Vol. 5, No. 2, 2010

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ISSN: 1559-3959
Decay properties of solutions of a Mindlin-type plate model for rhombic systems

Francesca Passarella, Vincenzo Tibullo and Vittorio Zampoli

Vol. 5 (2010), No. 2, 323–339
Abstract

In the present paper, we investigate the spatial behavior of transient and steady-state solutions for the problem of bending applied to a linear Mindlin-type plate model; the plate is supposed to be made of a material characterized by rhombic isotropy, with the elasticity tensor satisfying the strong ellipticity condition. First, using an appropriate family of measures, we show that the transient solution vanishes at distances greater than cT from the support of the given data on the time interval [0,T], where c is a characteristic material constant. For distances from the support less than cT, we obtain a spatial decay estimate of Saint-Venant type. Then, for a plate whose middle section is modelled as a (bounded or semiinfinite) strip, a family of measures is used to obtain an estimate describing the spatial behavior of the amplitude of harmonic vibrations, provided that the frequency is lower than a critical value.

Keywords
plates, rhombic systems, strong ellipticity, transient and steady-state solutions
Milestones
Received: 2 March 2009
Revised: 25 September 2009
Accepted: 30 September 2009
Published: 30 August 2010
Authors
Francesca Passarella
Department of Information Engineering and Applied Mathematics
University of Salerno
via Ponte Don Melillo
84084 Fisciano (SA)
Italy
Vincenzo Tibullo
Department of Information Engineering and Applied Mathematics
University of Salerno
via Ponte Don Melillo
84084 Fisciano (SA)
Italy
Vittorio Zampoli
Department of Information Engineering and Applied Mathematics
University of Salerno
via Ponte Don Melillo
84084 Fisciano (SA)
Italy