DataVXInternational Journal of Mechanics and Materials in DesignPaper
journal article·2026-09Open access

Thermomechanical wave propagation analysis of sandwich triply-periodic-minimal-surface-structures with magneto-electro-elastic nanocomposite surface layers

Kerim Gökhan Aktaş, Fatih Pehlivan, İsmail Esen

International Journal of Mechanics and Materials in Design· Volume 22· Issue 3
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Abstract

Abstract In this article, the thermomechanical wave propagation analysis of sandwich nanocomposite plates with a triply-periodic-minimal-surface (TPMS) core layer and magneto-electro-elastic (MEE) surface layers are evaluated using the high-order shear deformation theory (HSDT). MEE surface plates are composed of a mixture of cobalt ferrite (CoFe 2 O 4 ) and barium titanate (BaTiO 3 ) according to the rule of mixture, while the TPMS core layer is SUS304. Three different TPMS cells are considered for the core layer: Gyroid (G), Primitive (P), and Wrapped package-graph (IWP). It is assumed that the material properties of both MEE and TPMS plate structures exhibit temperature-dependent variations. The equations of motion for the sandwich structure are established using HSDT and nonlocal strain gradient elasticity theory (NSGT), while the wave equations are obtained through analytical solutions. The study explores the effect of nonlocal parameters, wave number, TPMS cell pattern, CoFe 2 O 4 and BaTiO 3 mixture ratio, temperature increase, and thermal and electrical load parameters on the phase velocity and wave frequency of the sandwich plate. Based on the results, it is concluded that the parameters which are addressed significantly affect the wave propagation phase velocity and frequency of the sandwich plate, and that sandwich plates can be modeled to adapt to variable environmental conditions and tune the desired properties with appropriate parameter selection. It is aimed that this study will contribute to advanced aerospace studies where the effect of temperature change is significant, and where both lightweight and high strength and energy absorption capabilities are prominent.
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Research context

Nanomaterials

OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Acoustic Wave Phenomena Research

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (85)

Show source-provided references
1. Abdoli, E., Zarastvand, M.R., Talebitooti, R.: Wave propagation numerical simulation approach based on a novel TPMS-based lattice metamaterial for improved vibration transmission of doubly curved sandwich systems. Eng. Comput. 41(5), 3737–3754 (2025). https://doi.org/10.1007/s00366-025-02181-510.1007/s00366-025-02181-5 ↗
2. Aktaş, 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 (2024a). https://doi.org/10.1007/s11043-024-09726-z10.1007/s11043-024-09726-z ↗
3. 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. 235(9), 5587–5619 (2024b). https://doi.org/10.1007/s00707-024-04001-110.1007/s00707-024-04001-1 ↗
4. Aktaş, K.G., Esen, I.: Dynamic response analysis and active vibration control of the smart sandwich composite plate with FGM core layers and MIMO FGPM actuators and sensors. Int. J. Mech. Syst. Dyn. 5(1), 3–19 (2025). https://doi.org/10.1002/msd2.7000110.1002/msd2.70001 ↗
