The differential transformation method (DTM) is applied to investigate free vibration of FGM sandwich beams with viscoelastic nonlinear material behaviour. . In the analytical formulation, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The governing equations for viscoelastic damped sandwich beams are derived using the virtual displacement principle. In this study, the core layer is modelled as frequency-dependent, resulting in a nonlinear eigenvalue problem. This problem is solved iteratively using the Differential Transformation Method (DTM) until the required convergence criteria are met. Within the framework of the Differential Transformation Method (DTM), variations in the first three natural frequencies and their corresponding loss factors are analyzed. A detailed numerical study is conducted to investigate the effects of the porosity coefficient, various thickness and geometric ratios, as well as material properties on the fundamental frequencies and loss factors of the sandwich beam. The results show excellent agreement with previous studies and underscore the accuracy and computational efficiency of DTM as a reliable method for the analysis, design, and optimization of FGM sandwich beams with nonlinear viscoelastic cores.
AktarerSMKucukomerogluTSekbanDM, et al. (2025) Analysis of the changes in microstructure, mechanical, and contact properties of multi-pass friction stir processed DP800 steel. Advances in nano research: 253–264. https://doi.org/10.12989/anr.2025.18.3.253
2.
Al-DulaijanSUYouzeraHMeftahSA, et al. (2024) Nonlinear damping and vibration assessment of sandwich beam with composite faces and viscoelastic core layer. International Journal of Structural Stability and Dynamics24(08): 2450083. https://doi.org/10.1142/S0219455424500834
3.
Al-OstaMAYouzeraHMeftahSA, et al. (2024) Effect of the normal transverse stress on the superharmonic resonance problem of three-layered sandwich beams with viscoelastic core. Journal of Vibration Engineering & Technologies12: 6185–6196. https://doi.org/10.1007/s42417-023-01246-3
4.
ArikogluAOzkolI (2010) Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method. Composite Structures92(12): 3031–3039. https://doi.org/10.1016/j.compstruct.2010.05.022
5.
BilasseMDayaEMAzrarL (2010) Linear and nonlinear vibrations analysis of viscoelastic sandwich beams. Journal of Sound and Vibration329(23): 4950–4969. https://doi.org/10.1016/j.jsv.2010.06.012
6.
BoumedieneFBekhouchaFDayaEM (2021) Modal analysis of rotating viscoelastic sandwich beams. Mechanics of Advanced Materials and Structures28(4): 405–417. https://doi.org/10.1080/15376494.2019.1567887
7.
DemirOBalkanDPekerRC, et al. (2020) Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method. Journal of sandwich structures & materials. https://doi.org/10.1177/1099636218767491
8.
DitarantoRA (1965) Theory of vibratory bending for elastic and viscoelastic layered finite-length beams. Journal of Applied Mechanics32(4): 881–886. https://doi.org/10.1115/1.3627330
9.
ErtenliMFEsenİ (2024) The effect of the various porous layers on thermomechanical buckling of FGM sandwich plates. Mechanics of Advanced Materials and Structures31(28): 10935–10961. https://doi.org/10.1080/15376494.2023.2299934
10.
EsenIÖzmenR (2024) Free and forced thermomechanical vibration and buckling responses of functionally graded magneto-electro-elastic porous nanoplates. Mechanics Based Design of Structures and Machines52(3): 1505–1542. https://doi.org/10.1080/15397734.2022.2152045
11.
EsenIAlazwariMAEltaherMA, et al. (2022) Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load. Steel and composite structures. International Journal42(6): 805–826. https://doi.org/10.12989/scs.2022.42.6.805
12.
FasanaAMarchesielloS (2001) Rayleigh–ritz analysis of sandwich beams. Journal of Sound and Vibration241(4): 643–652. https://doi.org/10.1006/jsvi.2000.3311
HuangBMingSChenH, et al. (2025) Stochastic static finite element model updating using the Bayesian method integrating homotopy surrogate model. Computers & Structures315: 107769. https://doi.org/10.1016/j.compstruc.2025.107769
15.
JinGYangCLiuZ (2016) Vibration and damping analysis of sandwich viscoelastic-core beam using Reddy’s higher-order theory. Composite Structures140: 390–409. https://doi.org/10.1016/j.compstruct.2016.01.017
16.
KarmiYKhadriYTekiliS, et al. (2021) Dynamic analysis of composite sandwich beams with a frequency-dependent viscoelastic core under the action of a moving load. Mechanics of Composite Materials56: 755–768. https://doi.org/10.1007/s11029-021-09921-w
17.
