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The decay of the energy in a viscoelastic body

Published online by Cambridge University Press:  26 February 2010

W. A. Day
W. A. Day
Affiliation:
Hertford College, Oxford
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Extract

Consider a homogeneous linear viscoelastic filament, one of whose ends is held fixed, while the other is subjected to a given traction τ(t) (t ≤ 0). I shall prove first that the total energy E(t), which is the sum of the kinetic and free energies, its derivative E′(t), and the rate of working W(t) satisfy

and

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 268 - 286
Copyright
Copyright © University College London 1980

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References

1.Dafermos, CM.. “An abstract Volterra equation with applications to linear viscoelasticity”, J. Differential Equations, 7 (1970), 554.CrossRefGoogle Scholar
2.Dafermos, C. M.. “Asymptotic stability in viscoelasticity”, Arch. Rational Meek Anal., 37 (1970), 297.CrossRefGoogle Scholar
3.Hale, J. K.. “Dynamical systems and stability”, J. Math. Analysis and Applications., 26 (1969), 39.CrossRefGoogle Scholar
4.Navarro, C. B.. “Asymptotic stability in linear thermoviscoelasticity”, J. Math. Analysis and Applications., 65 (1978), 399.CrossRefGoogle Scholar
5.Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities, Second edition (Cambridge, 1952).Google Scholar