5. Al-Ketan Oraib.,Rashid K Abu Al-Rub. MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Mater Design \ Process Commun. 3 (6), e205 (2021) https://doi.org/10.1002/mdp2.20510.1002/mdp2.205 ↗
6. Al-Osta., Mohammed, A: An efficient model for wave propagation of temperature-dependent E-FGM plates resting on viscoelastic foundation. Mater Today Commun 35 (March).(2023) https://doi.org/10.1016/j.mtcomm.2023.10578410.1016/j.mtcomm.2023.105784 ↗
7. Amini, Y., Emdad, H., Farid, M.: Finite element modeling of functionally graded piezoelectric harvesters. Compos. Struct. 129, 165–176 (2015). https://doi.org/10.1016/j.compstruct.2015.04.01110.1016/j.compstruct.2015.04.011 ↗
8. Aminipour, H., Janghorban, M., Li, L.: Wave dispersion in nonlocal anisotropic macro/nanoplates made of functionally graded materials. Waves Random Complex Media 31(6), 1945–1989 (2021). https://doi.org/10.1080/17455030.2020.171342210.1080/17455030.2020.1713422 ↗
9. Arefi Mohammad., Ashraf M, Zenkour.,: Free Vibration analysis of a three-layered microbeam based on Strain Gradient theory and three-unknown shear and normal deformation theory. Steel and Composite Structures. (2018) https://doi.org/10.12989/scs.2018.26.4.42110.12989/scs.2018.26.4.421 ↗
10. Arefi, M., Zenkour, A.M.: A Simplified Shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J. Sandw. Struct. Mater. (2016). https://doi.org/10.1177/109963621665258110.1177/1099636216652581 ↗
11. Barretta, R., de Sciarra, F., Vaccaro, M.S.: Nonlocal elasticity for nanostructures: a review of recent achievements. Encyclopedia 3(1), 279–310 (2023). https://doi.org/10.3390/encyclopedia301001810.3390/encyclopedia3010018 ↗
12. Belyankova, T I.,Vorovich, E., Valery Kalinchuk: Features of SH-wave propagation in a bimorphic piezoelectric/piezomagnetic plate made of functionally graded materials. PNRPU Mechanics Bulletin 0 (July: 14–29 (2025) https://doi.org/10.15593/perm.mech/2025.2.0210.15593/perm.mech/2025.2.02 ↗
13. Blanquer, Sébastien, Dirk, W., Grijpma. Triply periodic minimal surfaces (TPMS) for the generation of porous architectures using stereolithography. (2020). https://doi.org/10.1007/978-1-0716-0611-7_210.1007/978-1-0716-0611-7_2 ↗
14. Carrillo-Munoz, M., Caceres, N., Keattitorn, S., Sharma, B.: Elastic wave propagation in structures with triply periodic minimal surfaces. J. Acoust. Soc. America (2020). https://doi.org/10.1121/1.514715210.1121/1.5147152 ↗
15. Chan, D.Q., Phi, B.G., Nga, N.T.T., Le, M.Q., Dang, V.H.: An analytical approach for buckling of FG cylindrical nanopanels resting on Pasternak’s foundations in the thermal environment. Adv. Appl. Math. Mech. 16(2), 398–422 (2023). https://doi.org/10.4208/aamm.OA-2021-028910.4208/aamm.OA-2021-0289 ↗
16. Chen, J., Pan, E., Chen, H.: Wave propagation in magneto-electro-elastic multilayered plates. Int. J. Solids Struct. 44(3–4), 1073–1085 (2007). https://doi.org/10.1016/j.ijsolstr.2006.06.00310.1016/j.ijsolstr.2006.06.003 ↗
17. Chlup, Z., Drdlík, D., Hadraba, H., Ševeček, O., Šiška, F., Erhart, J., Maca, K.: Temperature effect on elastic and fracture behaviour of lead-free piezoceramic BaTiO3. J. European Ceram. Soc. (2023). https://doi.org/10.1016/j.jeurceramsoc.2022.11.03010.1016/j.jeurceramsoc.2022.11.030 ↗
18. Ebrahimi, F., Dabbagh, A.: On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory. Compos. Struct. 162, 281–293 (2017). https://doi.org/10.1016/j.compstruct.2016.11.05810.1016/j.compstruct.2016.11.058 ↗
