Estimation of the Dynamic Properties of Non-linear Packaging Materials Using a Reverse Multiple Input/Single Output Based Approach

Abstract

During the distribution phase, packaged consignments are exposed to a variety of environmental hazards (such as vibrations) that, if excessively severe, may cause damage to or even destroy the product. Structural deterioration can be tracked by monitoring variations in the packaging system's modal parameters, particularly its natural frequency (stiffness). Natural frequency estimates are often extracted using a least‐squares regression curve fit, applied to an estimate of the system's frequency response function (FRF). FRF estimates are generally obtained using the Fourier transform with a single input and single output (SISO). This approach is suitable for many applications; however, as the non‐linearity of the system under analysis increases, the ability of this technique to accurately monitor changes in the system will decrease. In addition, when the excitation to the non‐linear system is varied (increased or decreased amplitude), a SISO‐based approach may indicate a shift in natural frequency (as a result of the varied input) even though no change in the condition of the system has occurred. This paper discusses an approach that is designed to separate the linear component of the system's FRF using a reverse multiple input/single output (RMISO) algorithm. Such separation will allow traditional modal parameter extraction (curve fitting) techniques to be used to monitor the condition of non‐linear systems. The paper presents the results of experiments in which expanded polystyrene samples were subjected to broad‐band random base excitation with a free‐moving load placed atop the cushion sample. Continuous acceleration measurements of the vibration table and the free‐moving load were used to compute the FRFs of the cushions, and the differences between a conventional (SISO) approach and the proposed RMISO‐based parameter extraction technique were evaluated. Copyright © 2014 John Wiley & Sons, Ltd.

Effectiveness verification of the hybrid free‐fall test

“…As shown in Figure 11, the data are the impact velocity V s and the acceleration waveform, from which we can obtain the peak acceleration € According to Equation 4, values of ω n t and V t for the target freefall height are required when predicting € x max t . The value of V t can be obtained from h t of the target free-fall height using Equation 6, and we assume that ω n t is the average of ω n s values.…”

“…In this study, the regression equation was led as ω dt = − 20.265V i + 263.78, and so ω dt values can be calculated to substitute V i for V t at the target free-fall height in this equation. V t , which is the impact velocity of the target free-fall height, can be determined using Equation 6. The target free-fall height was defined as 60, 70 and 80 cm.…”

“…Lamb and Parker suggested a reverse multiple input/single output‐based technique, which allows a traditional model parameter extraction technique to be used for analysing a nonlinear cushioning system. Batt et al examined the accuracy and convergence of a reduced‐order model (ROM), which was derived from an idealised packaging system consisting of a rod of polymer foam with an attached end mass.…”

Static and Dynamic Strength of Paperboard Containers Subjected to Variations in Climatic Conditions

“…Extensive work has previously been carried out by the authors towards the development of a post‐processing technique that can determine the condition of packaging samples as a function of time. Various techniques have been developed, most of which make use of the overall system's FRF to extract continuous estimates of the system's natural frequency, which are in turn used as a quantifiable measure of damage (loss in stiffness).…”

Monitoring the Condition of Non-linear Packaging Materials Subject to Varying Excitation Levels Using a Reverse Multiple Input/Single Output Based Approach

“…Garcia‐Romeu‐Martinez et al , Rouillard et al and Lamb, showed that the least squares regression technique can be suitable for extracting modal estimates from physical packaging systems. However, for the evaluation of non‐linear systems, the approach is limited to extracting relative estimates (pre and post damage) and to tests, which use a constant excitation level . The authors introduced a non‐linear analysis technique, which separates the linear component of the system's FRF using an optimised reverse multiple input/single output (RMISO) algorithm.…”