Comptes Rendus
Free vibrations of linear viscoelastic polymer cantilever beams
Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 797-807.

Les vibrations libres d’une poutre encastrée de polymère, mesurées expérimentalement sont reproduites théoriquement à l’aide de l’hypothèse des poutres d’Euler–Bernoulli, une fois le comportement viscoélastique du matériau identifié classiquement. La théorie permet alors de simplement faire varier les paramètres matériaux et géométriques de la poutre afin de tester leurs impacts sur le test de vibration libre. En utilisant l’analyse théorique et en observant la réponse de deux matériaux lors d’un essai simple de traction/relaxation, il est possible de prédire leur comportement relatif en vibration libre.

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.

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DOI : 10.5802/crmeca.15
Mots clés : Polymer, Viscoelasticity, Vibration, Damping, Cantilever beam
Julie Diani 1

1 LMS, CNRS UMR 7649, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Free vibrations of linear viscoelastic polymer cantilever beams},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {797--807},
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Julie Diani. Free vibrations of linear viscoelastic polymer cantilever beams. Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 797-807. doi : 10.5802/crmeca.15. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.15/

[1] L. Struik Free damped vibrations of linear viscoelastic materials, Rheol. Acta, Volume 6 (1967), pp. 119-129 | DOI

[2] S. Mahmoodi; S. Khadem; M. Kokabi Non-linear free vibrations of Kelvin–Voigt visco-elastic beams, Int. J. Mech. Sci., Volume 49 (2007), pp. 722-732 | DOI

[3] M. llyasov Vibrations of linear viscoelastic materials for any herditary property, Mech. Time-Depend Mater., Volume 11 (2007), pp. 249-263

[4] M. Avcar Free vibration analysis of beams considering different geometric characteristics and boundary conditions, Int. J. Mech. Appl., Volume 4 (2014), pp. 94-100

[5] S. Mahmoodi; N. Jalili; S. Khadem An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams, J. Sound Vib., Volume 311 (2008), pp. 1409-1419 | DOI

[6] S. Timoshenko History of Strength of Materals, McGraw-Hill, New York, 1953

[7] R. M. Christiansen Theory of Viscoelasticity, Dover, New York, 2003

[8] Y. Lei; S. Adhikari; M. Friswell Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernouilli beams, Eur. J. Mech. A/Solids, Volume 42 (2013), pp. 125-136 | DOI | Zbl

[9] J. D. Ferry Viscoelastic Properties of Polymers, John Wiley & Sons, New York, 1980

[10] J. Diani; P. Gilormini On necessary precautions when measuring solid polymer linear viscoelasticity with dynamic analysis in torsion, Polym. Test., Volume 63 (2017), pp. 275-280 | DOI

[11] A. B. de Saint-Venant De la torsion des prismes avec des considérations sur leur flexion ainsi que sur l’équilibre des solides élastiques en général et des formules pratiques, Mémoires des Savants Etrangers, Paris, 1855

[12] J. P. Sheth; J. Xu; G. L. Wilkes Solid state structure-property behavior of semicrystalline poly(ether-block-amide) PEBAX® thermoplastic elastomers, Polymer, Volume 44 (2003), pp. 743-756 | DOI

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