19. Ebrahimi, F., Farazmandnia, N., Kokaba, M.R., Mahesh, V.: Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory. Eng. Comput. 37(2), 921–936 (2021). https://doi.org/10.1007/s00366-019-00864-410.1007/s00366-019-00864-4 ↗
20. Ejeh, Chukwugozie, J., Imad Barsoum., Rashid, K Abu Al-Rub: Impact Behavior of Periodic, Stochastic, and Anisotropic Minimal Surface-Lattice Sandwich Structures. Int J Mech Sci (2024) https://doi.org/10.1016/j.ijmecsci.2024.10935910.1016/j.ijmecsci.2024.109359 ↗
21. Engin, Y., Esen, I.: Thermal vibration buckling of smart magneto electro elastic sandwich nano plates with biocompatible FGM core layer. ZAMM-J. Appl. Math. Mech.zeitschrift Für Angewandte Mathematik und Mechanik (2025). https://doi.org/10.1002/zamm.7031110.1002/zamm.70311 ↗
22. Eringen, A Cemal: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys (1983) https://doi.org/10.1063/1.33280310.1063/1.332803 ↗
23. Eroğlu, M., Koç, M.A., Esen, İ: Multifunctional nanosensors based on piezoelectric and magnetoelectric sandwich structures. Mech. Based des. Struct. Mach. 54(1), 2608151 (2026). https://doi.org/10.1080/15397734.2025.260815110.1080/15397734.2025.2608151 ↗
24. Esen, I., Aktaş, K.G., Pehlivan, F.: Investigation of the critical buckling temperatures and free vibration response of porous functionally graded magneto-electro-elastic sandwich higher-order nanoplates with temperature-dependent material properties. J. Vib. Eng. Technol. 13(2), 162 (2025). https://doi.org/10.1007/s42417-024-01542-610.1007/s42417-024-01542-6 ↗
25. Ezzin, H., Ben Amor, M., Ben Ghozlen, M.H.: Lamb waves propagation in layered piezoelectric/piezomagnetic plates. Ultrasonics 76, 63–69 (2017). https://doi.org/10.1016/j.ultras.2016.12.01610.1016/j.ultras.2016.12.016 ↗
26. Farajpour, A., Rastgoo, A.: Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory. Results Phys. (2017). https://doi.org/10.1016/j.rinp.2017.03.03810.1016/j.rinp.2017.03.038 ↗
27. Fukuchi, T., Hayashi, T., Mori, N.: Ultrasonic focusing using a stacked thin-plate region. Jpn. J. Appl. Phys. 62(SJ), SJ1005 (2023). https://doi.org/10.35848/1347-4065/acb36110.35848/1347-4065/acb361 ↗
28. Gai, J., Yang, X., Zhao, Y.: Electroacoustic wave scattering from cylindrical inhomogeneities in transversely isotropic piezoelectric composites. Mater. des. (2026). https://doi.org/10.1016/j.matdes.2025.11529610.1016/j.matdes.2025.115296 ↗
29. Gao, M., Wang, G., Liu, J., He, Z.: Wave propagation analysis in functionally graded metal foam plates with nanopores. Acta Mech. 234(4), 1733–1755 (2023). https://doi.org/10.1007/s00707-022-03442-w10.1007/s00707-022-03442-w ↗
30. Gao, Y., Liu, B., Hao, Y., Li, Z., Li, Y., Guo, X., Zhang, F., Zhang, K.: Effect of cell size on the mechanical properties of the porous structure of a CuCrZr alloy formed by selective laser melting technology. Adv. Eng. Mater. 26(23), 2401059 (2024). https://doi.org/10.1002/adem.20240105910.1002/adem.202401059 ↗
31. Gao, Z., Xue, Y., Gao, Y., Zhang, C.: Free vibration analysis of in-plane bidirectional functionally graded plates with piezoelectric layers using RPT-IGA method. Adv. Eng. Softw. 215, 104122 (2026). https://doi.org/10.1016/j.advengsoft.2026.10412210.1016/j.advengsoft.2026.104122 ↗
32. Guo, K., Zhou, S., Cai, W., Mu, M., Chen, J., Zhu, L.: An analytical solution for dynamic plastic responses of PVC foam sandwich beams under ice impact. Thin-Walled Struct. (2026). https://doi.org/10.1016/j.tws.2026.11464710.1016/j.tws.2026.114647 ↗
