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Decay properties of
solutions of a Mindlin-type plate model for rhombic
systems
Francesca Passarella, Vincenzo Tibullo and Vittorio Zampoli |
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Vol. 5 (2010), No. 2, 323–339
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Abstract |
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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 from the support of the given data on the time interval , where is a characteristic material constant. For distances from the support less than , 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
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Milestones
Received: 2 March 2009
Revised: 25 September 2009
Accepted: 30 September 2009
Published: 30 August 2010
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Authors |
| Francesca Passarella | |
| Department of Information
Engineering and Applied Mathematics University of Salerno via Ponte Don Melillo 84084 Fisciano (SA) Italy |
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| Vincenzo Tibullo | |
| Department of Information
Engineering and Applied Mathematics University of Salerno via Ponte Don Melillo 84084 Fisciano (SA) Italy |
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| Vittorio Zampoli | |
| Department of Information
Engineering and Applied Mathematics University of Salerno via Ponte Don Melillo 84084 Fisciano (SA) Italy |
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