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Spatial evolution of
harmonic vibrations in linear elasticity
Stan Chiriţă and Michele Ciarletta |
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Vol. 3 (2008), No. 9, 1675–1693
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Abstract |
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In the present paper we consider a prismatic cylinder occupied by an anisotropic homogeneous compressible linear elastic material that is subject to zero body force and zero displacement on the lateral boundary. The elasticity tensor is strongly elliptic and the motion is induced by a harmonic time–dependent displacement specified pointwise over the base. We establish some spatial estimates for appropriate cross–sectional measures associated with the harmonic vibrations that describe how the corresponding amplitude evolves with respect to the axial distance at the excited base. The results are established for finite as well as for semi-infinite cylinders (where alternatives results of Phragmén-Lindelöf type are obtained) and the exciting frequencies can take appropriate low and high values. In fact, for the low frequency range the established spatial estimates are of exponential type, while for the high frequency range the spatial estimates are of a certain algebraic type. |
Keywords
spatial behavior, harmonic vibrations, linear elasticity,
strongly elliptic elasticity tensor
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Milestones
Received: 8 May 2008
Revised: 22 September 2008
Accepted: 23 September 2008
Published: 1 November 2008
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Authors |
| Stan Chiriţă | |
| Faculty of Mathematics Al.I. Cuza University of Iaşi Blvd. Carol I, nr. 11 700506 - Iaşi Romania |
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| Michele Ciarletta | |
| Dipartimento di Ingegneria
dell’Informazione e Matematica Applicata (DIIMA) Università di Salerno Via Ponte Don Melillo 84084 Fisciano (SA) Italy |
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