33. Hwu, C.: Piezoelectric and magneto-electro-elastic materials BT - anisotropic elasticity with Matlab. In: Hwu, C. (ed.) Anisotropic Elasticity with Matlab, pp. 265–287. Springer International Publishing, Cham (2021). https://doi.org/10.1007/978-3-030-66676-7_1110.1007/978-3-030-66676-7_11 ↗
34. Jabiri Ayoub., Yacoubi Abdelali., El Allami., Mhammed: Plotting Lamb waves dispersion curves of an aluminum plate by the semi-analytical finite element (SAFE) method and comparison with analytical curves. ITM Web Conf. 48: 2006. (2022) https://doi.org/10.1051/itmconf/20224802006.10.1051/itmconf/20224802006 ↗
35. Kiran, M.C.: Thermal and hygrothermal buckling characteristics of porous magneto-electro-elastic skewed plates using third-order shear deformation theory. Mech. Adv. Mater. Struct. 31(24), 6266–6281 (2024). https://doi.org/10.1080/15376494.2023.222718510.1080/15376494.2023.2227185 ↗
36. Kumar, P., Harsha, S.P.: Vibration response analysis of PZT-4/PZT-5H based functionally graded tapered plate subjected to electro-mechanical loading. Mech. Res. Commun. (2021). https://doi.org/10.1016/j.mechrescom.2021.10376510.1016/j.mechrescom.2021.103765 ↗
37. Li, P., Biwa, S.: Flexural waves in a periodic non-uniform Euler-Bernoulli beam: analysis for arbitrary contour profiles and applications to wave control. Int. J. Mech. Sci. (2020). https://doi.org/10.1016/j.ijmecsci.2020.10594810.1016/j.ijmecsci.2020.105948 ↗
38. Li, X., Li, H., Jiang, X., Liang, L.: Experimental and numerical investigation on the vibro-acoustic characteristics of periodic rib stiffened plate based on band gap theory. J. Vib. Control 30(13–14), 3064–3076 (2024). https://doi.org/10.1177/1077546323118884810.1177/10775463231188848 ↗
39. Li, X., Xie, M., Feng, J., Hu, Y.: Magnetoelastic free vibration of a microplate on an elastic foundation. Thin-Walled Struct. 224, 114652 (2026). https://doi.org/10.1016/j.tws.2026.11465210.1016/j.tws.2026.114652 ↗
40. Lim, C.W., Zhang, G., Reddy, J.N.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015). https://doi.org/10.1016/j.jmps.2015.02.00110.1016/j.jmps.2015.02.001 ↗
41. Maskery, I., Sturm, L., Aremu, A.O., Panesar, A., Williams, C.B., Tuck, C.J., Wildman, R.D., Ashcroft, I.A., Hague, R.J.M.: Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer 152, 62–71 (2018). https://doi.org/10.1016/j.polymer.2017.11.04910.1016/j.polymer.2017.11.049 ↗
42. Nguyen-Xuan, H., Tran, K.Q., Thai, C.H., Lee, J.: Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates. Compos. Struct. 315, 116981 (2023). https://doi.org/10.1016/j.compstruct.2023.11698110.1016/j.compstruct.2023.116981 ↗
43. Nouraei, M., Zamani, V., Civalek, Ö.: Vibration of smart sandwich plate with an auxetic core and Dual-FG nanocomposite layers integrated with piezoceramic actuators. Compos. Struct. 315, 117014 (2023). https://doi.org/10.1016/j.compstruct.2023.11701410.1016/j.compstruct.2023.117014 ↗
44. Olgirdas, T., Mažeika, L.: Determining the elastic constants of isotropic materials by measuring the phase velocities of the A0 and S0 modes of lamb waves. Sensors (2023). https://doi.org/10.3390/s2315667810.3390/s23156678 ↗
45. Ozalp, A.F.: Thermal vibration of butterfly auxetic metamaterial core sandwich nanoplate with piezoelectric surface layers. Z. Naturforsch. A 80(10), 1059–1076 (2025). https://doi.org/10.1515/zna-2025-014410.1515/zna-2025-0144 ↗
