler–Pasternak Foundation under Thermal Loading, Phys. Mesomech., 2023, vol. 26, no. 5, pp. 557–572. https://doi.org/10.1134/S102995992305008910.1134/S1029959923050089 ↗
83. Xu, J.-Q., She, G.-L., Li, Y.-P., and Gan, L.-L., Nonlinear Resonances of Nonlocal Strain Gradient Nanoplates Made of Functionally Graded Materials Considering Geometric Imperfection, Steel Compos. Struct., 2023, vol. 47, no. 6, pp. 795–811. https://doi.org/10.12989/SCS.2023.47.6.79510.12989/SCS.2023.47.6.795 ↗
84. Wang, Y., Tham, L., and Cheung, Y., Beams and Plates on Elastic Foundations: A Review, Prog. Struct. Eng. Mater., 2005, vol. 7, pp. 174–182. https://doi.org/10.1002/pse.20210.1002/pse.202 ↗
85. Ebrahimi, F. and Barati, M.R., Hydrothermal Effects on Vibration Characteristics of Viscoelastic FG Nanobeams Based on Nonlocal Strain Gradient Theory, Compos. Struct., 2017, vol. 159, pp. 433–444. https://doi.org/10.1016/j.compstruct.2016.09.09210.1016/j.compstruct.2016.09.092 ↗
86. Ghumare, S.M. and Sayyad, A.S., Analytical Solution Using Fifth Order Shear and Normal Deformation Theory for FG Plates Resting on Elastic Foundation Subjected to Hygro-Thermo-Mechanical Loading, Mater. Today Proc., 2020, vol. 21, pp. 1089–1093. https://doi.org/10.1016/j.matpr.2020.01.01010.1016/j.matpr.2020.01.010 ↗
87. Nebab, M., Ait Atmane, H., Bennai, R., and Tahar, B., Effect of Nonlinear Elastic Foundations on Dynamic Behavior of FG Plates Using Four-Unknown Plate Theory, Earthq. Struct., 2019, vol. 17, no. 5, pp. 447–462. https://doi.org/10.12989/eas.2019.17.5.44710.12989/eas.2019.17.5.447 ↗
88. Akbaş, Ş.D., Fageehi, Y.A., Assie, A.E., and Eltaher, M.A., Dynamic Analysis of Viscoelastic Functionally Graded Porous Thick Beams under Pulse Load, Eng. Comp., 2020, vol. 38, pp. 1–13. https://doi.org/10.1007/s00366-020-01070-310.1007/s00366-020-01070-3 ↗
89. Wattanasakulpong, N. and Ungbhakorn, V., Linear and Nonlinear Vibration Analysis of Elastically Restrained Ends FGM Beams with Porosities, Aerosp. Sci. Technol., 2014, vol. 32, no. 1, pp. 111–120. https://doi.org/10.1016/j.ast.2013.12.00210.1016/j.ast.2013.12.002 ↗
90. Gupta, A. and Talha, M., Influence of Porosity on the Flexural and Vibration Response of Gradient Plate Using Nonpolynomial Higher-Order Shear and Normal Deformation Theory, Int. J. Mech. Mater. Des., 2018, vol. 14, no. 2, pp. 277–296. https://doi.org/10.1007/s10999-017-9369-210.1007/s10999-017-9369-2 ↗
91. Wang, Q., Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics, J. Appl. Phys., 2005, vol. 98, p. 124301. https://doi.org/10.1002/pse.20210.1002/pse.202 ↗
92. Zenkour, A.M., Generalized Shear Deformation Theory for Bending Analysis of Functionally Graded Plates, Appl. Math. Model., 2006, vol. 30, pp. 67–84. https://doi.org/10.1016/j.apm.2005.03.00910.1016/j.apm.2005.03.009 ↗
93. Carrera, E., Brishetto, S., and Robaldo, A., Variable Kinematic Model for the Analysis of Functionally Graded Material Plates, AIAA J., 2008, vol. 46, pp. 194–203. https://doi.org/10.2514/1.3249010.2514/1.32490 ↗
94. Sobhy, M., A Comprehensive Study on FGM Nanoplates Embedded in an Elastic Medium, Compos. Struct., 2015, vol. 134, pp. 966–980. https://doi.org/10.1016/j.compstruct.2015.08.10210.1016/j.compstruct.2015.08.102 ↗
95. Yaylaci, M., The Investigation Crack Problem through Numerical Analysis, Struct. Eng. Mech. Int. J., 2016, vol. 57, no. 6, pp. 1143–1156. https://doi.org/10.12989/sem.2016.57.6.114310.12989/sem.2016.57.6.1143 ↗
96. Bourada, F., Amara, K., and Tounsi, A., Buckling Analysis of Isotropic and Orthotropic Plates Using a Novel Four Variable Refined Plate Theory, Steel Compos. Struct., 2016, vol. 21, no. 6, pp. 1287–1306. https://doi.org/10.12989/SCS.2016.21.6.128710.12989/SCS.2016.21.6.1287 ↗
97. Mehar, K., Panda, S.K., and Mahapatra, T.R., Thermoelastic Deflection Responses of CNT Reinforced Sandwich Shell Structure Using Finite Element Method, Sci. Iran., 2018, vol. 25, no. 5, pp. 2722–2737. https://doi.org/10.24200/sci.2017.452510.24200/sci.2017.4525 ↗
98. Mehar, K., Panda, S.K., and Patle, B.K., Stress, Deflection, and Frequency Analysis of CNT Reinforced Graded Sandwich Plate under Uniform and Linear Thermal Environment: A Finite Element Approach, Polymer Compos., 2018, vol. 39, no. 10, pp. 3792–3809. https://doi.org/10.1002/pc.2440910.1002/pc.24409 ↗
99. Mehar, K. and Panda, S.K., Nonlinear Finite Element Solutions of Thermoelastic Flexural Strength and Stress Values of Temperature Dependent Graded CNT-Reinforced Sandwich Shallow Shell Structure, Struct. Eng. Mech. Int. J., 2018, vol. 67, no. 6, pp. 565–578. https://doi.org/10.12989/sem.2018.67.6.56510.12989/sem.2018.67.6.565 ↗
100. Mehar, K. and Panda, S.K., Elastic Bending and Stress Analysis of Carbon Nanotube-Reinforced Composite Plate: Experimental, Numerical, and Simulation, Adv. Polymer Technol., 2018, vol. 37, no. 6, pp. 1643–1657. https://doi.org/10.1002/adv.2182110.1002/adv.21821 ↗