Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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
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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


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