Abstract
In this paper, the forced vibration of a functionally porous sandwich beam with a viscoelastic core has been investigated. The upper and lower layers of the beam are made of functionally porous materials, and the porosity gradient in porous layers is distributed through their thickness. The core of the beam is made of viscoelastic materials. The Golla–Hughes–McTavish (GHM) model is employed to simulate the viscoelastic behavior of the core. Applying the Hamilton principle and Euler–Bernoulli theory, the governing equation of motion is obtained for a simply supported beam. The Newmark method is applied to solve the time-dependent differential equation of the beam. The results are compared with data from the literature review and a commercial finite element software. In the Results and Discussion section of the paper, a parametric study is performed to investigate the effects of porosity and viscoelastic parameters on the forced vibration of the beam. Finally, the results obtained by the GHM model are compared with the Kelvin–Voigt model for constant and variable input frequencies. According to the results, both models predict identical behavior for constant input frequency. However, the GHM model provides better results for the case of variable input frequency.
Similar content being viewed by others
References
Sisemore, C.L., Darvennes, C.M.: Transverse vibration of elastic-viscoelastic-elastic sandwich beams: compression-experimental and analytical study. J. Sound Vib. 252, 155–167 (2002). https://doi.org/10.1006/jsvi.2001.4038
Wang, Y.: Viscoelastic behavior of a composite beam using finite element method: experimental and numerical assessment. In: International Conference on Composite Materials (2013)
Banerjee, J.R., et al.: Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment. Int. J. Solids Struct. 44, 7543–7563 (2007). https://doi.org/10.1016/j.ijsolstr.2007.04.024
Chen, D., Yang, J., Kitipornchai, S.: Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos. Struct. 133, 54–61 (2015). https://doi.org/10.1016/j.compstruct.2015.07.052
Pollien, A., et al.: Graded open-cell aluminium foam core sandwich beams. Mater. Sci. Eng. A 404, 9–18 (2005). https://doi.org/10.1016/j.msea.2005.05.096
Anirudh, B., et al.: A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: bending, vibration and buckling. Compos. Struct. 222, 110899 (2019). https://doi.org/10.1016/j.compstruct.2019.110899
He, J.-H., Moatimid, G.M., Zekry, M.H.: Forced nonlinear oscillator in a fractal space. Facta Univ. Ser. Mech. Eng. 20, 1–20 (2022). https://doi.org/10.22190/FUME220118004H
He, C.-H., Liu, C.: A modified frequency–amplitude formulation for fractal vibration systems. Fractals 30, 2250046 (2022). https://doi.org/10.1142/S0218348X22500463
Babaei, M., Asemi, K., Safarpour, P.: natural frequency and dynamic analyses of functionally graded saturated porous beam resting on viscoelastic foundation based on higher order beam theory. J. Solid Mech. 11, 615–634 (2019). https://doi.org/10.22034/JSM.2019.666691
Akbaş, ŞD., et al.: Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load. Eng. Comput. (2020). https://doi.org/10.1007/s00366-020-01070-3
Alnujaie, A., et al.: Forced vibration of a functionally graded porous beam resting on viscoelastic foundation. Geomech. Eng. 24, 91–103 (2021). https://doi.org/10.12989/gae.2021.24.1.091
Bensaid, I., Saimi, A.: Dynamic investigation of functionally graded porous beams resting on viscoelastic foundation using generalised differential quadrature method. Austr. J. Mech. Eng. (2022). https://doi.org/10.1080/14484846.2021.2017115
Al-Furjan, M.S.H., et al.: Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate. Mech. Syst. Signal Process. 178, 109269 (2022). https://doi.org/10.1016/j.ymssp.2022.109269
Alavi, S.K., et al.: On the dynamic response of viscoelastic functionally graded porous plates under various hybrid loadings. Ocean Eng. 264, 112541 (2022). https://doi.org/10.1016/j.oceaneng.2022.112541
Arikoglu, A., Ozkol, I.: Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method. Compos. Struct. 92, 3031–3039 (2010). https://doi.org/10.1016/j.compstruct.2010.05.022
Bakhsheshy, A., Mahbadi, H.: Free vibration analysis of functionally graded viscoelastic plate. Modares Mech. Eng. 17, 143–149 (2017)
Liang, Y.-H., Wang, K.-J.: A new fractal viscoelastic element: promise and applications to Maxwell-Rheological model. Therm. Sci. 25, 1221–1227 (2021). https://doi.org/10.2298/TSCI200301015L
Golla, D.F., Hughes, P.C.: Dynamics of viscoelastic structures—a time-domain, finite element formulation. J. Appl. Mech. 52, 897–906 (1985). https://doi.org/10.1115/1.3169166
McTavish, D., Hughes, P.: Finite element modeling of linear viscoelastic structures—The GHM method. In: 33rd Structures, Structural Dynamics and Materials Conference (1992). https://doi.org/10.2514/6.1992-2380
