Research Papers

Maxwell–Voigt and Maxwell Ladder Models for Multi-Degree-of-Freedom Elastomeric Isolation Systems

[+] Author and Article Information
Sudhir Kaul

Department of Engineering and Technology,
Western Carolina University,
Cullowhee, NC 28723
e-mail: skaul@wcu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 11, 2013; final manuscript received January 4, 2015; published online February 13, 2015. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 137(2), 021021 (Apr 01, 2015) (9 pages) Paper No: VIB-13-1397; doi: 10.1115/1.4029538 History: Received November 11, 2013; Revised January 04, 2015; Online February 13, 2015

This paper presents a model for an elastomeric isolation system consisting of a three degree-of-freedom (DOF) rigid body assembled to a frame through multiple isolators. Each elastomeric isolator is either represented by a Maxwell–Voigt (MV) model consisting of two Maxwell elements or by a Maxwell ladder (ML) model consisting of three Maxwell elements. The MV models and the ML models are characterized by using experimental data that are collected at multiple excitation frequencies. The characterized models are evaluated and used to simulate the performance of the isolation system. The models developed in this paper are capable of representing frequency-dependent behavior that is exhibited by elastomeric isolators and the overall isolation system. Furthermore, the proposed model is capable of directly associating the behavior of the isolation system with physical and geometrical properties of each isolator. The proposed model is expected to be a useful tool for the analysis and design optimization of elastomeric isolation systems. Most of the isolation systems in practical applications exhibit multiple DOF, this model will be particularly useful in such applications since it does not constrain motion to translation only. This is a shortcoming of the models in the current literature that the proposed model attempts to overcome.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Ibrahim, R. A., 2008, “Recent Advances in Nonlinear Passive Vibration Isolators,” J. Sound Vib., 314(3–5), pp. 371–452. [CrossRef]
Rivin, E. I., 2003, Passive Vibration Isolation, ASME Press, New York.
Zhang, J., and Richards, C. M., 2007, “Parameter Identification of Analytical and Experimental Rubber Isolators Represented by Maxwell Models,” Mech. Syst. Signal Process., 21(7), pp. 2814–2832. [CrossRef]
Zhang, J., and Richards, C. M., 2006, “Dynamic Analysis and Parameter Identification of a Single Mass Elastomeric Isolation System Using a Maxwell–Voigt Model,” ASME J. Vib. Acoust., 128(6), pp. 713–721. [CrossRef]
Renaud, F., Dion, J., Chevallier, G., Tawfiq, I., and Lemaire, R., 2011, “A New Identification Method of Viscoelastic Behavior: Application to the Generalized Maxwell Model,” Mech. Syst. Signal Process., 25(3), pp. 991–1010. [CrossRef]
Lu, Y. C., Anderson, M., and Nash, D., 2007, “Characterize the High-Frequency Dynamic Properties of Elastomers Using Fractional Calculus for FEM,” SAE Technical Paper No. 2007-01-2417. [CrossRef]
Hofer, P., and Lion, A., 2009, “Modelling of Frequency- and Amplitude-Dependent Material Properties of Filler-Reinforced Rubber,” J. Mech. Phys. Solids, 57(3), pp. 500–520. [CrossRef]
Shaska, K., Ibrahim, R. A., and Gibson, R. F., 2007, “Influence of Excitation Amplitude on the Characteristics of Nonlinear Butyl Rubber Isolators,” Nonlinear Dyn., 47(1–3), pp. 83–104. [CrossRef]
Ooi, L. E., and Ripin, Z. M., 2011, “Dynamic Stiffness and Loss Factor Measurement of Engine Rubber Mount by Impact Test,” Mater. Des., 32(4), pp. 1880–1887. [CrossRef]
Kulik, V. M., Semenov, B. N., Boiko, A. V., Seoudi, B. M., Chun, H. H., and Lee, I., 2009, “Measurement of Dynamic Properties of Viscoelastic Materials,” Exp. Mech., 49(3), pp. 417–425. [CrossRef]
Adhikari, S., and Pascual, B., 2011, “Iterative Methods for Eigenvalues of Viscoelastic Systems,” ASME J. Vib. Acoust., 133(2), p. 021002. [CrossRef]
Kaul, S., 2012, “Dynamic Modeling and Analysis of Mechanical Snubbing,” ASME J. Vib. Acoust., 134(2), p. 021020. [CrossRef]
Banks, H. T., Pinter, G. A., Potter, L. K., Gaitens, M. J., and Yanyo, L. C., 1999, “Modeling of Nonlinear Hysteresis in Elastomers Under Uniaxial Tension,” J. Intell. Mater. Syst. Struct., 10(2), pp. 116–134. [CrossRef]
Ackleh, A. S., Banks, H. T., and Pinter, G. A., 2002, “Well-Posedness Results for Models of Elastomers,” J. Math. Anal. Appl., 268(2), pp. 440–456. [CrossRef]
Jazar, G. N., Narimani, A., Golnaraghi, M. F., and Swanson, D. A., 2003, “Practical Frequency and Time Optimal Design of Passive Linear Vibration Isolation Mounts,” Veh. Syst. Dyn., 39(6), pp. 437–466. [CrossRef]
Lewandowski, R., and Chorazyczewski, B., 2010, “Identification of the Parameters of the Kelvin–Voigt and the Maxwell Fractional Models, Used to Modeling of Viscoelastic Dampers,” Comput. Struct., 88(1–2), pp. 1–17. [CrossRef]
Sjoberg, M., and Kari, L., 2002, “Nonlinear Behavior of a Rubber Isolator System Using Fractional Derivatives,” Veh. Syst. Dyn., 37(3), pp. 217–236. [CrossRef]
Angeli, P., Russo, G., and Paschini, A., 2013, “Carbon Fiber-Reinforced Rectangular Isolators With Compressible Elastomer: Analytical Solution for Compression and Bending,” Int. J. Solids Struct., 50(22–23), pp. 3519–3527. [CrossRef]
Chang, T. S., and Singh, M. P., 2009, “Mechanical Model Parameters for Viscoelastic Dampers,” J. Eng. Mech., 135(6), pp. 581–584. [CrossRef]
Peng, Z. K., and Lang, Z. Q., 2008, “The Effects of Nonlinearity on the Output Frequency Response of a Passive Engine Mount,” J. Sound Vib., 318(1–2), pp. 313–328. [CrossRef]
Peng, Z. K., Meng, G., Lang, Z. Q., Zhang, W. M., and Chu, F. L., 2012, “Study of the Effects of Cubic Nonlinear Damping on Vibration Isolations Using Harmonic Balance Method,” Int. J. Nonlinear Mech., 47(10), pp. 1073–1080. [CrossRef]
Park, S. W., 2001, “Analytical Modeling of Viscoelastic Dampers for Structural and Vibration Control,” Int. J. Solids Struct., 38(44–45), pp. 8065–8092. [CrossRef]
MathWorks, 2007, “MATLAB User Guide,” MathWorks, Natick, MA.
Sprague, M. A., and Geers, T. L., 2006, “A Spectral-Element/Finite-Element Analysis of a Ship-Like Structure Subjected to an Underwater Explosion,” Comput. Methods Appl. Mech. Eng., 195(17–18), pp. 2149–2167. [CrossRef]


