Identification of viscoelastic material parameters based on DMA analysis results
https://doi.org/10.33979/2073-7416-2025-119-3-60-72
Abstract
The article addresses the problem of identifying parameters for viscoelastic material models made from closed-cell polyurethane foam based on results obtained using a dynamic mechanical analyzer (DMA). DMA testing allows determining viscoelastic characteristics of materials — complex elastic modulus over a wide frequency range. For engineering applications, the most important practical application is within the frequency range of 1–1000 Hz to solve problems related to dynamics (vibration isolation and seismic insulation), as well as acoustics (protection against structural sound transmission). In engineering practice, various phenomenological material models are used, ranging from Kelvin-Voigt (KV) model and standard linear solid (SLS) model up to fractional derivative-based models such as fractional KV model, fractional SLS model including those with multiple fractional parameters. Using DMA test results—dependencies of real and imaginary parts of elastic modulus versus frequency, these models' parameters are adjusted by means of least squares method. The accuracy of approximation along with identified model parameters specific to the chosen type of material are evaluated.
Keywords
viscoelastic materials,
frequency range,
phenomenological material models,
dynamic modulus,
fractional model
Supporting agencies: This research was supported by the Russian Science Foundation (Project No. 25-11-00140).
About the Author
V. A. Smirnov
Moscow State University of Civil Engineering (National Research University) (MGSU); Research Institute of Building Physics of the Russian Academy of Architecture and Construction Sciences (NIISF RAASN)
Russian Federation
Russian Federation
Vladimir A. Smirnov - PhD in Technical Sciences, Associate Professor of Theoretical and Structural Mechanics Department; Leading Researcher at the "Complex Problems of Vibroacoustics" Laboratory,
Moscow.
References
1. Skuratova T.B., Kirillov S.E., Syatkovskiy A.I. Dissipative Properties of Polymer Films and Composite Materials Based on Polyvinyl Acetate. Russian Journal of Applied Chemistry. 2019. Vol. 92, No. 7. Pp. 952-957. doi: 10.1134/S1070427219070115
2. Volkova N. Vibroizolyatsiya ventilyatsionnogo oborudovaniya [Vibration Isolation of Ventilation Equipment]. SOK. 2011. No. 10. (rus).
3. Gusev V.P. Vibratsiya kak istochnik strukturnogo shuma, sozdaemogo oborudovaniem inzhenernykh sistem, i sredstva vibroizolyatsii [Vibration as a Source of Structural Noise Created by Engineering Systems Equipment and Vibration Isolation Means]. Academia. Arkhitektura i stroitelstvo. 2010. No. 3. (rus).
4. Yakovlev S.N., Mazurin V.L. Vibroizoliruyushchie svoystva poliuretanovykh elastomerov, primenyaemykh v stroitelstve [Vibration Isolation Properties of Polyurethane Elastomers Used in Construction]. Inzhenerno-stroitelnyy zhurnal. 2017. No. 6(74). Pp. 53-60. doi: 10.18720/MCE.74.5 (rus).
5. Yasafova S.A. Issledovanie optimizatsii vibroizoliruyushchikh materialov stroitelnykh konstruktsiy [Study of Optimization of Vibration Isolation Materials for Building Structures]. E-Scio. 2021. No. 2(53). (rus).
6. U.S. Department of Transportation Federal Transit Administration. Guidelines for Vibration Prediction in Rail Projects. 2020.
7. Cortazar-Noguerol J., Cortés F., Sarría I., Elejabarrieta M.J. Preload Influence on the Dynamic Properties of a Polyurethane Elastomeric Foam. Polymers. 2024. Vol. 16, No. 13. 1844. doi: 10.3390/polym16131844
8. Somarathna H.M.C.C., Raman S.N., Mohotti D., Mutalib A.A., Badri K.H. The Use of Polyurethane for Structural and Infrastructural Engineering Applications: A State-of-the-Art Review. Construction and Building Materials. 2018. Vol. 190. Pp. 995-1014.