Felippe, W.N., Barbosa, F.S.: A nondeterministic GHM based model applied to sandwich beams. Procedia Eng. 199, 1098–1103 (2017). https://doi.org/10.1016/j.proeng.2017.09.200
Huang, Z.-C., et al.: Parameter determination for the Mini-Oscillator Model of the Viscoelastic Material. In: IOP Conference Series: Earth and Environmental Science, vol. 267, p. 032100 (2019). https://doi.org/10.1088/1755-1315/267/3/032100
Safari, M., Biglari, H.: Transient response of sandwich plate with transversely flexible and viscoelastic frequency-dependent material core based on a three-layered theory. J. Sandw. Struct. Mater. 23, 1081–1117 (2021). https://doi.org/10.1177/1099636219854187
Khoshmanesh, S., Watson, S., Zarouchas, D.: The effect of the fatigue damage accumulation process on the damping and stiffness properties of adhesively bonded composite structures. Compos. Struct. 287, 115328 (2022). https://doi.org/10.1016/j.compstruct.2022.115328
Wang, Y., et al.: Wave localization in randomly disordered periodic piezoelectric rods with initial stress. Acta Mech. Solida Sin. 21, 529–535 (2008). https://doi.org/10.1007/s10338-008-0863-9
Ning, L., Wang, Y.-Z., Wang, Y.-S.: Broadband square cloak in elastic wave metamaterial plate with active control. J. Acoust. Soc. Am. 150, 4343–4352 (2021). https://doi.org/10.1121/10.0008974
Ning, L., Wang, Y.-Z., Wang, Y.-S.: Active control of a black hole or concentrator for flexural waves in an elastic metamaterial plate. Mech. Mater. 142, 103300 (2020). https://doi.org/10.1016/j.mechmat.2019.103300
Li, G.-H., et al.: Active control on topological immunity of elastic wave metamaterials. Sci. Rep. 10, 9376 (2020). https://doi.org/10.1038/s41598-020-66269-2
Wagg, D., Neild, S.: Nonlinear Vibration with Control: For Flexible and Adaptive Structures. Springer Netherlands, Dordrecht (2010)
He, J.-H.: Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178, 257–262 (1999). https://doi.org/10.1016/S0045-7825(99)00018-3
Lee, M.K., Hosseini Fouladi, M., Narayana Namasivayam, S.: Natural frequencies of thin rectangular plates using homotopy-perturbation method. Appl. Math. Model. 50, 524–543 (2017). https://doi.org/10.1016/j.apm.2017.05.050
Snehashish, C., et al.: Variational iteration method. In: Advanced Numerical and Semi-Analytical Methods for Differential Equations, pp. 141–147. Wiley, USA (2019)
He, J.-H.: Solution of nonlinear equations by an ancient Chinese algorithm. Appl. Math. Comput. 151, 293–297 (2004). https://doi.org/10.1016/S0096-3003(03)00348-5
He, J.-H.: Preliminary report on the energy balance for nonlinear oscillations. Mech. Res. Commun. 29, 107–111 (2002). https://doi.org/10.1016/S0093-6413(02)00237-9
Eslami, M.R.: Finite Elements Methods in Mechanics. Springer International Publishing, Switzerland (2014)
Zhao, J., et al.: Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions. Compos. B Eng. 168, 106–120 (2019). https://doi.org/10.1016/j.compositesb.2018.12.044
Findley, W.N., Lai, J.S., Onaran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear Viscoelasticity. Dover Publications, New York (1989)
Meunier, M., Shenoi, R.A.: Forced response of FRP sandwich panels with viscoelastic materials. J. Sound Vib. 263, 131–151 (2003). https://doi.org/10.1016/S0022-460X(02)01101-X
Vasques, C.M.A., Rodrigues, J.D., Moreira, R.A.S.: Experimental Identification of GHM and ADF Parameters for Viscoelastic Damping Modeling. Springer Netherlands, Dordrecht (2006)
Meunier, M., Shenoi, R.A.: Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory. Compos. Struct. 54, 243–254 (2001). https://doi.org/10.1016/S0263-8223(01)00094-0
Martin, L.A., Inman, D.J.: A novel viscoelastic material modulus function for modifying the Golla–Hughes–McTavish method. Int. J Acoust. Vib. 18, 102–108 (2013). https://doi.org/10.20855/ijav.2013.18.3325
Chen, D., Yang, J., Kitipornchai, S.: Free and forced vibrations of shear deformable functionally graded porous beams. Int. J. Mech. Sci. 108, 14–22 (2016). https://doi.org/10.1016/j.ijmecsci.2016.01.025
Rojas, J.I., et al.: Viscoelastic behavior of a novel aluminum metal matrix composite and comparison with pure aluminum, aluminum alloys, and a composite made of Al–Mg–Si alloy reinforced with SiC particles. J. Alloy. Compd. 744, 445–452 (2018). https://doi.org/10.1016/j.jallcom.2018.02.103
Funding
The authors did not receive support from any organization for the submitted work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tafreshi, E.S., Darabi, B., Hamedi, J. et al. Forced vibration analysis of a sandwich beam with functionally porous faces and viscoelastic core using Golla–Hughes–McTavish model. Acta Mech 234, 4343–4364 (2023). https://doi.org/10.1007/s00707-023-03600-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-023-03600-8