Evaluation of dynamic properties of rubber mounts by Levenberg–Marquardt method


  • Lu Ean Ooi School of Mechanical Engineering, Universiti Sains Malaysia,14300 Nibong Tebal Penang, Malaysia
  • Wan Mohd Amri Wan Mamat Ali School of Mechanical Engineering, Universiti Sains Malaysia,14300 Nibong Tebal Penang, Malaysia
  • Iskandazaqwan Zikrullah Zainudin School of Mechanical Engineering, Universiti Sains Malaysia,14300 Nibong Tebal Penang, Malaysia


hysteresis loop, loss factor, non-linearity, rubber mount, stiffness


Rubber mounts are widely used as vibration isolators as they are cheaper and available in different sizes. The performance of a rubber mount varies under different loading conditions, such as excitation force and frequency. The actual dynamic properties of a rubber mount cover linear and non-linear regions; thus, a characterization method is required that can capture and identify the dynamic properties for both regions. This paper proposes a method to identify the dynamic properties of rubber mounts by comparing the Levenberg–Marquardt method and the classical hysteresis loop method. The rubber mounts are excited under different excitation forces and frequencies. The excitation condition where the rubber mounts behave non-linearly is identified. The dynamic properties from the rubber mounts are analysed by fitting the Levenberg–Marquardt method to identify the parameters from the measured hysteresis loop. The results show that the proposed approach can capture the stiffness and loss factor of rubber mounts, including both linear and non-linear regions. Then, the measured results are compared with the impact technique for validation, with low percentage differences found between the classical hysteresis loop method and impact technique. This study indicates that the dynamic characterisation of rubber mounts using the Levenberg–Marquardt method could provide an alternative solution for identification of rubber mount properties, including their hysteresis behaviour. Overall, this work represents an important contribution in understanding the non-linear identification of rubber mount properties.


Amabili, M. (2016). Nonlinear vibrations of viscoelastic rectangular plates. Journal of Sound and Vibration, 362, 142-156. DOI: https://doi.org/10.1016/j.jsv.2015.09.035

Arikoglu, A. (2014). A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms. Rheologica Acta, 53(3), 219-233. DOI: https://doi.org/10.1007/s00397-014-0758-2

Asokan, D., & Hussain, J. I. I. (2018). Loss Factor of Elastomeric Dampers for Rotating Machinery Application. International Journal of Engineering & Technology, 7(4.35), 107. DOI: https://doi.org/10.14419/ijet.v7i4.35.22337

Balasubramanian, P., Ferrari, G., Amabili, M., & del Prado, Z. J. G. N. (2017). Experimental and theoretical study on large amplitude vibrations of clamped rubber plates. International Journal of Non-Linear Mechanics, 94, 36-45. DOI: https://doi.org/10.1016/j.ijnonlinmec.2016.12.006

Berg, M. (1998). A Non-Linear Rubber Spring Model for Rail Vehicle Dynamics Analysis. Vehicle System Dynamics, 30(3-4), 197-212. DOI: https://doi.org/10.1080/00423119808969447

Busse, S. K., Sinclair, A. N., Redda, D. T., & Wondimu, D. H. (2021). Evaluation of the vibration characteristics and handle vibration damping of diesel-fueled 15-HP single-axle tractor. Advances in Mechanical Engineering, 13(8), 168781402110406. DOI: https://doi.org/10.1177/16878140211040648

Fan, Z. J., Lee, J. H., Kang, K. H., & Kim, K. J. (1998). The forced vibration of a beam with viscoelastic boundary supports. Journal of Sound and Vibration, 210(5), 673-682. DOI: https://doi.org/10.1006/jsvi.1997.1353

Ferry, J. D. (1980). Viscoelastic Properties of Polymers. John Wiley & Sons.

Tárrago, M. G., Kari, L., Vinolas, J., & Gil-Negrete, N. (2007). Frequency and amplitude dependence of the axial and radial stiffness of carbon-black filled rubber bushings. Polymer Testing, 26(5), 629-638. DOI: https://doi.org/10.1016/j.polymertesting.2007.03.011

Haupt, P., & Lion, A. (2002). On finite linear viscoelasticity of incompressible isotropic materials. Acta Mechanica, 159(1), 87-124. DOI: https://doi.org/10.1007/bf01171450

Höfer, P., & Lion, A. (2009). Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber. Journal of the Mechanics and Physics of Solids, 57(3), 500-520. DOI: https://doi.org/10.1016/j.jmps.2008.11.004

Ibrahim, R. (2008). Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314(3–5), 371-452. DOI: https://doi.org/10.1016/j.jsv.2008.01.014

Johnson, A. R., & Quigley, C. J. (1992). A Viscohyperelastic Maxwell Model for Rubber Viscoelasticity. Rubber Chemistry and Technology, 65(1), 137-153. DOI: https://doi.org/10.5254/1.3538596

Kari, L. (2003). On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments. The Journal of the Acoustical Society of America, 113(4), 1909-1921. DOI: https://doi.org/10.1121/1.1557214

Kikuchi, M & Aiken, I. D. (1998). An analytical hysteresis model for elastomeric seismic isolation bearings. Earthquake Engineering and Structural Dynamics, 26(2), 215-231.

