Comparison of Vibration Response Spectrum With Linear and Reverse-Miso Frequency Response Functions for Non-Linear Cushioning Systems

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There are two main characteristics of cushioning materials, such as expanded polystyrene (EPS), that are required to design a robust protection of critical element against environmental 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 judged by a Shock Response Spectrum (SRS). The Frequency Response Function (FRF) performs similar function in relation to vibrations. This paper is concerned with the latter. Cushioning materials are generally non-linear and, together with the interacting mass, form a non-linear dynamic system. Parker et al. [1,2], who used the Reverse MISO method ([3]), have shown that a typical linear Frequency Response Function is not able to adequately characterise the vibration transmissibility of cushioning materials, in contrast to the R-MISO method. However, the R-MISO technique results in more than one FRF term, which creates ambiguity in relation to the effect of transmitted vibration on the critical element (Fig. 2). This paper proposes to resolve it, by analogy to the SRS, through a numerical calculation of the Vibration Response Spectrum (VRS) for a hypothetical critical element, using either experimental cushion response data or synthesised via R-MISO FRFs, as the excitation of the critical element. Values of the VRS are defined as the ratio of acceleration rms of critical element to the rms of its excitation (Fig. 2), although other descriptors of critical element’s exertion can also be considered. Since the cushion system is non-linear, the excitation of the critical element will generally be non-Gaussian (Fig. 1). A chosen hypothetical critical element can be linear or, if its characteristics can be determined in advance, non-linear. In this paper experimental data of vibration transmissibility for broadband excitation (5-100Hz) is used to calculate the linear and the R-MISO non-linear FRFs. The measured cushion response signal is then used in a numerical SDOF model with an arbitrary damping ratio (0.05 in this case) to predict the response of critical element. The results for the EPS, subjected to the static load associated with the optimum shock attenuation (5.2 kPa), are shown as an example of results.