Abstract
Constrained-layer damping treatment with viscoelastic material as a core is the most effective passive vibration control technique. Identifying the mechanical properties of viscoelastic materials can be difficult, as polymers combined with different reinforcements and fillers often show variable mechanical characteristics. The present research proposes an inverse identification method to characterize the frequency-dependent mechanical properties of a viscoelastic material utilizing the experimental modal analysis test results. For this purpose, a sandwich beam with a core layer of viscoelastic material constrained between two isotropic face layers is considered. Free vibration test utilizing the impact hammer technique is carried out on the sandwich beam with a core material of natural rubber. The proposed inverse method integrates the response surface method with a constrained optimization approach to identify natural rubber's frequency-dependent shear storage modulus and material loss factor. A fit for these frequency-dependent material parameters is executed to obtain the analytical expressions for a wide frequency range. The identified material parameters of natural rubber are then compared with those obtained from experimental dynamic mechanical analysis (DMA) tests to ensure the accuracy of the proposed inverse method. The results obtained from analytical solutions are in line with the experimental test results, confirming the efficacy of the present research approach. The proposed inverse methodology has the potential to significantly improve the testing and characterization of materials, leading to better design and optimization of materials and structures for specific applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- 1:
-
Constraining layer
- 2:
-
Core layer
- 3:
-
Base layer
- \(e\) :
-
Related to beam elements
- ':
-
Partial differentiation with respect to x
- \(L\) :
-
Length of sandwich beam
- \(h_{k}\) :
-
Thickness of kth layer
- \(A_{k}\) :
-
Cross-sectional area of kth layer
- \(I_{k}\) :
-
Moment of inertia of kth layer
- \(f_{n}\) :
-
The resonance frequency of the sandwich beam for nth mode
- \(f_{1n}\) :
-
The resonance frequency of the bare elastic beam for nth mode
- \(E\) :
-
Young's modulus for the elastic face layers
- \(G\) :
-
Shear modulus of the viscoelastic core layer
- \(\rho_{k}\) :
-
The density of beam material of kth layer
- \(\eta_{v}\) :
-
The loss factor of the viscoelastic material
- \(\eta\) :
-
The modal loss factor of the sandwich beam
- \(C_{n}\) :
-
Coefficient corresponding to the nth mode of the clamped-free beam
References
Allahverdizadeh A, Mahjoob MJ, Maleki M, Nasrollahzadeh N, Naei MH (2013) Structural modeling, vibration analysis and optimal viscoelastic layer characterization of adaptive sandwich beams with electrorheological fluid core. Mech Res Commun 51:15–22. https://doi.org/10.1016/j.mechrescom.2013.04.009
Araujo AL, Mota Soares CM, Herskovits J, Pedersen P (2009) Estimation of piezoelastic and viscoelastic properties in laminated structures. Comp Struct 87(2):168–174. https://doi.org/10.1016/j.compstruct.2008.05.009
Armaghani DJ, Tonnizam Mohamad E, Momeni E, Monjezi M, Sundaram Narayanasamy M (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9(1):1–16. https://doi.org/10.1007/s12517-015-2057-3
Barkanov E, Skukis E, Petitjean B (2009) Characterization of viscoelastic layers in sandwich panels via an inverse technique. J Sou Vib. https://doi.org/10.1016/j.jsv.2009.07.011
Cortes F, Elejabarrieta MJ (2007) Viscoelastic materials characterization using the seismic response. Mater Des. https://doi.org/10.1016/j.matdes.2006.05.032
De Espindola JJ, Da Silva Neto JM, Lopes EM (2005) A generalized fractional derivative approach to viscoelastic material properties measurement. Appl Math Comput 164(2):493–506. https://doi.org/10.1016/j.amc.2004.06.099
Hamdaoui M, Ledi KS, Robin G, Daya EM (2019) Identification of frequency-dependent viscoelastic damped structures using an adjoint method. J Sou Vib 453:237–252. https://doi.org/10.1016/j.jsv.2019.04.022
Jamshidi B, Hematiyan MR, Mahzoon M (2019) An improved time domain meshfree method for analysis of quasi-static and dynamic inhomogeneous viscoelastic problems. Eng Anal Bound Elem 106:59–67. https://doi.org/10.1016/j.enganabound.2019.04.031
