Aerospace Mechanics

Aerospace Mechanics

Investigation of the Natural Frequency and Damping Coefficient of the Sandwich Beam Consisting of a Viscoelastic Core and Nanocomposite Face-Sheets

Document Type : Solid Mechanics

Authors
Hadi Teymouri 1
Aliasghar Naderi 2
1 PhD Student, University of Tabriz, Tabriz, Iran
2 Associate Professor, Imam Ali Military University, Tehran, Iran
10.47176/MAJ.2025.1531
Abstract
In this research, the free vibrations of a sandwich beam with a viscoelastic core and carbon nanotube-reinforced polymer face sheets, under simply supported boundary conditions and using the three-layer sandwich beam theory, have been investigated. Given the fundamental application of sandwich structures with viscoelastic cores in critical industries such as military and aerospace, they are of significant importance for vibration reduction and noise control. The Kelvin-Voigt model has been used to model the viscoelastic core, and using the aforementioned theory and Hamilton's principle, the governing equations of the sandwich structure are derived. The obtained equations are in the form of partial differential equations, and to solve these equations of motion, the analytical Navier method in the spatial domain has been employed. To ensure the validity and accuracy of the numerical results, a comparative approach with reputable published articles has been presented. Finally, the effects of various material and geometric parameters on the natural frequency of the system have been examined. The results indicate that as the structural loss factor increases, the damping of the sandwich beam also increases, consequently reducing the natural frequency of the system

Graphical Abstract

Investigation of the Natural Frequency and Damping Coefficient of the Sandwich Beam Consisting of a Viscoelastic Core and Nanocomposite Face-Sheets
Keywords
Sandwich Beam Viscoelastic Core Nanocomposite Three
layer Sandwich Beam Theory Kelvin
Voigt Model
Subjects


