On the effect of foam structures on thermo-mechanical vibration response of functionally graded piezoelectric smart plates
Source abstract
Abstract
Abstract This study models and investigates the effects of foam structure and thermal load on the thermomechanical vibration behavior of functionally graded (FGM) piezoelectric plates made of PZT-5H and BaTiO3. The Navier technique is used to solve the equation of motion of the plates, which is derived from Hamilton's principle and higher-order shear theory. The FGM plate is made of BaTiO3 on the bottom and PZT-5H solid/foam material on the top, and the study investigates four different foam models: uniform, symmetric, bottom, and top foam. In addition to temperature loading and applied external electric current, the study looked at how different material grading indices and foam topologies affected the smart plate's vibration buckling behavior. PZT-5H is the material with the highest thermal vibration buckling resistance of the solid smart plate, whereas the Symmetric Foam structure has the highest thermal resistance and the Uniform Foam structure has the lowest. In addition to the thermal load, the applied external electric potential causes a softening effect due to electro-elastic behavior, and the foam structure has been shown to improve the thermal vibration behavior of the smart FGM plate. It was also discovered that the usage of BaTiO3 and PZT-5H, as well as the foam structure, improved the electro-elastic behavior of the smart FGM plate.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Railway Engineering and Dynamics · Vibration and Dynamic Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (98)
Show source-provided references
1. Aabid, A., Parveez, B., Raheman, M.A., Ibrahim, Y.E., Anjum, A., Hrairi, M., Parveen, N., Mohammed Zayan, J.: A review of piezoelectric material-based structural control and health monitoring techniques for engineering structures: challenges and opportunities. Actuators 10(5), 101 (2021). https://doi.org/10.3390/act1005010110.3390/act10050101 ↗
2. Aktaş, K.G.: Three-dimensional thermomechanical wave propagation analysis of sandwich nanoplate with graphene-reinforced foam core and magneto-electro-elastic face layers using nonlocal strain gradient elasticity theory. Acta Mech. Mech. 235(9), 5587–5619 (2024). https://doi.org/10.1007/s00707-024-04001-110.1007/s00707-024-04001-1 ↗
3. Aktas, K.G.: 3D wave dispersion analysis of graphene platelet-reinforced ultra-stiff double functionally graded nanocomposite sandwich plates with metamaterial honeycomb core layer. Mech. Time-Depend. Mater. 28(3), 1873–1908 (2024). https://doi.org/10.1007/S11043-024-09726-Z10.1007/S11043-024-09726-Z ↗
4. Almajid, A., Taya, M., Takagi, K., Li, J.-F., Watanabe, R.: In: Davis, L.P. (Ed.) Fabrication and Modeling of Porous FGM Piezoelectric Actuators, pp. 467–476. https://doi.org/10.1117/12.47468310.1117/12.474683 ↗
5. Alshenawy, R., Sahmani, S., Safaei, B., Elmoghazy, Y., Al-Alwan, A., Nuwairan, M.A.: Three-dimensional nonlinear stability analysis of axial-thermal-electrical loaded FG piezoelectric microshells via MKM strain gradient formulations. Appl. Math. Comput. Comput. 439, 127623 (2023a). https://doi.org/10.1016/J.AMC.2022.12762310.1016/J.AMC.2022.127623 ↗
