Free vibrations of linear viscoelastic polymer cantilever beams

Julie Diani

doi:10.5802/crmeca.15

Abstract

The free vibrations of cantilever slender beams of polymers, which are viscoelastic materials, are theoretically described using the simple Euler–Bernoulli assumption. The comparison between the theory and the experimental data collected for a thermoplastic elastomer, polyether block amide, shows very satisfactory results. Consequently, the theory is used for a thoughtful analysis of the impact of the material parameters and the beam geometry on its free vibration. Finally, the comparison of the dynamic behaviors of two polymers, using the free vibration test and a simple uniaxial tension/relaxation test, is discussed.

Highlights

In shoe sole applications, polymers are preferred for various reasons such as comfort, lightness, resistance to wear, cushioning effect, and so on
This study aimed at providing quantitative insight into the test of free vibration of a viscoelastic cantilever beam to compare polymers for dynamic applications
Applying the simple Euler– Bernoulli beam theory for linear viscoelastic materials, a very satisfactory quantitative comparison between the theory and the experimental data was obtained for a homogeneous slender beam of PEBAX® showing a rather extended spectrum of relaxation times

Summary

Introduction

Polymers are preferred for various reasons such as comfort, lightness, resistance to wear, cushioning effect, and so on. Good shock absorption is often desired, but in some sport applications, like running, elastic energy recovery is crucial to providing good bouncing. For this reason, sport brands together with polymer companies are looking for materials offering a perfect compromise. The free vibration of a slender cantilever beam was introduced by Arkema as a characterization test. To obtain a quantitative analysis of this test, the vibration of a linear viscoelastic cantilever beam was calculated using the Euler–Bernoulli beam theory. The theory was first validated on actual experimental data and ISSN (electronic) : 1873-7234 https://comptes- rendus.academie- sciences.fr/mecanique/

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Conclusion