Primary resonance behavior of expanded polymer cushion material under low-intensity harmonic excitations

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 behavior of packaging systems. In this dissertation, the free and forced vibration response of a nonlinear, distributed-parameter model of a viscoelastic rod with an applied tip-mass is used to investigate the response of expanded polymer cushion materials to low-intensity harmonic excitations. The rod and tip-mass represent an idealized packaged product system. A nonlinear model is developed from constitutive relations. A classical Maxwell-Weichert model, represented via a Prony series, is used to model the viscoelastic behavior. The model parameters are experimentally identified through the use of static and quasi-static test results. Three different solution techniques are applied, free and forced vibration solutions derived, and used to study the behavior of an idealized packaging system containing Nova Chemicals' Arcel foam. Each solution is validated against experimental results. The first part of this work focuses on the study of the system response linearized about a static equilibrium position. The exact solution to the free and forced vibration problem is considered first, followed by the development of a reduced-order model (ROM). It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss moduli necessitate the use of additional Prony series terms. Comparison of the ROM solution with that of the exact solution are used to determine the number of modal equations needed for the ROM to accurately capture the steady-state dynamic behavior of the packaging system. It is also shown that both models are able to predict the modal frequencies and the primary resonance response at low acceleration levels with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a solution to the nonlinear elastic model. It is concluded that, although proven in its ability to absorb high frequency inputs (impact and shock), Arcel is not an ideal material for energy dissipation at lower frequencies, especially close to the first modal frequency of the mass/rod system. The second part of the dissertation covers solution of the nonlinear model. 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. Results show that the single-mode analytical solution is capable of capturing the nonlinear bending behavior missed by the 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 linearized system response, nonlinear modeling can benefit from further work done in the low strain characterization of expanded polymer foam.