Reduced-order Modelling of the Linear Vibration Response of Expanded Polymer Cushion Material

• Published in: Packaging technology & science 2015-01, Vol.28 (1), p.59-74
• Main Authors: Batt, Gregory S., Gibert, James M., Daqaq, Mohammed
• Format: Article
• Language: English
• Subjects: assumed mode; cushion; Dynamical systems; Eigenvalues; Mathematical analysis; Nonlinearity; Packaging; Plastic foam; reduced order; Softening; Stress-strain relationships; vibration; viscoelastic
• ISSN: 0894-3214; 1099-1522
• DOI: 10.1002/pts.2086

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. Copyright © 2014 John Wiley & Sons, Ltd. 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. Approximate eigenvalues and frequency response functions are compared with both exact and experimental eigenvalues reported in literature.