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.