Grahic Jump Location
Fig. 1

MMV model—3DOF system

Grahic Jump Location
Fig. 2

ML model—3DOF system

Grahic Jump Location
Fig. 3

Experimental setup and fixture—isolator data collection

Grahic Jump Location
Fig. 4

Front isolator—vertical data

Grahic Jump Location
Fig. 5

Rear isolator—fore-aft data

Grahic Jump Location
Fig. 6

Front isolator—force-deflection—simulation

Grahic Jump Location
Fig. 7

Rear isolator—force-deflection—simulation

Grahic Jump Location
Fig. 8

Displacement time history—vertical—CG

Grahic Jump Location
Fig. 9

Rotational displacement—CG

Grahic Jump Location
Fig. 10

Storage modulus comparison—front isolator

Grahic Jump Location
Fig. 11

Loss modulus comparison—front isolator

Grahic Jump Location
Fig. 12

Front isolator—force-deflection (vertical) at 10 Hz—validation—MMV model

Grahic Jump Location
Fig. 13

Front isolator—force-deflection (vertical) at 10 Hz—validation—ML model

Grahic Jump Location
Fig. 14

Rear isolator—force-deflection (fore-aft) at 12 Hz—validation—MMV model

Grahic Jump Location
Fig. 15

Rear isolator—force-deflection (fore-aft) at 12 Hz—validation—ML model

Grahic Jump Location
Fig. 16

Rear isolator—time response (fore-aft)—validation



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In