Abstract
Identification of the vibrational behavior of polyurethanefoams used in automotive seats is described. The dynamic system consistsof a rigid block mounted on a 3″ cube of foam material, which serves asthe only flexible component. When constrained to undergo linearunidirectional motion, the dynamic system is modeled as a single degreeof freedom system, governed by an integro-differential equation. Inaddition to a relaxation kernel representing the linear viscoelasticbehavior of the foam, the model includes a polynomial type stiffness toaccount for the foam's strain-based nonlinearities. The relaxationkernel is assumed to be of an exponential type. Experimentalmethodologies for obtaining repeatable, accurate measurements of thesystem's response to an impulse and to single frequency harmonic baseexcitations are described. Analysis methods are then investigated forextracting the relevant linear, nonlinear, and viscoelastic parameters.Characterization of these foam properties as functions of compressionlevel is also presented.
Similar content being viewed by others
References
Cavender, K. D., 'Real time foam performance testing', Journal of Cellular Plastics 29, 1993, 350–364.
Leenslag, J. W., Huygens, E., and Tan, A., 'Recent advances in the development and characterisation of automotive comfort seating foams', Cellular Polymers 16(4), 1997, 411–430.
Hilyard, N. C., Lee, W. L., and Cunningham, A., 'Energy dissipation in polyurethane cushion foams and its role in dynamic ride comfort', in Cellular Polymers, London, UK, March 20–22, RAPRA Technology Ltd., 1991, pp. 187–191.
Casati, F. M., Herrington, R. M., Broos, R., and Miyazaki, Y., 'Tailoring the performance of molded flexible polyurethane foams for car seats', Journal of Cellular Plastics 34(5), 1998, 430–465.
Cavender, K. D. and Kinkelaar, M. R., 'Real time dynamic comfort and performance factors of polyurethane foam in automotive seating', Society of Automotive Engineers, Technical Paper 960509, 1996.
Nashif, A. D., Jones, D. I. G., and Henderson, J. P., Vibration Damping, Wiley Interscience, New York, 1985.
Muravyov, A. and Hutton, S. G., 'Closed form solutions and the eigenvalue problem for vibration of discrete viscoelastic systems', Journal of Applied Mechanics 64, 1997, 684–691.
Fosdick, R., Ketema, Y., and Yu, J. H., 'Vibration damping through the use of materials with memory', International Journal of Solids and Structures 35(5–6), 1997, 403–420.
Gandhi, F. and Chopra, I., 'A time-domain non-linear viscoelastic damper model', Smart Materials and Structures 5, 1996, 517–528.
Hager, S. L. and Craig, T. A., 'Fatigue testing of high performance flexible polyurethane foam', Journal of Cellular Plastics 28, 1992, 284–303.
Vorspohl, K., Mertes, J., Zschiesche, R., Lutter, H. D., and Drumm, R., 'Time dependence of hardness of cold cure molded flexible foams and its importance for system development', Journal of Cellular Plastics 30, 1994, 361–373.
Bagley, R. L. and Torvik, P. J., 'Fractional calculus-A different approach to the analysis of viscoelastically damped structures', AIAA Journal 21(5), 1983, 741–748.
Bagley, R. L. and Torvik, P. J., 'On the fractional calculus model of viscoelastic behavior', Journal of Rheology 30(1), 1986, 133–155.
Suarez, L. E. and Shokooh, A., 'An eigenvector expansion method for the solution of motion containing fractional derivatives', Journal of Applied Mechanics 64, 1997, 629–635.
Glöckle, W. G. and Nonnenmacher, T. F., 'Fractional integral operators and Fox functions in the theory of viscoelasticity', Macromolecules 24(24), 1991, 6426–6434.
Enelund, M., Fenander, A., and Olsson, P., 'Fractional integral formulation of constitutive equations of viscoelasticity', AIAA Journal 35(8), 1997, 1356–1362.
Sidoroff, F., 'Un modele Viscoelastique non lineare avec configuration intermediaire', Journal de Méchanique 13, 1974, 679–713.
