Natural Frequencies of Functionally Graded Sandwich Plates Resting on an Elastic Foundation Using Chebyshev Finite Element Method

1. Hosseini HS, Taher HRD, Akhavan H, Omidi M. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl. Math. Model. 2010;34(5):1276-91. Available from: https://doi.org/10.1016/j.apm.2009.08.008 Hosseini HS Taher HRD Akhavan H Omidi M. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory . Appl. Math. Model . 2010 ; 34 ( 5 ): 1276 - 91 . Available from: https://doi.org/10.1016/j.apm.2009.08.008 Search in Google Scholar

2. Reddy JN. Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 2000;47:663-84. Reddy JN. Analysis of functionally graded plates . Int. J. Numer. Methods Eng . 2000 ; 47 : 663 - 84 . Search in Google Scholar

3. Zenkour AM. Bending analysis of functionally graded sandwich plates using a simple four unknown shear and normal deformations theory. J. Sandw. Struct. Mater. 2013;15:629-56. Available from: https://doi.org/10.1177/1099636213498886 Zenkour AM. Bending analysis of functionally graded sandwich plates using a simple four unknown shear and normal deformations theory . J. Sandw. Struct. Mater . 2013 ; 15 : 629 - 56 . Available from: https://doi.org/10.1177/1099636213498886 Search in Google Scholar

4. Reddy JN. A general nonlinear third-order theory of functionally graded plates. Int. J. Aerosp. Lightweight Struct. 2011;1:1-21. Available from: https://doi.org/10.3850/S201042861100002X Reddy JN. A general nonlinear third-order theory of functionally graded plates . Int. J. Aerosp. Lightweight Struct . 2011 ; 1 : 1 - 21 . Available from: https://doi.org/10.3850/S201042861100002X Search in Google Scholar

5. Talha M, Singh BN. Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl. Math. Model. 2010;34:3991-4011. Available from: https://doi.org/10.1016/j.apm.2010.03.034 Talha M Singh BN. Static response and free vibration analysis of FGM plates using higher order shear deformation theory . Appl. Math. Model . 2010 ; 34 : 3991 - 4011 . Available from: https://doi.org/10.1016/j.apm.2010.03.034 Search in Google Scholar

6. Zenkour AM. Generalized shear deformation theory for bending analysis of functionally graded materials. Appl. Math. Model. 2006;30(1):67-84. Available from: https://doi.org/10.1016/j.apm.2005.03.009 Zenkour AM. Generalized shear deformation theory for bending analysis of functionally graded materials . Appl. Math. Model . 2006 ; 30 ( 1 ): 67 - 84 . Available from: https://doi.org/10.1016/j.apm.2005.03.009 Search in Google Scholar

7. Yaghoobi H, Fereidoon A. Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory. Compos. B: Eng. 2014;62:54-64. Available from: https://doi.org/10.1016/j.com-positesb.2014.02.014 Yaghoobi H Fereidoon A. Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory . Compos. B: Eng . 2014 ; 62 : 54 - 64 . Available from: https://doi.org/10.1016/j.com-positesb.2014.02.014 Search in Google Scholar

8. Sobhy M, Al-Mukahal FH. Magnetic control of vibrational behavior of smart FG sandwich plates with honeycomb core via a quasi 3D plate theory. Adv. Eng. Mater. 2023;25(13):2300096. Available from: https://doi.org/10.1002/adem.202300096 Sobhy M Al-Mukahal FH. Magnetic control of vibrational behavior of smart FG sandwich plates with honeycomb core via a quasi 3D plate theory . Adv. Eng. Mater . 2023 ; 25 ( 13 ): 2300096 . Available from: https://doi.org/10.1002/adem.202300096 Search in Google Scholar

9. Zarga D, Tounsi A, Bousahla AA, Bourada F, Mahmoud SR. Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory. Steel Compos. Struct. 2019;32(3):389-410. Available from: https://doi.org/10.12989/scs.2019.32.3.389 Zarga D Tounsi A Bousahla AA Bourada F Mahmoud SR. Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory . Steel Compos. Struct . 2019 ; 32 ( 3 ): 389 - 410 . Available from: https://doi.org/10.12989/scs.2019.32.3.389 Search in Google Scholar

10. Alibeigloo A, Alizadeh M. Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method. Eur. J. Mech. A/Solids. 2015;54:252-66. Available from: https://doi.org/10.1016/j.euromechsol.2015.06.011 Alibeigloo A Alizadeh M. Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method . Eur. J. Mech. A/Solids . 2015 ; 54 : 252 - 66 . Available from: https://doi.org/10.1016/j.euromechsol.2015.06.011 Search in Google Scholar

11. Natarajan S, Manickam G. Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite Elem. Anal. Des. 2012;57:32-42. Available from: https://doi.org/10.1016/j.finel.2012.03.006 Natarajan S Manickam G. Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite Elem . Anal. Des . 2012 ; 57 : 32 - 42 . Available from: https://doi.org/10.1016/j.finel.2012.03.006 Search in Google Scholar

