Primary Resonance Behaviour of a Nonlinear, Viscoelastic Model of Expanded Polymer Cushion Material

Gregory S. Batt, James M. Gibert, Mohammed Daqaq

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)694-709
Number of pages16
JournalPackaging Technology and Science
Issue number8
StatePublished - Aug 2015


  • cushion
  • method of multiple scales
  • nonlinear
  • vibration
  • viscoelastic

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Mechanical Engineering


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