Smiley face

[1]     Teymouri H, Biglari H. Evaluation of wave propagation in a transversely isotropic monolayer with finite thickness by the potential functions method. Aerospace Mechanics. 2022; 18(3): 13-26. (In Persian) DOR: https://dor.isc.ac/dor/20.1001.1.26455323.1401.18.3.2.4
[2]     Teymouri H, Biglari H. Elastodynamic Green's functions for sandwich panels with aluminum foam core and transversely isotropic face sheets using potential functions method. Engineering Analysis with Boundary Elements. 2024; 160: 258-272. DOI:
https://doi.org/10.1016/j.enganabound.2023.12.033
[3]     Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis. CRC press. 2004.
[4]     Yang J, Chen Y, Xiang Y, Jia X. Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load. Journal of Sound and Vibration. 2008; 312(1): 166-181. DOI:
https://doi.org/10.1016/j.jsv.2007.10.034
[5]     Rahnama M, Morad Sheikhi M, Hamzeloo SR. Free vibration behavior of three-skin conical shells with composite lattice core based on semi-analytical and finite element methods. Aerospace Mechanics. 2024; 20(3): 75-86. (In Persian) DOR:
https://dor.isc.ac/dor/20.1001.1.26455323.1403.20.3.5.1
[6]     Şimşek M, Kocatürk T. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Composite Structures. 2009; 90(4): 465-473. DOI:
https://doi.org/10.1016/j.compstruct.2009.04.04
[7]     Safaei B, Onyibo EC, Goren M, Kotrasova K, Yang Z, Arman S, Asmael M. Free vibration investigation on RVE of proposed honeycomb sandwich beam and material selection optimization. Facta Universitatis, Series: Mechanical Engineering. 2023; 21(1): 31-50. DOI:https://doi.org/10.22190/FUME220806042S
[8]     Belkhodja MEA, Chorfi SM, Belalia SA, Belkhodja Y. Bending and free vibrations analysis of sandwich beams with porous functionally graded face sheets and a graphene platelets-reinforced aluminum core using a new quasi-3D beam theory. Journal of Vibration Engineering & Technologies. 2025; 13(1): 122. DOI:  https://doi.org/10.1007/s42417-024-01646-z
[9]     Yousefzadeh S, Doostdar M. Natural Frequencies Analysis of a Rotating Tapered Timoshenko Beam Made of Functionally Graded Material with Actuated Piezoelectric Layer. Aerospace Mechanics. 2022; 18(2): 143-156. (In Persian) DOR: https://dor.isc.ac/dor/20.1001.1.26455323.1401.18.2.10.0
[10]  Dzenis Y. Structural nanocomposites. Science. 2008; 319(5862): 419-420. DOI: https://doi.org/ 10.1126/science.1151434
[11]  Ke L-L, Yang J, Kitipornchai S. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures. 2010; 92(3): 676-683. DOI: https://doi.org/10.1016/j.compstruct.2009.09.04
[12]   Ebrahimi F, Dabbagh A, Rastgoo A. Free vibration analysis of multi-scale hybrid nanocomposite plates with agglomerated nanoparticles. Mechanics Based Design of Structures and Machines. 2021; 49(4): 487-510. DOI: https://doi.org/10.1080/15397734.2019.1692665
[13]  Moradi-Dastjerdi R, Payganeh GH, Malek-Mohammadi H. Free Vibration Analyses of Functionally Graded CNT Reinforced Nanocomposite Sandwich Plates Resting on Elastic Foundation. Journal of Solid Mechanics. 2015; 7(2): 158-172.  DOR: https://dor.isc.ac/dor/20.1001.1.20083505.2015.7.2.4.7
[14]  Biglari H, Teymouri H, Shokouhi A. Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass. Mechanics of Composite Materials. 2024; 60(1): 163-182. DOI:
https://doi.org/10.1007/s11029-024-10181-7
[15]  Lakes R. Viscoelastic materials. Cambridge university press. 2009.
[16]  Hamed E, Rabinovitch O. Modeling and Dynamics of Sandwich Beams with a Viscoelastic Soft Core. AIAA Journal. 2009; 47(9): 2194-2211. DOI: https://doi.org/10.2514/1.41840
[17]  Meunier M, Shenoi RA. Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory. Composite Structures. 2001; 54(2-3): 243-454. DOI: https://doi.org/10.1016/S02638223(01)00094-0
[18]  Won SG, Bae SH, Cho JR, Bae SR, Jeong WB. Three-layered damped beam element for forced vibration analysis of symmetric sandwich structures with a viscoelastic core. Finite Elements in Analysis and Design. 2013; 68: 39-51. DOI:
https://doi.org/10.1016/j.finel.2013.01.004
[19]  Tafreshi ES, Darabi B, Hamedi J, Mahbadi H. Forced vibration analysis of a sandwich beam with functionally porous faces and viscoelastic core using Golla–Hughes–McTavish model. Acta Mechanica. 2023; 234(9): 4343-4364. DOI:
https://doi.org/10.1007/s00707-023-03600-8
[20]  Teymouri H, Biglari H, Sadeghi MH. Effects of Frequency Dependency of Materials Behavior on the Dynamic Response of the Viscoelastic Beam Under the Moving Mass. International Journal of Structural Stability and Dynamics. 2025: 2650266.
DOI: https://doi.org/10.1142/S0219455426502664
[21]  Ghorbanpour Arani A, Haghparast E, Ghorbanpour Arani AH. Size‐dependent vibration of double‐bonded carbon nanotube‐reinforced composite microtubes conveying fluid under longitudinal magnetic field. Polymer Composite. 2016; 37(5): 1375-1383. DOI: https://doi.org/10.1002/pc.23306
DOI:               https://doi.org/10.1061/(ASCE)0733-9399(1992)118:5(1026)
[22]  Ke LL, Yang J, Kitipornchai S. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures. 2010; 92(3): 676-683. DOI: https://doi.org/10.1016/j.compstruct.2009.09.024
[23]  Mohammadimehr M, Okhravi SV, Akhavan Alavi SM. Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT. Journal of Vibration and Control. 2018; 24(8): 1551-1569. DOI: https://doi.org/10.1177/1077546316664022
[24]  Lakes RS, Wineman A. On Poisson’s Ratio in Linearly Viscoelastic Solids. Journal of Elasticity. 2006; 85: 287-297. DOI:
https:// doi.org / 10.1007/s10659-006-9070-4 
[25]  Farfan-Cabrera LI, Pascual‑Francisco JB. An Experimental Methodological Approach for Obtaining Viscoelastic Poisson’s Ratio of Elastomers from Creep Strain DIC‑Based Measurements. Experimental Mechanics. 2022; 62: 45-63. DOI:
https://doi.org/10.1007/s11340-021-00792-9 
[26]  Biglari H, Teymouri H, Foroutan M. Application of Auxetic Core to Improve Dynamic Response of Sandwich Panels Under Low-Velocity Impact. Arabian Journal for Science and Engineering. 2024; 49: 11683-11697. DOI:
https://doi.org/10.1007/s13369-024-08817-w
[27]  Gao JX, Liao WH. Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments. Journal of sound and Vibration. 2005; 280: 329-357.    DOI: https://doi.org/10.1016/j.jsv.2003.12.019
[28]  Yang M, Qiao P. Higher-order impact modeling of sandwich structures with flexible core. International Journal of Solids and Structures. 2005; 42: 5460-5490. DOI:
https://doi.org/10.1016/j.ijsolstr.2005.02.037
[29]  Bilasse M, Daya EM, Azrar L. Linear and nonlinear vibrations analysis of viscoelastic sandwich beams. Journal of Sound and Vibration. 2010; 329(23): 4950-4969. DOI: https://doi.org/10.1016/j.jsv.2010.06.012
[30]  Li C, Li P, Zhong B, Miao X. Large-amplitude vibrations of thin-walled rotating laminated composite cylindrical shell with arbitrary boundary conditions. Thin-Walled Struct. 2020; 156: 106966. DoI: https://doi.org/10.1016/j.tws.2020.106966.
 
 
 
Aerospace Mechanics
Volume 21, Issue 4 - Serial Number 82
Winter
Winter 2026
Pages 53-64

  • Receive Date 26 September 2025
  • Revise Date 04 December 2025
  • Accept Date 13 December 2025
  • Publish Date 21 January 2026