46. Ozalp, A.F., Esen, I.: Wave dispersion analysis with FGM face layers and GPL-Reinforced metallic foam core thermally loaded sandwich nanoplate using NSGT. Arch. Appl. Mech. (2025). https://doi.org/10.1007/s00419-025-02919-z10.1007/s00419-025-02919-z ↗
47. Ozdemir, M.T., Das, T., Esen, I.: Effect of the hexachiral auxetic metamaterial on the 3D wave dispersion characteristics of sandwich nanoplate with foam FGM face layers. ZAMM - J. Appl. Math. Mech. 106(1), e70322 (2026). https://doi.org/10.1002/zamm.7032210.1002/zamm.70322 ↗
48. Öztürk, F.H., Aktaş, K.G., Karaca, M.M., Temiz, A., Pehlivan, F.: Design-dependent mechanical performance of additively manufactured hybrid hierarchical TPMS-Based auxetic polymer structures. Mater. Test. 68(2), 194–207 (2026). https://doi.org/10.1515/mt-2025-024710.1515/mt-2025-0247 ↗
49. Pehlivan, F.: Thermo-mechanical vibration analysis of GPLs reinforced foam core smart sandwich nanosensor/actuator plates. Mech. Based des. Struct. Mach. 54(1), 2532742 (2026). https://doi.org/10.1080/15397734.2025.253274210.1080/15397734.2025.2532742 ↗
50. Qiang, X., Wang, C., Zhang, H.: Interval theory-embedded data-driven identification framework for uncertain thermo-elastic parameters. Appl. Math. Model. (2026). https://doi.org/10.1016/j.apm.2026.116743. (September 2025)10.1016/j.apm.2026.116743 ↗
51. 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 ↗
52. Reddy, JN. Energy principles and variational methods. In Theory and Analysis of Elastic Plates and Shells. (2020) https://doi.org/10.1201/9780849384165-610.1201/9780849384165-6 ↗
53. Roudbari, M.A., Jorshari, T.D., Li, C., Ansari, R., Kouzani, A.Z., Amabili, M.: A review of size-dependent continuum mechanics models for micro- and nano-structures. Thin-Walled Struct. (2022). https://doi.org/10.1016/j.tws.2021.10856210.1016/j.tws.2021.108562 ↗
54. Sh, E.L., Kattimani, S., Vinyas, M.: Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates. Arch. Civ. Mech. Eng. 22(1), 38 (2022). https://doi.org/10.1007/s43452-021-00357-610.1007/s43452-021-00357-6 ↗
55. Sharma, S.R., Mehalwal, J.C., Sarkar, N., Sharma, D.K.: Nonlocal elasticity and thermal dual-phase-lag effect on the vibration analysis of transversely isotropic electro-magneto generalized thermoelastic sphere with voids. ZAMM - J. Appl. Math. Mech. 102(5), e202100200 (2022). https://doi.org/10.1002/zamm.20210020010.1002/zamm.202100200 ↗
56. Shen, X., Zhao, L., Kumar, P., Liu, D.: The symplectic method for free vibration, buckling and dynamics analysis of partial-interaction composite beams based on Timoshenko theory. Mech. Adv. Mater. Struct. 0(0), 1–16 (2026). https://doi.org/10.1080/15376494.2025.259885710.1080/15376494.2025.2598857 ↗
57. Shevchenko, V Ya., Oryshchenko,AS., Balabanov,SV., Sychev,MM., Пaвлoвa,E A: Gibson–Ashby equation for cellular materials based on triply periodic minimal surfaces. Voprosy Materialovedeniya. (2024) https://doi.org/10.22349/1994-6716-2024-119-3-122-132.10.22349/1994-6716-2024-119-3-122-132 ↗
58. Simsek, U., Arslan, T., Kavas, B., Gayir, C.E., Sendur, P.: Parametric studies on vibration characteristics of triply periodic minimum surface sandwich lattice structures. Int. J. Adv. Manuf. Technol. 115(3), 675–690 (2021). https://doi.org/10.1007/s00170-020-06136-610.1007/s00170-020-06136-6 ↗
59. Sobhy, M., Mukahal, F.H.H.A.: Wave dispersion analysis of functionally graded GPLs-Reinforced sandwich piezoelectromagnetic plates with a honeycomb core. Mathematics (2022). https://doi.org/10.3390/math1017320710.3390/math10173207 ↗