Lin, T. R., Farag, N. H., & Pan, J. (2005). Evaluation of frequency dependent rubber mount stiffness and damping by impact test. Applied Acoustics, 66(7), 829-844. DOI: https://doi.org/10.1016/j.apacoust.2004.10.004

Lin, H., Bengisu, T. & Mourelatos, Z. (2011). Modeling the Stiffness and Damping Properties of Styrene-Butadiene Rubber. SAE Technical Paper 2011-01-1628. DOI: https://doi.org/10.4271/2011-01-1628

Liu, C. H., Hsu, Y. Y., & Yang, S. H. (2021). Geometry Optimization for a Rubber Mount with Desired Stiffness Values in Two Loading Directions Considering Hyperelasticity and Viscoelasticity. International Journal of Automotive Technology, 22(3), 609-619. DOI: https://doi.org/10.1007/s12239-021-0057-8

Luo, H., Guo, S., Yu, C., Fu, J., Wang, H., Liu, G., & Luo, Z. (2021). Vibration suppression analysis and experimental test of additional constrained damping layer in space science experiment cabinet. Composites and Advanced Materials, 30, 633366X2097865. DOI: https://doi.org/10.1177/2633366x20978659

Mallamace, F., Micali, N., & Vasi, C. (1990). Viscoelastic properties of charged colloids, polystyrene, and silica-water suspensions. Physical Review A, 42(12), 7304-7311. DOI: https://doi.org/10.1103/physreva.42.7304

Medalia, A. I. (1978). Effect of Carbon Black on Dynamic Properties of Rubber Vulcanizates. Rubber Chemistry and Technology, 51(3), 437-523. DOI: https://doi.org/10.5254/1.3535748

Nasonov, D., Ilichev, V., & Raevsky, V. (2021a). The experimental study of elastic-hysteresis properties of rubber elements of sleeve-pin couplings. Vibroengineering PROCEDIA, 38, 193-197. DOI: https://doi.org/10.21595/vp.2021.22055

Ooi, L. E., & Ripin, Z. M. (2011). Dynamic stiffness and loss factor measurement of engine rubber mount by impact test. Materials & Design, 32(4), 1880-1887. DOI: https://doi.org/10.1016/j.matdes.2010.12.015

Penas, R., Gaudin, A., Kreis, A. & Balmes, E. (2019). Dissipation in hysteretic rubber mount models. European Conference on Constitutive Models for Rubber, 1-6.

Sommer, J., & Meyer, D. (1974). Factors Controlling the Dynamic Properties of Elastomeric Products. Journal of Elastomers & Plastics, 6(1), 49-68. DOI: https://doi.org/10.1177/009524437400600105

Sun, D. W., Chen, Z. G., Zhang, G. Y., & Eberhard, P. (2011). Modeling and parameter identification of amplitude- and frequency-dependent rubber isolator. Journal of Central South University, 18(3), 672-678. DOI: https://doi.org/10.1007/s11771-011-0746-y

Tolpekina, T., Pyckhout-Hintzen, W., & Persson, B. (2019). Linear and Nonlinear Viscoelastic Modulus of Rubber. Lubricants, 7(3), 22. DOI: https://doi.org/10.3390/lubricants7030022

Tschoegl, N. W., & Tschoegl, C. A. (2011). The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction (Softcover reprint of the original 1st ed. 1989 ed.). Springer.

Ucar, H., & Basdogan, I. (2018). Vibration Response Prediction on Rubber Mounts with a Hybrid Approach. The International Journal of Acoustics and Vibration, 23(1). DOI: https://doi.org/10.20855/ijav.2018.23.11109

Wollscheid, D., & Lion, A. (2013). The benefit of fractional derivatives in modelling the dynamics of filler-reinforced rubber under large strains: a comparison with the Maxwell-element approach. Computational Mechanics, 53(5), 1015-1031. DOI: https://doi.org/10.1007/s00466-013-0946-4

Xiao, H., Xu, C., Wang, R., Yu, P., Zhou, J., & Bai, J. (2021). A Nonlinear Model and Parameter Identification Method for Rubber Isolators under Shock Excitation in Underwater Vehicles. Journal of Marine Science and Engineering, 9(11), 1282. DOI: https://doi.org/10.3390/jmse9111282

Yang, Q., & Zhou, Y. (2020). Experimental Study on Hysteresis Characteristics of Fluorosilicone Rubber Damper. IOP Conference Series: Materials Science and Engineering, 887(1), 012023. DOI: https://doi.org/10.1088/1757-899x/887/1/012023

Yin, B., Hu, X., Luo, W., & Song, K. (2017). Application of fractional calculus methods to asymmetric dynamical response of CB-Filled rubber. Polymer Testing, 61, 416-420. DOI: https://doi.org/10.1016/j.polymertesting.2017.06.002

Yin, B., Hu, X., & Song, K. (2018). Evaluation of classic and fractional models as constitutive relations for carbon black–filled rubber. Journal of Elastomers & Plastics, 50(5), 463-477. DOI: https://doi.org/10.1177/0095244317733767

Yu, Y., Naganathan, N. G., & Dukkipati, R. V. (2001). A literature review of automotive vehicle engine mounting systems. Mechanism and Machine Theory, 36(1), 123-142. DOI: https://doi.org/10.1016/s0094-114x(00)00023-9

Zaitsev, S., Shtempluck, O., Buks, E., & Gottlieb, O. (2011). Nonlinear damping in a micromechanical oscillator. Nonlinear Dynamics, 67(1), 859-883. DOI: https://doi.org/10.1007/s11071-011-0031-5

Zhang, J., & Richards, C. M. (2007). Parameter identification of analytical and experimental rubber isolators represented by Maxwell models. Mechanical Systems and Signal Processing, 21(7), 2814-2832. DOI: https://doi.org/10.1016/j.ymssp.2007.02.007




How to Cite

Lu Ean Ooi, Wan Mohd Amri Wan Mamat Ali, & Iskandazaqwan Zikrullah Zainudin. (2023). Evaluation of dynamic properties of rubber mounts by Levenberg–Marquardt method. Journal of Current Science and Technology, 12(2), 274–285. Retrieved from https://ph04.tci-thaijo.org/index.php/JCST/article/view/289



Research Article