Characterisation of the Nonlinear Behaviour of Expanded Polystyrene Cushions


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There are two main characteristics of cushioning materials that are required to design a robust cushioning system for the protection of critical element against enviro-mechanical hazards: the attenuation of shocks as a function of the static load and the vibration transmissibility. The effect of a shock on a hypothetical critical element is normally evaluated by the Shock Response Spectrum (SRS) whereas the Frequency Response Function (FRF) performs similar function in relation to vibrations. This paper is concerned with the latter. Cushioning materials are generally nonlinear and, together with the interacting mass, form a nonlinear dynamic system. This paper shows how the Reverse Multiple Input-Single-Output (R-MISO) method can be used to describe the nonlinear characteristics of cushioning systems by generating a series of FRF terms. However, this creates ambiguity in relation to the effect of transmitted vibration on the critical element. This paper proposes to resolve this, by analogy to the SRS, through a numerical calculation of the Vibration Response Spectrum (VRS) for a hypothetical critical element, using as the excitation of the critical element either experimental cushion response data or data synthesised via R-MISO FRFs. Values of the VRS are defined as the ratio of acceleration rms of the critical element to the rms of the cushion excitation, although other descriptors of critical element's exertion can also be considered. The VRS can be considered as the true transmissibility. It is shown that the R-MISO method is superior over the Single Input-Single-Output (SISO) method in determining the transmissibility of polystyrene cushions. Since the cushion system is nonlinear, the excitation of the linear critical element will in general be non-Gaussian, although this paper has shown that it is near- Gaussian in the vicinity of cushion resonance. A chosen hypothetical critical element can be linear or, if its characteristics is known in advance, nonlinear. Results presented in this paper demonstrate how the R-MISO and the VRS can be used to determine the dynamic characteristics of EPS as a nonlinear cushioning material.



Edited by:

J. Quinta da Fonseca




M. A. Sek et al., "Characterisation of the Nonlinear Behaviour of Expanded Polystyrene Cushions", Applied Mechanics and Materials, Vols. 7-8, pp. 283-288, 2007

Online since:

August 2007




[1] Bendat, J.S. Nonlinear system analysis and identification from random data. John Wiley & Sons, New York, NY, (1990).

[2] Schetzen, M. The Volterra & Weiner theories of nonlinear systems. Wiley-Interscience, New York, NY, (1980).

[3] Bendat, J.S. and Piersol, A.G., Spectral analysis of nonlinear systems involving square law operations. Journal of Sound and Vibration 81 (2), 199 - 213, (1982).


[4] Bendat, J.S. and Piersol, A.G., Random Data: Analysis and Measurement Procedures, 2nd Edition, Wiley-Interscience, New York, (1986).

[5] Rice, H.J. and Fitzpatrick, J.A., A generalized technique for spectral analysis of nonlinear systems. Mechanical Systems and Signal Processing 2 (2), 195 - 207, (1988).

[6] Bendat, J.S., Nonlinear systems techniques and applications. New York, John Wiley & Sons, New York, NY, (1998).

[7] Liagre, P.F.B. Investigation of nonlinear identification techniques. PhD dissertation, Texas A&M University, 2002. Figure 7. Probability Density of the vibration response of critical element: (a) at resonance, and (b) at frequency away from resonance (b).