60. Sun Dan., Song-Nan Luo: Wave propagation of functionally graded material plates in thermal environments. Ultrasonics 51 (8): 940–52. (2011) https://doi.org/10.1016/j.ultras.2011.05.009.10.1016/j.ultras.2011.05.009 ↗
61. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation. Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.194231010.1080/17455030.2021.1942310 ↗
62. Tang, Li., Xiongliang Yao., Guoxun Wu., Dong Tang: Band gaps characteristics analysis of periodic oscillator coupled damping beam. Materials. 13 (24) (2020) https://doi.org/10.3390/ma13245748.10.3390/ma13245748 ↗
63. Temiz, A., Yılmaz, A.F., Öztürk, F.H., Pehlivan, F., Karaca, M.M.: Design and evaluation of hierarchical strut-based lattices with triply periodic minimal surface-inspired shells for bioinspired applications. J. Mater. Eng. Perform. 35(13), 12667–12681 (2026). https://doi.org/10.1007/s11665-025-12520-810.1007/s11665-025-12520-8 ↗
64. Thai, C.H., Ferreira, A.J.M., Bordas, S.P.A., Rabczuk, T., Nguyen-Xuan, H.: Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory. Eur. J. Mech. A/Solids 43, 89–108 (2014). https://doi.org/10.1016/j.euromechsol.2013.09.00110.1016/j.euromechsol.2013.09.001 ↗
65. Touloukian, Y.S.: Thermophysical Properties of High Temperature Solid Materials. Macmillan, New York (1967)
66. Tran, Phuong, and Chenxi Peng. 2021. “Triply Periodic Minimal Surfaces Sandwich Structures Subjected to Shock Impact.” Journal of Sandwich Structures \& Materials 23 (6): 2146–75. https://doi.org/10.1177/1099636220905551.10.1177/1099636220905551 ↗
67. Tumšys Olgirdas: Experimental method for simultaneous determination of the lamb wave A0 modes group and phase velocities. Materials 15 (9) (2022) https://doi.org/10.3390/ma1509297610.3390/ma15092976 ↗
68. Verma, R., Kumar, J., Singh, N.K., Rai, S.K., Kumta, S., Sehgal, S., Saxena, K.: Low elastic modulus and highly porous triply periodic minimal surfaces architectured implant for orthopedic applications. Proc. Inst. Mech. Eng. E J. Process Mech. Eng. 239(4), 1553–1561 (2025). https://doi.org/10.1177/0954408922111125810.1177/09544089221111258 ↗
69. Viet, N.V., Karathanasopoulos, N., Zaki, W.: Mechanical attributes and wave propagation characteristics of TPMS lattice structures. Mech. Mater. (2022). https://doi.org/10.1016/j.mechmat.2022.10436310.1016/j.mechmat.2022.104363 ↗
70. Vinh, P.V., Belarbi, M.-O., Tounsi, A.: Wave propagation analysis of functionally graded nanoplates using nonlocal higher-order shear deformation theory with spatial variation of the nonlocal parameters. Waves Random Complex Media (2022). https://doi.org/10.1080/17455030.2022.203638710.1080/17455030.2022.2036387 ↗
71. Vinyas, M., Harursampath, D., Kattimani, S.C.: On vibration analysis of functionally graded carbon nanotube reinforced magneto-electro-elastic plates with different electro-magnetic conditions using higher order finite element methods. Def. Technol. 17(1), 287–303 (2021). https://doi.org/10.1016/j.dt.2020.03.01210.1016/j.dt.2020.03.012 ↗
72. Wang, X., Liu, J., Hu, B., Zhang, B., Shen, H.: Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory. Appl. Math. Mech. 44(10), 1821–1840 (2023). https://doi.org/10.1007/s10483-023-3043-710.1007/s10483-023-3043-7 ↗
73. Wu Yaozhong, X., Qi, L.S., Wang, B., Li, H., Wang, P., Li, W.: Sound transmission loss and bending properties of sandwich structures based on triply periodic minimal surfaces. Thin-Walled Str. (2024). https://doi.org/10.1016/j.tws.2024.11232410.1016/j.tws.2024.112324 ↗