6. Alshenawy, R., Sahmani, S., Safaei, B., Elmoghazy, Y., Al-Alwan, A., Sobhy, M.: Nonlinear dynamical performance of microsize piezoelectric bridge-type energy harvesters based upon strain gradient-based meshless collocation approach. Eng. Anal. Boundary Elem. 151, 199–215 (2023b). https://doi.org/10.1016/j.enganabound.2023.03.00210.1016/j.enganabound.2023.03.002 ↗
7. Bajoria, K.M., Patare, S.A.: Shape control of hybrid functionally graded plate through smart application of piezoelectric material using simple plate theory. SN Appl. Sci. 3(2), 209 (2021). https://doi.org/10.1007/s42452-020-04121-y10.1007/s42452-020-04121-y ↗
8. Barati, M.R., Zenkour, A.M., Shahverdi, H.: Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos. Struct. 141, 203–212 (2016). https://doi.org/10.1016/j.compstruct.2016.01.05610.1016/j.compstruct.2016.01.056 ↗
9. Barati, M.R., Shahverdi, H., Zenkour, A.M.: Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory. Mech. Adv. Mater. Struct. 24(12), 987–998 (2017). https://doi.org/10.1080/15376494.2016.119679910.1080/15376494.2016.1196799 ↗
10. Belabed, Z., Bousahla, A.A., Tounsi, A.: Vibrational and elastic stability responses of functionally graded carbon nanotube reinforced nanocomposite beams via a new Quasi-3D finite element model. Comput. Concr. 34(5), 625–648 (2024a). https://doi.org/10.12989/cac.2024.34.5.62510.12989/cac.2024.34.5.625 ↗
11. Belabed, Z., Tounsi, A., Bousahla, A.A., Tounsi, A., Bourada, M., Al-Osta, M.A.: Free vibration analysis of bi-directional functionally graded beams using a simple and efficient finite element model. Struct. Eng. Mech. 90(3), 233–252 (2024b). https://doi.org/10.12989/sem.2024.90.3.23310.12989/sem.2024.90.3.233 ↗
12. Belabed, Z., Tounsi, A., Bousahla, A.A., Tounsi, A., Khedher, K.M., Salem, M.A.: Mechanical behavior analysis of FG-CNTRC porous beams resting on Winkler and Pasternak elastic foundations: a finite element approach. Comput. Concr. 34(4), 447–476 (2024c). https://doi.org/10.12989/CAC.2024.34.4.44710.12989/CAC.2024.34.4.447 ↗
13. Belabed, Z., Tounsi, A., Bousahla, A.A., Tounsi, A., Yaylacı, M.: Accurate free and forced vibration behavior prediction of functionally graded sandwich beams with variable cross-section: A finite element assessment. Mech. Based des. Struct. Mach. (2024d). https://doi.org/10.1080/15397734.2024.233791410.1080/15397734.2024.2337914 ↗
14. Berkia, A., Benguediab, M., Bouhadra, A., Mansouri, K., Tounsi, A., Chitour, M.: Influence of mechanical and geometric characteristics on thermal buckling of functionally graded sandwich plates. J. Nano- Electron. Phys. 14(3), 03031-1–03031-6 (2022). https://doi.org/10.21272/jnep.14(3).0303110.21272/jnep.14(3).03031 ↗
15. Bian, Z.G., Lim, C.W., Chen, W.Q.: On functionally graded beams with integrated surface piezoelectric layers. Compos. Struct. 72(3), 339–351 (2006). https://doi.org/10.1016/j.compstruct.2005.01.00510.1016/j.compstruct.2005.01.005 ↗
16. Biglar, M., Gromada, M., Stachowicz, F., Trzepieciński, T.: Synthesis of barium titanate piezoelectric ceramics for multilayer actuators (MLAs). Acta Mech. Autom. 11(4), 275–279 (2017). https://doi.org/10.1515/ama-2017-004210.1515/ama-2017-0042 ↗
17. Bose, A., Sathujoda, P.: Effect of thermal gradient on vibration characteristics of a functionally graded shaft system. Math. Model. Eng. Probl. 7(2), 212–222 (2020). https://doi.org/10.18280/mmep.07020710.18280/mmep.070207 ↗
18. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A., Bedia, E.A.A.: Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory. Struct. Eng. Mech. 57(4), 617–639 (2016). https://doi.org/10.12989/sem.2016.57.4.61710.12989/sem.2016.57.4.617 ↗
19. DinhDuc, N., Hong Cong, P.: Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations. J. Sandwich Struct. Mater. 20(2), 191–218 (2018). https://doi.org/10.1177/109963621664848810.1177/1099636216648488 ↗
20. Doroushi, A., Eslami, M.R., Komeili, A.: Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory. J. Intell. Mater. Syst. Struct. 22(3), 231–243 (2011). https://doi.org/10.1177/1045389X1139816210.1177/1045389X11398162 ↗
21. 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/10.1155/2021/552024010.1155/2021/5520240 ↗
22. Ebrahimi, F., Barati, M.R.: Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment. Int. J. Smart Nano Mater. 7(2), 69–90 (2016). https://doi.org/10.1080/19475411.2016.119155610.1080/19475411.2016.1191556 ↗
23. Ebrahimi, F., Sepiani, H.A.: Vibration and buckling analysis of cylindrical shells made of functionally graded materials under combined static and periodic axial forces. Adv. Compos. Lett. (2010). https://doi.org/10.1177/09636935100190020210.1177/096369351001900202 ↗
24. Ebrahimi, F., Ghasemi, F., Salari, E.: Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51(1), 223–249 (2016). https://doi.org/10.1007/s11012-015-0208-y10.1007/s11012-015-0208-y ↗
25. Ercument, D.B., Sahmani, S., Safaei, B.: A review on computational linear and nonlinear dynamic analysis of shell-type composite structures. Comput. Struct. 306, 107596 (2025). https://doi.org/10.1016/J.COMPSTRUC.2024.10759610.1016/J.COMPSTRUC.2024.107596 ↗
26. Eroğlu, M., Esen, İ, Koç, M.A.: Managing the surface piezoelectricity effect of the smart ZnO sandwich nanoplates using metal foam core layer and GPRL reinforced rim layers. Microsyst. Technol. (2024). https://doi.org/10.1007/s00542-024-05772-210.1007/s00542-024-05772-2 ↗
27. Esen, I., Özmen, R.: Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity. Compos. Struct. 296, 115878 (2022). https://doi.org/10.1016/j.compstruct.2022.11587810.1016/j.compstruct.2022.115878 ↗
28. Feng, J., Gao, C., Safaei, B., Qin, Z., Wu, H., Chu, F., Scarpa, F.: Exceptional damping of CFRPs: unveiling the impact of carbon fiber surface treatments. Compos. B Eng. 290, 111973 (2025). https://doi.org/10.1016/J.COMPOSITESB.2024.11197310.1016/J.COMPOSITESB.2024.111973 ↗
29. Garg, A., Chalak, H.D., Li, L., Belarbi, M.-O., Sahoo, R., Mukhopadhyay, T.: Vibration and buckling analyses of sandwich plates containing functionally graded metal foam core. Acta Mech. Solida Sin. 35(4), 1–16 (2022). https://doi.org/10.1007/s10338-021-00295-z10.1007/s10338-021-00295-z ↗
30. Gohari, S., Mozafari, F., Moslemi, N., Mouloodi, S., Sharifi, S., Rahmanpanah, H., Burvill, C.: Analytical solution of the electro-mechanical flexural coupling between piezoelectric actuators and flexible-spring boundary structure in smart composite plates. Arch. Civ. Mech. Eng. 21(1), 33 (2021). https://doi.org/10.1007/s43452-021-00180-z10.1007/s43452-021-00180-z ↗
31. Guo, X., Kong, D.: Simulation analysis of thermal shock response of piezoelectric shock wave pressure sensor. Vibroeng. Procedia 51, 134–140 (2023). https://doi.org/10.21595/vp.2023.2359210.21595/vp.2023.23592 ↗
32. Huang, Y., Zhang, Z., Li, C., Wang, J., Li, Z., Mao, K.: Sound radiation of orthogonal antisymmetric composite laminates embedded with pre-strained SMA wires in thermal environment. Materials 13(17), 3657 (2020). https://doi.org/10.3390/ma1317365710.3390/ma13173657 ↗