12. Li Q, Iu VP, Kou KP. Three-dimensional vibration analysis of functionally graded material sandwich plates. J. Sound Vib. 2008;311:498– 515. Available from: https://doi.org/10.1016/j.jsv.2007.09.018 Li Q Iu VP Kou KP. Three-dimensional vibration analysis of functionally graded material sandwich plates . J. Sound Vib . 2008 ; 311 : 498 – 515 . Available from: https://doi.org/10.1016/j.jsv.2007.09.018 Search in Google Scholar

13. Liu N, Jeffers AE. Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory. Compos. Struct. 2017;176(15):143-53. Available from: https://doi.org/10.1016/j.compstruct.2017.05.037 Liu N Jeffers AE. Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory . Compos. Struct . 2017 ; 176 ( 15 ): 143 - 53 . Available from: https://doi.org/10.1016/j.compstruct.2017.05.037 Search in Google Scholar

14. Neves A, Ferreira A, Carrera E, Cinefra M, Roque C, Jorge R, Soares CM. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. B: Eng. 2013;44:657-74. Available from: https://doi.org/10.1016/j.compositesb.2012.01.089 Neves A Ferreira A Carrera E Cinefra M Roque C Jorge R Soares CM. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique . Compos. B: Eng . 2013 ; 44 : 657 - 74 . Available from: https://doi.org/10.1016/j.compositesb.2012.01.089 Search in Google Scholar

15. Wang Y, Tham L, Cheung Y. Beams and plates on elastic foundations: a review. Prog Struct Eng Mat. 2005;7:174–82. Available from: https://doi.org/10.1002/pse.202 Wang Y Tham L Cheung Y. Beams and plates on elastic foundations: a review . Prog Struct Eng Mat . 2005 ; 7 : 174 – 82 . Available from: https://doi.org/10.1002/pse.202 Search in Google Scholar

16. Winkler E. Die Lehre von der Elastizität und Festigkeit (The Theory of Elasticity and Stiffness), H. Dominicus, Prague, Czechoslovakia. 1867. Winkler E. Die Lehre von der Elastizität und Festigkeit (The Theory of Elasticity and Stiffness), H . Dominicus, Prague, Czechoslovakia . 1867 . Search in Google Scholar

17. Kolahchi R, Safari M, Esmailpour M. Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium, Compos. Struct. 2016;150:255–65. Available from: https://doi.org/10.1016/j.compstruct.2016.05.023 Kolahchi R Safari M Esmailpour M. Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium , Compos. Struct . 2016 ; 150 : 255 – 65 . Available from: https://doi.org/10.1016/j.compstruct.2016.05.023 Search in Google Scholar

18. Pasternak P. On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow. 1954. Pasternak P. On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture , Moscow . 1954 . Search in Google Scholar

19. Kneifati MC. Analysis of plates on a Kerr foundation model. J. Eng. Mech. 1985;111:1325–42. Kneifati MC. Analysis of plates on a Kerr foundation model . J. Eng. Mech . 1985 ; 111 : 1325 – 42 . Search in Google Scholar

20. Mohamed M, Samir B, Abdelkader M, Abdelouahed T, Abdelmoumen AB, Mahmoud SR. Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions. J. Sandw. Struct. Mater. 2021;23(3):1028-57. Available from: https://doi.org/10.1177/1099636219851281 Mohamed M Samir B Abdelkader M Abdelouahed T Abdelmoumen AB Mahmoud SR. Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions . J. Sandw. Struct. Mater . 2021 ; 23 ( 3 ): 1028 - 57 . Available from: https://doi.org/10.1177/1099636219851281 Search in Google Scholar

21. Guerroudj HZ, Yeghnem R, Kaci A, Zaoui FZ, Benyoucef S. Eigenfre-quencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory. Smart Struct. Syst. 2018;22(1):121-32. Available from: https://doi.org/10.12989/sss.2018.22.1.121 Guerroudj HZ Yeghnem R Kaci A Zaoui FZ Benyoucef S. Eigenfre-quencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory . Smart Struct. Syst . 2018 ; 22 ( 1 ): 121 - 32 . Available from: https://doi.org/10.12989/sss.2018.22.1.121 Search in Google Scholar

22. Lazreg H, Mehmet A, Nafissa Z. Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation. Mater. Today: Proc. 2022;53(1):153-60. Available from: https://doi.org/10.1016/j.matpr.2021.12.485 Lazreg H Mehmet A Nafissa Z. Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation . Mater. Today: Proc . 2022 ; 53 ( 1 ): 153 - 60 . Available from: https://doi.org/10.1016/j.matpr.2021.12.485 Search in Google Scholar

