No abstract

Cushion curves enable packaging designers to optimize a design solution for a given product fragility and expected distribution environment drop height. The industry accepted techniques for developing these curves are time intensive and devoid of a physical understanding of the materials and the physics involve in energy absorption. This paper delves into a qualitative understanding of the dynamics of a platen impacting an open cell foam cushion material. An hyperelastic material model is used to describe the foam's nonlinear stress-strain relationship, while its damping and hysteretic behaviour are represented with linear viscoelasticity. Using a simple nonlinear, discontinuous model of a drop test along with numerical simulations, the study examines the physics of the impact. The numerical studies show that the model is able to provide predictions of the shock pulse's shape, duration and amplitude at various static stresses and drop heights. The dynamic cushion curves generated by the model retain the characteristic concave upward 'trough' shape of the experimental curves. Furthermore, the model shows that the optimal amplitude of shock absorbed for a given set of drop conditions depends on the foam's thickness and cross-sectional area. Lastly, the model is validated using the comparison of a predicted curve and experimental data captured using a cushion tester.

The demand to lower costs and reduce the amount of packaging materials utilized in a packaged product system has placed increased importance on the development of tools to model the behaviour of packaging systems. This manuscript examines the accuracy and convergence of a reduced-order model (ROM). The ROM is derived from an idealized packaging system consisting of a rod of polymer foam with an attached end mass. The work begins with an introduction to the complex cyclic softening and the viscoelastic and nonlinear stress-strain behaviour exhibited by expanded polymer foam. The partial differential equations and associated boundary conditions governing the motion of the system are obtained. The equations are reduced to an ROM using the assumed modes method. Approximate eigenvalues are compared with both exact and experimental eigenvalues reported in literature. Finally, the ROM is compared with the frequency response functions of the exact solution and those obtained experimentally. Both results are used to determine the number of modal equations needed for the ROM to accurately capture the steady-state dynamic behaviour of the packaging system.

A data recorder was utilized to record in-fl ight vibration of a twin engine turbo propeller (feeder) aircraft. The data recorded produced power spectral density (PSD) profi les which are currently used in laboratory settings to drive vibration tables in order to simulate a particular vehicle type. Overall Grms values were averaged and compared to previous research studies.The data collected from this research study could be utilized for packaging research when developing products and packages that will pass through a distribution cycle which includes transportation via a feeder aircraft. One example of this type of distribution cycle is the small parcel shipping environment. The PSD profi les which were analyzed from this research could simulate in-fl ight aircraft vibration of the aircraft chassis in a laboratory environment. This will enable further research in the air transport environment.

This manuscript highlights an analytical solution to a nonlinear, viscoelastic model of expanded polymer foam. The governing partial differential equation is discretized into a single-mode nonlinear ordinary differential equation (ODE). Solution of the nonlinear ODE is analytically approximated using the method of multiple scales. Comparison to experimental data reveals that the single-mode analytical solution is capable of capturing the nonlinear bending behaviour missed by a previously solved linearized model. It is also shown that limitations due to the system-identification data-collection method affect the ability of the model to capture the degree of nonlinearity present at lower strain levels. While this limitation has no observable effect on the previously studied linearized system response, nonlinear modelling can benefit from further work performed in the low strain characterization of expanded polymer foam. Lastly, the nonlinear solution is used to study the effect of varying excitation acceleration and static stress on the frequency response of expanded polymer foam.