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Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

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The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.

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  1. Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1980)

  2. Gent, A.N.: Engineering with Rubber. Oxford University Press, New York (1992)

  3. Gibson, R.F.: Principles of Composite Material Mechanics. McGraw-Hill, New York (1994)

  4. Lazan, B.J.: Damping of Materials and Members in Structural Mechanics. Pergamon Press, New York (1968)

  5. McKenna, G.B., Simon, S.L.: Time dependent volume and enthalpy responses in polymers. Am. Soc. Test. Mater. 1357, 18–46 (2000)

    Google Scholar 

  6. Snowdon, J.C.: Vibration and Shock in Damped Mechanical Systems. Wiley, New York (1968)

  7. Jones, D.I.G.: Temperature-frequency dependence of dynamic properties of damping materials. J. Sound Vib. 33, 451–470 (1973)

    Article  Google Scholar 

  8. Sharma, M.G.: Dynamic behavior of rubber. In: Vibration and Acoustics Measurements Handbook. Chapter 8, pp. 205–261. Spartan Books, New York (1972)

  9. Scallamach, A., Sellen, D.B., Greensmith, H.W.: Dynamic behavior of rubber during moderate extensions. Br. J Appl. Phys. 16, 241–249 (1965)

    Article  Google Scholar 

  10. Harwood, J.A.C., Schallamach, A.: Dynamic behavior of natural rubber during large extensions. J. Appl. Polym. Sci. 2, 1835–1845 (1967)

    Article  Google Scholar 

  11. McCallion, H., Davies, D.M.: Behavior of rubber in compression under dynamic conditions. Proc. Inst. Mech. Eng. (Lond) 169, 1124–1134 (1955)

    Google Scholar 

  12. Mitchell, W.S.: Physical properties of rubber. In: Vibration and Acoustics Measurements Handbook. Chapter 7, pp. 181–203. Spartan Books, New York (1972)

  13. Kim, H.Y., Bang, W.J., Kim, J.S.: Large Deformation FEA of Automotive Rubber Components by Using ABAQUS, ABAQUS User’s Conference Procedure, Newport, RI, pp. 255–269 (1992)

  14. Jones, G.D.: Handbook of Viscoelastic Vibration Damping. Wiley, New York (2001)

  15. Lee, N.K., Lee, M.S., Kim, H.Y., Kim, J.J.: Design of engine mount using finite element method and optimization technique. Soc. Autom. Eng. 980379 (1998)

  16. Morman Jr.K.N., Kao, B.G., Nagragaal, J.C.: Finite element analysis of viscoelastic elastomeric structures vibrating about non-linear statically stressed configurations. Soc. Auto. Eng. 811309 (1981)

  17. Ver, I.L.: Measurement of dynamic stiffness and loss factor of elastic mounts as a function of frequency and static loads. Noise Contr. Eng. 3, 37–42 (1974)

    Google Scholar 

  18. Culbertstone, P., Yang, H., Peng, J., Huang, M., Kang, S.: Use of body mount stiffness and damping in CAE crash modeling. Soc. Autom. Eng. 2000-01-0120 (2000)

  19. Lockett, F.J.: Nonlinear Viscoelastic Solids. Academic Press, New York (1972)

  20. Christensen, R.M.: Theory of Viscoelasticity. Academic Press, New York (1971)

  21. Skrypnyk, I.D., Spoormaker, J.L., Kandachar, P.: A constitutive model for long-term behavior of polymer. Am. Soc. Test. Mat. 1357, 71–82 (2000)

    Google Scholar 

  22. Skrypnyk, I.D., Spoormaker, J.L., Smit, W.: Implementation of constitutive model in FEA for nonlinear behavior of plastics. Am. Soc. Test. Mat. 1357, 83–97 (2000)

    Google Scholar 

  23. Mark, J.E., Erman, B., Eirich, F.R.: Science and Technology of Rubber. Academic Press, London (1994)

  24. Golden, H.J., Strganac, T.W., Schapery, R.A.: An approach to characterize nonlinear viscoelastic material behavior using dynamic mechanical tests and analysis. J. Appl. Mech. 66, 872–878 (1999)

    Google Scholar 

  25. Schapery, R.A., Cantey, D.A.: Thermomechanical response studies of solid propellants subjected to cyclic and random loading. AAIA J. 4, 255–264 (1966)

    Article  Google Scholar 

  26. Schapery, R.A.: On characterization of nonlinear viscoelastic materials. J. Polym. Eng. Sci. 9, 295–310 (1969)

    Article  Google Scholar 

  27. ASTM D-945-92 (Reapproved, 2001), Standard test Methods for Rubber Properties in Compression or Shear (Mechanical Oscillograph), American Society of Testing and Materials.

  28. Macioce, P.J., Nashif, A.D., Lewis, T.M.: Direct measurement of the dynamic material properties of polymers for low frequency. Processing of Damping 2, San Diego, EBA 1–EBA 17 (1991)

  29. Murayama, T.: Dynamic Mechanical Analysis of Polymeric Material. Elsevier Scientific, New York (1978)

  30. Sattinger, S.S.: Direct method for measuring the dynamic shear properties of damping polymers. Am. Chem. Soc. Symp. Ser. 424, 79–91 (1990)

    Google Scholar 

  31. Weissman, P.T., Chartoff, R.P.: Extrapolation viscoelastic data in the temperature-frequency domain. Am. Chem. Soc. Symp. Ser. 424, 111–131 (1990)

    Google Scholar 

  32. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

  33. Ruelle, D.: Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press, New York (1989)

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Correspondence to R. A. Ibrahim.

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Shaska, K., Ibrahim, R.A. & Gibson, R.F. Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators. Nonlinear Dyn 47, 83–104 (2007).

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