Jrad H, Dion JL, Renaud F, Tawfiq I, Haddar M (2013) Experimental characterization, modeling and parametric identification of the non linear dynamic behavior of viscoelastic components. Euro J Mech A/Sol 42:176–187. https://doi.org/10.1016/j.euromechsol.2013.05.004
Kang L, Sun C, Liu H, Liu B (2022) Determination of frequency-dependent shear modulus of viscoelastic layer via a constrained sandwich beam. Polym 14(18):3751. https://doi.org/10.3390/polym14183751
Kim SY, Lee DH (2009) Identification of fractional-derivative-model parameters of viscoelastic materials from measured FRFs. J Sou Vib. https://doi.org/10.1016/j.jsv.2009.02.040
Kumar S, Kumar R, Sehgal R (2011) Enhanced ACLD treatment using stand-off-layer: FEM based design and experimental vibration analysis. Appl Acou 72(11):856–872. https://doi.org/10.1016/J.APACOUST.2011.05.010
Lall AK, Asnani NT, Nakra BC (1987) Vibration and damping analysis of rectangular plate with partially covered constrained viscoelastic layer. J Vib Acou Stress Reli Des 109(3):241–247. https://doi.org/10.1115/1.3269427
Ledi KS, Hamdaoui M, Robin G, Daya EM (2018) An identification method for frequency dependent material properties of viscoelastic sandwich structures. J Sou Vib 428:13–25. https://doi.org/10.1016/J.JSV.2018.04.031
Martinez-Agirre M, Elejabarrieta MJ (2011) Dynamic characterization of high damping viscoelastic materials from vibration test data. J Sou Vib 330(16):3930–3943. https://doi.org/10.1016/j.jsv.2011.03.025
Melo JD, Radford DW (2005) Time and temperature dependence of the viscoelastic properties of CFRP by dynamic mechanical analysis. Compos Struct 70(2):240–253. https://doi.org/10.1016/j.compstruct.2004.08.025
Myers RH (1999) Response surface methodology—current status and future directions. J Qual Tech 31(1):30–44. https://doi.org/10.1080/00224065.1999.11979891
Nashif AD, Jones DI, Henderson JP (1991) Vibration damping. Wiley, New York
Patnaik SS, Roy T (2021) Viscoelastic and mechanical properties of CNT-reinforced polymer-based hybrid composite materials using hygrothermal creep. Poly Poly Comp. https://doi.org/10.1177/09673911211052730
Rao MD (2003) Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. J Sou Vib 262(3):457–474. https://doi.org/10.1016/S0022-460X(03)00106-8
Ross D, Ungar EE, Kerwin Jr. EM (1959) Damping of plate flexural vibrations by means of viscoelastic laminae. ASME, 49–87
Rouleau L, Pirk R, Pluymers B, Desmet W (2015) Characterization and modeling of the viscoelastic behavior of a self-adhesive rubber using dynamic mechanical analysis tests. J Aero Tech Manag 7(2):200–208. https://doi.org/10.5028/jatm.v7i2.474
Schwaar M, Gmur T, Frieden J (2012) Modal numerical-experimental identification method for characterizing the elastic and damping properties in sandwich structures with a relatively stiff core. Compos Struct 94(7):2227–2236. https://doi.org/10.1016/j.compstruct.2012.02.017
Shi Y, Sol H, Hua H (2006) Material parameter identification of sandwich beams by an inverse method. J Sou Vib 290(3–5):1234–1255. https://doi.org/10.1016/j.jsv.2005.05.026
Sun W, Wang Z, Yan X, Zhu M (2018) Inverse identification of the frequency-dependent mechanical parameters of viscoelastic materials based on the measured FRFs. Mech Syst Sign Proc 98:816–833. https://doi.org/10.1016/j.ymssp.2017.05.031
Van Leeuwen T, Herrmann FJ (2016) A penalty method for PDE-constrained optimization in inverse problems. Inv Prob 32(1):015007. https://doi.org/10.1088/0266-5611/32/1/015007
Xie X, Zheng H, Jonckheere S, Pluymers B, Desmet W (2019) A parametric model order reduction technique for inverse viscoelastic material identification. Comput Struct 212:188–198. https://doi.org/10.1016/j.compstruc.2018.10.013
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Cnflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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
Prusty, J.K., Sahu, D.P. & Mohanty, S.C. Identification of Viscoelastic Material Properties of a Layer Through a Constrained Sandwich Beam in the Frequency Domain. Iran J Sci Technol Trans Mech Eng 48, 363–379 (2024). https://doi.org/10.1007/s40997-023-00660-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40997-023-00660-y