33. Islak, S., Abushraıda, A.M.: Characterization of functionally graded bronze matrix ceramic reinforced composite materials. Sakarya Univ. J. Sci. 23(6), 1137–1143 (2019). https://doi.org/10.16984/SAUFENBILDER.57425110.16984/SAUFENBILDER.574251 ↗
34. Jalaei, M.H., Arani, A.G.: Analytical solution for static and dynamic analysis of magnetically affected viscoelastic orthotropic double-layered graphene sheets resting on viscoelastic foundation. Phys. b: Condens. Matter 530(November 2017), 222–235 (2018)10.1016/j.physb.2017.11.049 ↗
35. Jayashri, V.S., Chua, G., Valavan, S.E.: Novel piezoelectric tactile sensor materials with improved properties. Solid State Phenom. 185, 65–68 (2012). https://doi.org/10.4028/www.scientific.net/SSP.185.6510.4028/www.scientific.net/SSP.185.65 ↗
36. Jiang, C., Chen, F., Yu, F., Tian, S., Cheng, X., Zhang, S., Zhao, X.: Thermal expansion and electro-elastic features of Ba2TiSi2O8 high temperature piezoelectric crystal. Crystals 9(1), 11 (2018). https://doi.org/10.3390/cryst901001110.3390/cryst9010011 ↗
37. Ju, M., Dou, Z., Li, J.-W., Qiu, X., Shen, B., Zhang, D., Yao, F.-Z., Gong, W., Wang, K.: Piezoelectric materials and sensors for structural health monitoring: fundamental aspects, current status, and future perspectives. Sensors 23(1), 543 (2023). https://doi.org/10.3390/s2301054310.3390/s23010543 ↗
38. Kaddari, M., Balubaid, M., Mahmoud, S.R., Kaci, A., Bousahla, A.A., Tounsi, A., Al-Osta, M.A., Tounsi, A.: Influence of porosity distribution on buckling behavior of FG sandwich plates using a quasi-3D refined plate theory. Mech. Based des. Struct. Mach. (2024). https://doi.org/10.1080/15397734.2024.243455210.1080/15397734.2024.2434552 ↗
39. Kang, S.H., Kim, J.H.: Characteristics of power law and sigmoid FGMs models in thermal effect. Appl. Mech. Mater. 829, 90–94 (2016). https://doi.org/10.4028/www.scientific.net/AMM.829.9010.4028/www.scientific.net/AMM.829.90 ↗
40. Karakaş, A.İ, Daloğlu, A.: A parametric frequency analysis for functionally graded cylinders using graded harmonic FEM. J. Struct. Eng. Appl. Mech. 2(4), 190–206 (2019). https://doi.org/10.31462/jseam.2019.0419020610.31462/jseam.2019.04190206 ↗
41. Kiani, Y., Eslami, M.R.R.: An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos. Part B Eng. 45(1), 101–110 (2013). https://doi.org/10.1016/j.compositesb.2012.09.03410.1016/j.compositesb.2012.09.034 ↗
42. Kiani, Y., Rezaei, M., Taheri, S., Eslami, M.R.: Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams. Int. J. Mech. Mater. des. 7(3), 185–197 (2011). https://doi.org/10.1007/s10999-011-9158-210.1007/s10999-011-9158-2 ↗
43. Kiyono, C.Y., Silva, E.C.N., Reddy, J.N.: Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach. Int. J. Numer. Meth. Eng. 90(12), 1452–1484 (2012). https://doi.org/10.1002/nme.337110.1002/nme.3371 ↗
44. Komijani, M., Kiani, Y., Esfahani, S.E., Eslami, M.R.: Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams. Compos. Struct. 98, 143–152 (2013). https://doi.org/10.1016/j.compstruct.2012.10.04710.1016/j.compstruct.2012.10.047 ↗
45. Lafi, D.E., Bouhadra, A., Mamen, B., Menasria, A., Bourada, M., Bousahla, A.A., Bourada, F., Tounsi, A., Tounsi, A., Yaylacı, M.: Combined influence of variable distribution models and boundary conditions on the thermodynamic behavior of FG sandwich plates lying on various elastic foundations. Struct. Eng. Mech. Int. J. 89(2), 103–119 (2024)