74. Xu, K., Cao, J., Zheng, Z., Zhao, R., Xu, G., Wang, H., Wang, J., Hur, B., Yue, X.: Deformation behavior of Inconel 625 alloy with TPMS structure. Materials (2025). https://doi.org/10.3390/ma1802039610.3390/ma18020396 ↗
75. Yang, X., Gai, J., Zheng, X., Xie, Y., Yu, X., Gong, R., Meng, Z., Zhai, S., Zhao, X.: Analysis of thermal wave scattering and temperature distribution in sub-surface, defects of gradient construction materials. Sci. Rep. 15(1), 1–9 (2025). https://doi.org/10.1038/s41598-025-06196-210.1038/s41598-025-06196-2 ↗
76. Yildirim, E., Esen, İ: Thermomechanical buckling of magneto-electro-elastic embedded smart sandwich nano plates. Int. J. Mech. Mater. des. 21(4), 701–736 (2025). https://doi.org/10.1007/s10999-025-09758-410.1007/s10999-025-09758-4 ↗
77. Yıldız, T., Esen, I.: A comprehensive study on determining the flexural wave propagation properties of biocompatible sandwich nanoplate exposed to thermal and magnetic fields. Mech. Based des. Struct. Mach. 54(1), 2549472 (2026). https://doi.org/10.1080/15397734.2025.254947210.1080/15397734.2025.2549472 ↗
78. Zarastvand, M.R., Abdoli, E., Talebitooti, R.: A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface. Appl. Math. Mech. 46(11), 2035–2054 (2025). https://doi.org/10.1007/s10483-025-3314-910.1007/s10483-025-3314-9 ↗
79. Zhang, R., Sun, L., Wang, Z., Hao, W., Cao, E., Zhang, Y.: Dielectric and magnetic properties of CoFe2O4 prepared by sol-gel auto-combustion method. Mater. Res. Bulletin (2018). https://doi.org/10.1016/j.materresbull.2017.08.00610.1016/j.materresbull.2017.08.006 ↗
80. Zhang, X., Hao, C., Luo, H., Kong, D., Li, C.: Flexural wave band gaps of steel bridge decks periodically stiffened with U-Ribs: mechanism and influencing factors. J. Low Freq. Noise Vib. Act. Control. 41(2), 799–809 (2022). https://doi.org/10.1177/1461348421106825110.1177/14613484211068251 ↗
81. Zhao, L., Kumar, P., Sharma, N., Shen, X., Harsha, S.P.: Multifield vibration analysis of a porosity-tailored bidirectional functionally graded piezoelectric nano-plate on variable elastic foundations under hygro-thermoelectric effects. Front. Struct. Civ. Eng. 19(10), 1669–1701 (2025a). https://doi.org/10.1007/s11709-025-1223-210.1007/s11709-025-1223-2 ↗
82. Zhao, L., Kumar, P., Sharma, N., Shen, X., Harsha, S.P.: Thermo-electromechanical nonlinear dynamic response of PZT-4/PZT-5H bidirectional functionally graded porous plates subjected to the variable external harmonic load. Mater. Design (2025b). https://doi.org/10.1016/j.matdes.2025.11513910.1016/j.matdes.2025.115139 ↗
83. Zhao, L., Sharma, N., Kumar, P., Panwar, V.S., Shen, X.: Direct probability integral assisted machine learning framework for uncertain vibration response of porous bi-directional functionally graded sandwich structures. Mater. des. 263, 115641 (2026). https://doi.org/10.1016/j.matdes.2026.11564110.1016/j.matdes.2026.115641 ↗
84. Žnidarič, Ž, Nečemer, B., Novak, N., Vesenjak, M., Glodež, S.: Fatigue of triply periodic minimal surface (TPMS) metamaterials–A review. Stroj. Vestn. (2025). https://doi.org/10.5545/sv-jme.2025.136910.5545/sv-jme.2025.1369 ↗
85. 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. Part B Eng. (2020). https://doi.org/10.1016/j.compositesb.2019.10760110.1016/j.compositesb.2019.107601 ↗