On spatial behavior in linear viscoelasticity

Authors:
Catalin Gales and Stan Chirita

Journal:
Quart. Appl. Math. **67** (2009), 707-723

MSC (2000):
Primary 74D05, 74G50; Secondary 74H45, 74E10

DOI:
https://doi.org/10.1090/S0033-569X-09-01149-0

Published electronically:
May 12, 2009

MathSciNet review:
2588231

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Within the framework of linear viscoelasticity this paper deals with the study of spatial behavior of solutions describing harmonic vibrations in a right cylinder of finite extent. Some exponential decay estimates of Saint-Venant type, in terms of the distance from the excited end of the cylinder are obtained from a first-order differential inequality concerning an appropriate measure associated with the amplitude of the steady-state vibration. The dissipative mechanism guarantees the validity of the result for every value of the frequency of vibration and for the class of viscoelastic materials compatible with thermodynamics whose relaxation tensor is supposed to be symmetric and sufficiently regular. The case of a semi-infinite cylinder is also studied, and some alternatives of Phragmé n-Lindelöf type are established.

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Additional Information

**Catalin Gales**

Affiliation:
Faculty of Mathematics, Al. I. Cuza University of Iaşi, Blvd. Carol I, no. 11, 700506 – Iaşi, Romania

Email:
cgales@uaic.ro

**Stan Chirita**

Affiliation:
Faculty of Mathematics, Al. I. Cuza University of Iaşi, Blvd. Carol I, no. 11, 700506 – Iaşi, Romania

Email:
schirita@uaic.ro

DOI:
https://doi.org/10.1090/S0033-569X-09-01149-0

Keywords:
Viscoelastic cylinder,
harmonic vibrations,
spatial behavior,
dissipative effects

Received by editor(s):
May 16, 2008

Published electronically:
May 12, 2009

Additional Notes:
The authors are very grateful to the reviewer for useful observations which have led to the improvement of this paper. The authors were supported by the Romanian Ministry of Education and Research, CNCSIS Grant code ID-401, Contract no. 15/28.09.2007.

Article copyright:
© Copyright 2009
Brown University