46. Lariski, F.M., Zangina, T., Ndikilar, C.E., Mohammed, J.: Advances in the synthesis, characterizations and applications of barium titanate. A review. Dutse J. Pure Appl. Sci. 9(3a), 117–136 (2023). https://doi.org/10.4314/dujopas.v9i3a.1310.4314/dujopas.v9i3a.13 ↗
47. Li, S.B., Huang, J., Qin, R.: Natural vibration analysis of piezoelectric smart FGM plate by spline finite point method. Appl. Mech. Mater. 444–445, 66–71 (2013). https://doi.org/10.4028/www.scientific.net/AMM.444-445.6610.4028/www.scientific.net/AMM.444-445.66 ↗
48. Li, C., Han, Q., Wang, Z., Wu, X.: Analysis of wave propagation in functionally graded piezoelectric composite plates reinforced with graphene platelets. Appl. Math. Model. 81, 487–505 (2020). https://doi.org/10.1016/J.APM.2020.01.01610.1016/J.APM.2020.01.016 ↗
49. Mahapatra, S.D., Mohapatra, P.C., Aria, A.I., Christie, G., Mishra, Y.K., Hofmann, S., Thakur, V.K.: Piezoelectric materials for energy harvesting and sensing applications: roadmap for future smart materials. Adv. Sci. (2021). https://doi.org/10.1002/advs.20210086410.1002/advs.202100864 ↗
50. Markworth, A.J., Ramesh, K.S., P. J. W.: Modelling studies applied to functionally graded materials. J. Mater. Sci. 30, 2183–2193 (1995)10.1007/BF01184560 ↗
51. Mechab, B., Mechab, I., Benaissa, S., Ameri, M., Serier, B.: Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations. Appl. Math. Model. 40(2), 738–749 (2016). https://doi.org/10.1016/j.apm.2015.09.09310.1016/j.apm.2015.09.093 ↗
52. Mohammadimehr, M., Mohandes, M., Moradi, M.: Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory. J. Vib. Control 22(7), 1790–1807 (2016). https://doi.org/10.1177/107754631454451310.1177/1077546314544513 ↗
53. Motta Mello, L.A., Kiyono, C.Y., Nakasone, P.H., Nelli Silva, E.C.: Design of quasi-static piezoelectric plate based transducers by using topology optimization. Smart Mater. Struct. 23(2), 025035 (2014). https://doi.org/10.1088/0964-1726/23/2/02503510.1088/0964-1726/23/2/025035 ↗
54. Mudhaffar, I.M., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Zahrani, M.M., Al-Dulaijan, S.U.: Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads. Struct. Eng. Mech. 86(2), 167–180 (2023). https://doi.org/10.12989/sem.2023.86.2.16710.12989/sem.2023.86.2.167 ↗
55. Namitha, L.K., Sebastian, M.T.: High permittivity ceramics loaded silicone elastomer composites for flexible electronics applications. Ceram. Int. 43(3), 2994–3003 (2017). https://doi.org/10.1016/j.ceramint.2016.11.08010.1016/j.ceramint.2016.11.080 ↗
56. Oshkour, A., Abu Osman, N., Yau, Y., Tarlochan, F., Wan Abas, W.: Design of new generation femoral prostheses using functionally graded materials: a finite element analysis. Proc. Inst. Mech. Eng. [h] 227(1), 3–17 (2013). https://doi.org/10.1177/095441191245942110.1177/0954411912459421 ↗
57. Ozalp, A.F., Esen, I.: Magnetic field effects on the thermomechanical vibration behavior of functionally graded biocompatible material sandwich nanobeams. Mech. Adv. Mater. Struct. (2024). https://doi.org/10.1080/15376494.2024.234996610.1080/15376494.2024.2349966 ↗
58. Pal, S., Das, D.: Axisymmetric bending vibration analysis of bidirectional functionally graded rotating micro-disk under thermo-mechanical loading. J. Vib. Control 30(1–2), 220–236 (2024). https://doi.org/10.1177/1077546322114345810.1177/10775463221143458 ↗