9. Ngamkhanong C., Kaewunruen S. Effects of under Sleeper Pads on Dynamic Responses of Railway Prestressed Concrete Sleepers Subjected to High Intensity Impact Loads. Engineering Structures. 2020. Vol. 214. 110604.
10. Gusev V.P. Opyt borby s shumom oborudovaniya inzhenernykh sistem [Experience in Combating Noise from Engineering Systems Equipment]. Academia. Arkhitektura i stroitelstvo. 2009. No. 5. (rus).
11. Mohammad K., Asthana A., Cockerham G., Almond M. Innovative acoustic jacketing for oil and gas pipelines. Proceedings of 6th World PetroCoal Congress. New Delhi, India, 2016.
12. Anton Paar GmbH. Basics of Dynamic Mechanical Analysis (DMA). URL: https://wiki.antonpaar.com/us-en/basics-of-dynamic-mechanical-analysis-dma
13. Tain Instruments. Introduction to dynamic mechanical analysis and its application to testing of polymer solids. 2023. URL: https://www.tainstruments.com/applications-notes/introduction-to-dynamic-mechanical-analysisand-its-application-to-testing-of-polymer-solids
14. Xu Y., Dong Y., Huang X., Luo Y., Zhao S. Properties Tests and Mathematical Modeling of Viscoelastic Damper at Low Temperature With Fractional Order Derivative. Frontiers in Materials. 2019. Vol. 6. 194. doi: 10.3389/fmats.2019.00194
15. Lucklum R., Soares D. Viscoelastic Properties of Macromolecules. In: Piezoelectric Transducers and Applications. Berlin, Heidelberg: Springer, 2009. doi: 10.1007/978-3-540-77508-9_7
16. Ferry J.D. Vyazkouprugie svoystva polimerov [Viscoelastic Properties of Polymers]. Moscow: Izdatinlit, 1963. 536 p. (rus).
17. Christensen R. Vvedenie v mekhaniku kompozitov [Introduction to Mechanics of Composites]. Moscow: Mir, 1982. 336 p. (rus).
18. Pritz T. Five-parameter fractional derivative model for polymeric damping materials. Journal of Sound and Vibration. 2003. Vol. 265. Pp. 935-952. doi: 10.1016/S0022-460X(02)01530-4
19. Bagley R.L., Torvik P.J. Fractional Calculus—A Different Approach to the Analysis of Viscoelastically Damped Structures. AIAA Journal. 1983. Vol. 21. Pp. 741-748. doi: 10.2514/3.8142
20. Koeller R.C. Applications of Fractional Calculus to the Theory of Viscoelasticity. Journal of Applied Mechanics. 1984. Vol. 51. Pp. 299-307. doi: 10.1115/1.3167616
21. Rossikhin Y.A., Shitikova M.V. Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids. Applied Mechanics Reviews. 1997. Vol. 50, No. 1. Pp. 15-67. doi: 10.1115/1.3101682
22. Schiessel H., Metzler R., Blumen A., Nonnenmacher T. Generalized viscoelastic models: Their fractional equations with solutions. Journal of Physics A: Mathematical and General. 1995. Vol. 28. Pp. 6567-6584. doi: 10.1088/0305-4470/28/23/012
23. Rossikhin Yu.A., Shitikova M.V. Comparative analysis of viscoelastic models involving fractional derivatives of different orders. Fractional Calculus and Applied Analysis. 2007. Vol. 10.
24. Shitikova M.V. Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review. Mechanics of Solids. 2021. Vol. 57. doi: 10.3103/S0025654422010022
Review
For citations:
Smirnov V.A. Identification of viscoelastic material parameters based on DMA analysis results. Building and Reconstruction. 2025;(3):60-72. (In Russ.) https://doi.org/10.33979/2073-7416-2025-119-3-60-72
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