Govindjee, S. and Reese, S., 'A presentation and comparison of two large deformation viscoelasticity models', Journal of Engineering Materials and Technology 119, 1997, 251–255
Flugge, W., Viscoelasticity, Blaisdell, Waltham, MA, 1967.
Yu, P. and Haddad, Y. M., 'A dynamic system identification method for the characterization of the rheological response of a class of viscoelastic materials', International Journal of Pressure Vessels and Piping 61, 1994, 87–97.
Yu, P. and Haddad, Y. M., 'On the dynamic system identification of the response behavior of linear viscoelastic materials', International Journal of Pressure Vessels and Piping 67, 1996, 45–54.
Gutzer, U., Seemann, W., and Hagedorn, P., 'Nonlinear structural damping described by the Masing model and the method of slowly varying amplitude and phase', in Proceedings of the 1995 Design Engineering Technical Conferences, 15th Biennial Conference on Vibration and Noise, Boston, MA, September, Vol. 3, Part A, DE Vol. 48–1, American Society of Mechanical Engineers, New York, 1995, pp. 773–779.
Liang, J. W. and Feeny, B. F., 'Identifying Coulomb and viscous friction from free-vibration decrements', Nonlinear Dynamics 16, 1998, 337–347.
Bendat, J. S. and Piersol, A. G., Random Data-Analysis and Measurement Procedures, Wiley, New York, 1986.
Cunningham, A., Huygens, E., and Leenslag, J. W., 'MDI comfort cushioning for automotive applications', Cellular Polymers 13(6), 1994, 461–472.
Moreland, J. C., Wilkes, G. L., and Turner, R. B., 'Viscoelastic behavior of flexible slabstock polyurethane foams: Dependence on temperature and relative humidity. I. Tensile and compression stress (load) relaxation', Journal of Applied Polymer Science 52, 1994, 549–568.
Moreland, J. C., Wilkes, G. L., and Turner, R. B., 'Viscoelastic behavior of flexible slabstock polyurethane foams as a function of temperature and relative humidity. II. Compressive creep behavior', Journal of Applied Polymer Science 52, 1994, 569–574.
Marple, S. L., Digital Spectral Analysis: With Applications, Prentice-Hall, Englewood Cliffs, NJ, 1987.
Davies, P., 'A recursive approach to Prony parameter estimation', Journal of Sound and Vibration 89(4), 1983, 571–583.
Jordan, D. W. and Smith, P., Nonlinear Ordinary Differential Equations, Oxford University Press, New York, 1987.
Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.
Yasuda, K. and Kawamura, S., 'A nonparametric identification technique for nonlinear vibratory systems (Proposition of the technique)', Japan Society of Mechanical Engineers International Journal 32(3), 1989, 365–372.
Yasuda, K. and Kamiya, K., 'Identification of a nonlinear beam (Proposition of an identification technique)', Japan Society of Mechanical Engineers International Journal 33(4), 1990, 535–540.
White, S. W., Kim, S. K., Davies, P., Bajaj, A. K., Liedtke, P. E., and Showers, D. K., 'Modeling and measurement of occupied car seats', in Proceedings of the 1999 SAE Noise and Vibration Conference, Paper 99NV-206, Traverse City, MI, May 1999, Vol. 1, SAE P-342, Society of Automotive Engineers, Warrendale, PA, 1999, pp. 319–330.
Nishiyama, S., 'Development of simulation system on vehicle-occupant dynamic interaction. First report: Theoretical analysis and system verification', Transactions of the Japan Society of Mechanical Engineers 59(568), 1993, 3613–3621.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
White, S.W., Kim, S.K., Bajaj, A.K. et al. Experimental Techniques and Identification of Nonlinear and Viscoelastic Properties of Flexible Polyurethane Foam. Nonlinear Dynamics 22, 281–313 (2000). https://doi.org/10.1023/A:1008302208269
Issue Date:
DOI: https://doi.org/10.1023/A:1008302208269