59. Panchal, Y., K, P.: Functionally graded materials: a review of computational materials science algorithms, production techniques, and their biomedical applications. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 236(22), 10969–10986 (2022). https://doi.org/10.1177/0954406222110926110.1177/09544062221109261 ↗
60. Pandey, S., Pradyumna, S., Gupta, S.S.: Static and dynamic analyses of functionally graded sandwich skew shell panels. J. Sandwich Struct 23(8), 4135–4169 (2021). https://doi.org/10.1177/109963622098365310.1177/1099636220983653 ↗
61. Pehlivan, F., Esen, I., Aktas, K.G.: Thermomechanical response of smart magneto-electro-elastic FGM nanosensor beams with intended porosity. Arab. J. Sci. Eng. 1–23 (2024)10.1007/s13369-024-09197-x ↗
62. Pu, Y., Yao, C., Li, X., Liu, Z.: Adaptive active vibration control for piezoelectric smart structure with online hysteresis identification and compensation. J. Vib. Control 28(5–6), 626–636 (2022). https://doi.org/10.1177/107754632098057410.1177/1077546320980574 ↗
63. Ramirez, F., Heyliger, P.R., Pan, E.: Free vibration response of two-dimensional magneto-electro-elastic laminated plates. J. Sound Vib.vib. 292(3–5), 626–644 (2006). https://doi.org/10.1016/j.jsv.2005.08.00410.1016/j.jsv.2005.08.004 ↗
64. Reddy, J.N., Chin, C.D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21(6), 593–626 (1998). https://doi.org/10.1080/0149573980895616510.1080/01495739808956165 ↗
65. Rezaiee-Pajand, M., Sadeghi, Y.: A bending element for isotropic, multilayered and piezoelectric plates. Latin Am. J. Solids Struct. 10(2), 323–348 (2013). https://doi.org/10.1590/S1679-7825201300020000610.1590/S1679-78252013000200006 ↗
66. Rouzegar, J., Abad, F.: Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory. Thin-Wall. Struct. 89, 76–83 (2015). https://doi.org/10.1016/j.tws.2014.12.01010.1016/j.tws.2014.12.010 ↗
67. Ruan, M., Wang, Z.-M.: Transverse vibrations of moving skew plates made of functionally graded material. J. Vib. Control 22(16), 3504–3517 (2016). https://doi.org/10.1177/107754631456396710.1177/1077546314563967 ↗
68. Safaei, B., Erdem, S., KarimzadehKolamroudi, M., Arman, S.: State-of-the-art review of energy harvesting applications by using thermoelectric generators. Mech. Adv. Mater. Struct. 31(22), 5605–5637 (2024). https://doi.org/10.1080/15376494.2023.221766010.1080/15376494.2023.2217660 ↗
69. Sahmani, S., Fan, F., Safaei, B.: Modified strain gradient plate model for nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric laminated microharvesters. Commun. Nonlinear Sci. Numer. Simul. 132, 107861 (2024a). https://doi.org/10.1016/J.CNSNS.2024.10786110.1016/J.CNSNS.2024.107861 ↗
70. Sahmani, S., Safaei, B., Rabczuk, T.: Nonlinear in-plane buckling of small-curved and large-curved FG porous microbeams via strain gradient-based isogeometric collocation formulations. Compos. Struct. 334, 117969 (2024b). https://doi.org/10.1016/J.COMPSTRUCT.2024.11796910.1016/J.COMPSTRUCT.2024.117969 ↗
71. Santiuste, C., Thomsen, O.T., Frostig, Y.: Thermo-mechanical load interactions in foam cored axi-symmetric sandwich circular plates—high-order and FE models. Compos. Struct. 93(2), 369–376 (2011). https://doi.org/10.1016/j.compstruct.2010.09.00510.1016/j.compstruct.2010.09.005 ↗
