Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T21:42:52.233Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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