KoçMAEsenİEroğluM (2024) Thermomechanical vibration response of nanoplates with magneto-electro-elastic face layers and functionally graded porous core using nonlocal strain gradient elasticity. Mechanics of Advanced Materials and Structures31(18): 4477–4509. https://doi.org/10.1080/15376494.2023.2199412
18.
KoutoatiKMohriFCarreraE, et al. (2021) A finite element approach for the static and vibration analyses of functionally graded material viscoelastic sandwich beams with nonlinear material behavior. Composite Structures274: 114315. https://doi.org/10.1016/j.compstruct.2021.114315
19.
LoghmanEAliKEABakhtiari-NejadaF, et al. (2022) On the combined shooting-pseudo-arclength method for finding frequency response of nonlinear fractional-order differential equations. Journal of Sound and Vibration516: 116521.
20.
MahmoudkhaniSKolbadi HajikalaeiS (2025) Effects of temperature rise and curvature on damping properties of sandwich beams with thick viscoelastic cores. Journal of the Brazilian Society of Mechanical Sciences and Engineering47(7): 1–18. https://doi.org/10.1007/s40430-025-05629-3
21.
MeadDJMarkusS (1969) The forced vibration of a three-layer damped sandwich beam with arbitrary boundary conditions. Journal of Sound and Vibration10(2): 163–175. https://doi.org/10.1016/0022-460X(69)90193-X
22.
ÖnerEOktayMGUzunYE, et al. (2025) Tri-method analysis of contact mechanics in orthotropic-isotropic materials. Archive of Applied Mechanics95(5): 116. https://doi.org/10.1007/s00419-025-02832-5
23.
ÖzmenREsenI (2023) Thermomechanical flexural wave propagation responses of FG porous nanoplates in thermal and magnetic fields. Acta Mechanica234(11): 5621–5645. https://doi.org/10.1007/s00707-023-03679-z
24.
ÖzmenRKılıçREsenI (2024) Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal fields. Mechanics of Advanced Materials and Structures31(4): 834–853. https://doi.org/10.1080/15376494.2022.2124000
PukhovGE (1982) Differential transforms and circuit theory. International Journal of Circuit Theory and Applications10(10): 265–276. https://doi.org/10.1002/cta.4490100307
27.
ReddyJN (1990) A general non-linear third-order theory of plates with moderate thickness. International Journal of Non-Linear Mechanics25(6): 677–686. https://doi.org/10.1016/0020-7462(90)90006-U
28.
SekbanDMYaylacıEUÖzdemirME, et al. (2025) Investigating formability behavior of friction stir-welded high-strength shipbuilding steel using experimental, finite element, and artificial neural network methods. Journal of Materials Engineering and Performance34(6): 4942–4950. https://doi.org/10.1007/s11665-024-09501-8
29.
TaşkinMDemirÖ (2023) Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core. Engineering Computations40(3): 538–563. https://doi.org/10.1108/EC-04-2022-0269
30.
TouratierM (1991) An efficient standard plate theory. Int J Eng Sci29(8): 901–916.
31.
WangYChenNXuX, et al. (2025) Vibration analysis of periodic viscoelastic sandwich beams by the wave method. European Journal of Mechanics - A: Solids112: 105647. https://doi.org/10.1016/j.euromechsol.2025.105647
32.
YangCJinGYeX, et al. (2016) A modified fourier–ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials. International Journal of Mechanical Sciences106: 1–18. https://doi.org/10.1016/j.ijmecsci.2015.11.031
33.
YaylacıMYazıcıoğluAYaylacıEU, et al. (2025) Evaluation of the contact problem of two layers one of functionally graded, loaded by circular rigid block and resting on a pasternak foundation by analytical and numerical (FEM and MLP) methods. Archive of Applied Mechanics95(4): 1–23. https://doi.org/10.1007/s00419-025-02787-7
34.
YazıcıoğluAYaylacıMSekbanDM, et al. (2025) Analysis of the contact problem functionally graded layer placed on a pasternak foundation. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik105(8): e70152. https://doi.org/10.1002/zamm.70152
35.
YouzeraHMeftahSATounsiA, et al. (2025) Nonlinear forced vibration analysis of FG-CNTRC sandwich beams with viscoelastic core under various boundary conditions. Mechanics of Advanced Materials and Structures: 1–10. https://doi.org/10.1080/15376494.2025.2473691