72. Sharifi, S., MohammadiNasab, A., Chen, P.-E., Liao, Y., Jiao, Y., Shan, W.: Robust bicontinuous elastomer-metal foam composites with highly tunable stiffness. Adv. Eng. Mater. (2022). https://doi.org/10.1002/adem.20210153310.1002/adem.202101533 ↗
73. Sobhy, M.: Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Compos. Struct. 99, 76–87 (2013). https://doi.org/10.1016/j.compstruct.2012.11.01810.1016/j.compstruct.2012.11.018 ↗
74. Sobhy, M., Mukahal, Al., Fatemah, H.H.: Magnetic control of vibrational behavior of smart FG sandwich plates with honeycomb core via a quasi-3D plate theory. Adv. Eng. Mater. (2023). https://doi.org/10.1002/adem.20230009610.1002/adem.202300096 ↗
75. Song, X., Li, S.R., Zhao, Y.G.: Buckling behavior of FGM elastic arches subjected to uniformly distributed radial follow load. Adv. Mater. Res. 239–242, 422–427 (2011). https://doi.org/10.4028/www.scientific.net/AMR.239-242.42210.4028/www.scientific.net/AMR.239-242.422 ↗
76. Sun, J., Sahmani, S., Safaei, B.: Nonlinear dynamical instability characteristics of FG piezoelectric microshells incorporating nonlocality and strain gradient size dependencies. Int. J. Struct. Stab. Dyn. 23(07), 2350074 (2023)10.1142/S0219455423500748 ↗
77. Thai, H.-T., Choi, D.-H.: A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation. Compos. B Eng. 43(5), 2335–2347 (2012). https://doi.org/10.1016/j.compositesb.2011.11.06210.1016/j.compositesb.2011.11.062 ↗
78. Tounsi, A., Mostefa, A., Attia, A., Mechanics, A.B., et al.: Free vibration investigation of functionally graded plates with temperaturedependent properties resting on a viscoelastic foundation. Struct. Eng. Mech. 86(1), 1–16 (2023a). https://doi.org/10.12989/sem.2023.86.1.00110.12989/sem.2023.86.1.001 ↗
79. Tounsi, A., Mostefa, A.H., Bousahla, A.A., Tounsi, A., Ghazwani, M.H., Bourada, F., Bouhadra, A.: Thermodynamical bending analysis of P-FG sandwich plates resting on nonlinear visco-Pasternak’s elastic foundations. Steel Compos. Struct. 49(3), 307–323 (2023b). https://doi.org/10.12989/SCS.2023.49.3.30710.12989/SCS.2023.49.3.307 ↗
80. Tounsi, A., Tahir, S.I., Al-Osta, M.A., Do-Van, T., Bourada, F., Bousahla, A.A., Tounsi, A.: An integral quasi-3D computational model for the hygro-thermal wave propagation of imperfect FGM sandwich plates. Comput. Concr. 32(1), 61–74 (2023c). https://doi.org/10.12989/CAC.2023.32.1.06110.12989/CAC.2023.32.1.061 ↗
81. Tounsi, A., Belabed, Z., Bounouara, F., Balubaid, M., Mahmoud, S.R., Bousahla, A.A., Tounsi, A.: A finite element approach for forced dynamical responses of porous FG nanocomposite beams resting on viscoelastic foundations. Int. J. Struct. Stab. Dyn. (2024a). https://doi.org/10.1142/S021945542650078110.1142/S0219455426500781 ↗
82. Tounsi, A., Bousahla, A.A., Tahir, S.I., Mostefa, A.H., Bourada, F., Al-Osta, M.A., Tounsi, A.: Influences of different boundary conditions and hygro-thermal environment on the free vibration responses of FGM sandwich plates resting on viscoelastic foundation. Int. J. Struct. Stab. Dyn. (2024b). https://doi.org/10.1142/S021945542450117710.1142/S0219455424501177 ↗
83. Wang, W., Yuan, H., Li, X., Shi, P.: Stress concentration and damage factor due to central elliptical hole in functionally graded panels subjected to uniform tensile traction. Materials 12(3), 422 (2019). https://doi.org/10.3390/ma1203042210.3390/ma12030422 ↗