23. Kurpa L, Shmatko T, Linnik A. Buckling Analysis of Functionally Graded Sandwich Plates Resting on an Elastic Foundation and Subjected to a Nonuniform Loading. Mech. Compos. Mater. 2023;59:645-58. Available from: https://doi.org/10.1007/s11029-023-10122-w Kurpa L Shmatko T Linnik A. Buckling Analysis of Functionally Graded Sandwich Plates Resting on an Elastic Foundation and Subjected to a Nonuniform Loading . Mech. Compos. Mater . 2023 ; 59 : 645 - 58 . Available from: https://doi.org/10.1007/s11029-023-10122-w Search in Google Scholar

24. Pham VV, Le QH. Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory. Def. Technol. 2022;18(3):490-508. Available from: https://doi.org/10.1016/j.dt.2021.03.006 Pham VV Le QH. Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory . Def. Technol . 2022 ; 18 ( 3 ): 490 - 508 . Available from: https://doi.org/10.1016/j.dt.2021.03.006 Search in Google Scholar

25. Dang TH, Yang DJ, Liu Y. Improvements in shear locking and spurious zero energy modes using Chebyshev finite element method. J. Comput. Inf. Sci. Eng. 2019;19:011006. Available from: https://doi.org/10.1115/1.4041829 Dang TH Yang DJ Liu Y. Improvements in shear locking and spurious zero energy modes using Chebyshev finite element method . J. Comput. Inf. Sci. Eng . 2019 ; 19 : 011006 . Available from: https://doi.org/10.1115/1.4041829 Search in Google Scholar

26. Ton-That HL, Nguyen-Van H, Chau-Dinh T. A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets. Arch. Appl. Mech. 2021;91:2435-66. Available from: https://doi.org/10.1007/s00419-021-01893-6 Ton-That HL Nguyen-Van H Chau-Dinh T. A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets . Arch. Appl. Mech . 2021 ; 91 : 2435 - 66 . Available from: https://doi.org/10.1007/s00419-021-01893-6 Search in Google Scholar

27. Fornberg B, Zuev J. The Runge Phenomenon and Spatially Variable Shape Parameters in RBF Interpolation. Comput. Math. Appl. 2007;54(3):379–98. Available from: https://doi.org/10.1016/j.camwa.2007.01.028 Fornberg B Zuev J. The Runge Phenomenon and Spatially Variable Shape Parameters in RBF Interpolation . Comput. Math. Appl . 2007 ; 54 ( 3 ): 379 – 98 . Available from: https://doi.org/10.1016/j.camwa.2007.01.028 Search in Google Scholar

28. Lee SJ. Free Vibration Analysis of Plates by Using a Four-Node Finite Element Formulated With Assumed Natural Transverse Shear Strain. J. Sound Vib. 2004;278(3):657–84. Available from: https://doi.org/10.1016/j.jsv.2003.10.018 Lee SJ. Free Vibration Analysis of Plates by Using a Four-Node Finite Element Formulated With Assumed Natural Transverse Shear Strain . J. Sound Vib . 2004 ; 278 ( 3 ): 657 – 84 . Available from: https://doi.org/10.1016/j.jsv.2003.10.018 Search in Google Scholar

29. Abassian F, Haswell DJ, Knowles NC. Free Vibration Benchmarks. National Agency for Finite Element Methods and Standards, Glasgow, UK. 1987. Abassian F Haswell DJ Knowles NC. Free Vibration Benchmarks . National Agency for Finite Element Methods and Standards , Glasgow, UK . 1987 . Search in Google Scholar

30. Shahsavari D, Shahsavari M, Li L, Karami B. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp. Sci. Technol. 2018;72:134-49. Available from: https://doi.org/10.1016/j.ast.2017.11.004 Shahsavari D Shahsavari M Li L Karami B. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation . Aerosp. Sci. Technol . 2018 ; 72 : 134 - 49 . Available from: https://doi.org/10.1016/j.ast.2017.11.004 Search in Google Scholar

31. Baferani AH, Saidi A, Ehteshami H. Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Compos. Struct. 2011;93(7):1842-53. Available from: https://doi.org/10.1016/j.compstruct.2011.01.020 Baferani AH Saidi A Ehteshami H. Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation . Compos. Struct . 2011 ; 93 ( 7 ): 1842 - 53 . Available from: https://doi.org/10.1016/j.compstruct.2011.01.020 Search in Google Scholar

32. Akavci S. Mechanical behaviour of functionally graded sandwich plates on elastic foundation. Compos. B: Eng. 2016;96:136-52. Available from: https://doi.org/10.1016/j.compositesb.2016.04.035 Akavci S. Mechanical behaviour of functionally graded sandwich plates on elastic foundation . Compos. B: Eng . 2016 ; 96 : 136 - 52 . Available from: https://doi.org/10.1016/j.compositesb.2016.04.035 Search in Google Scholar