84. Xin, W., Jun, H.Z., Li, W.Y.: Research on the dynamic buckling of functionally graded material plates under conditions of one edge fixed and three edges simply supported. E3S Web Conf. 38, 02013 (2018). https://doi.org/10.1051/e3sconf/2018380201310.1051/e3sconf/20183802013 ↗
85. Xue, Y., Li, J., Li, F., Song, Z.: Active control of plates made of functionally graded piezoelectric material subjected to thermo-electro-mechanical loads. Int. J. Struct. Stab. Dyn. 19(09), 1950107 (2019). https://doi.org/10.1142/S021945541950107410.1142/S0219455419501074 ↗
86. Yang, T., Huang, Q.: Vibro-acoustic response of FGM plates considering the thermal effects. In Proceedings of the 2016 3rd International Conference on Materials Engineering, Manufacturing Technology and Control (2016). https://doi.org/10.2991/icmemtc-16.2016.20610.2991/icmemtc-16.2016.206 ↗
87. Yıldız, T.: Thermomechanical vibration response of solid and foam FGM nano actuator/sensor plates. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01475-010.1007/s42417-024-01475-0 ↗
88. Yu, S.R., De, S.H., Fan, J.L.: Free vibration of functionally graded material beams in a uniform electric field. Appl. Mech. Mater. 157–158, 3–6 (2012). https://doi.org/10.4028/www.scientific.net/AMM.157-158.310.4028/www.scientific.net/AMM.157-158.3 ↗
89. Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment. Thin-Wall. Struct. 170, 108549 (2022). https://doi.org/10.1016/J.TWS.2021.10854910.1016/J.TWS.2021.108549 ↗
90. Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects. Eng. Comput. 39(2), 1127–1141 (2023). https://doi.org/10.1007/s00366-021-01498-110.1007/s00366-021-01498-1 ↗
91. Zenkour, A.M., Alghanmi, R.A.: Hygro-thermo-electro-mechanical bending analysis of sandwich plates with FG core and piezoelectric faces. Mech. Adv. Mater. Struct. 28(3), 282–294 (2021). https://doi.org/10.1080/15376494.2018.156213410.1080/15376494.2018.1562134 ↗
92. Zenkour, A.M., Mashat, D.S.: Thermal buckling analysis of ceramic-metal functionally graded plates. Nat. Sci. 02(09), 968–978 (2010). https://doi.org/10.4236/ns.2010.2911810.4236/ns.2010.29118 ↗
93. Zghal, S., Dammak, F.: Vibrational behavior of beams made of functionally graded materials by using a mixed formulation. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 234(18), 3650–3666 (2020). https://doi.org/10.1177/095440622091653310.1177/0954406220916533 ↗
94. Zhang, D.G.: Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Meccanica 49(2), 283–293 (2014). https://doi.org/10.1007/S11012-013-9793-910.1007/S11012-013-9793-9 ↗
95. Zhang, J., Wei, H., Wang, Z., Zhao, L.: Dynamic crushing of uniform and density graded cellular structures based on the circle arc model. Latin Am. J. Solids Struct. 12(6), 1102–1125 (2015). https://doi.org/10.1590/1679-7825163010.1590/1679-78251630 ↗
96. Zhang, N., Khan, T., Guo, H., Shi, S., Zhong, W., Zhang, W.: Functionally graded materials: an overview of stability, buckling, and free vibration analysis. Adv. Mater. Sci. Eng. 2019, 1–18 (2019). https://doi.org/10.1155/2019/135415010.1155/2019/1354150 ↗
97. Zhou, W., Chu, B.: Strong electromechanical response in lead zirconate titanate metamaterials. J. Am. Ceram. Soc. 99(10), 3317–3324 (2016). https://doi.org/10.1111/jace.1435310.1111/jace.14353 ↗
98. Żur, K.K., Arefi, M., Kim, J., Reddy, J.N.: Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Compos. B Eng. 182, 107601 (2020). https://doi.org/10.1016/j.compositesb.2019.10760110.1016/j.compositesb.2019.107601 ↗