Vol. 3, No. 9, 2008

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Spatial evolution of harmonic vibrations in linear elasticity

Stan Chiriţă and Michele Ciarletta

Vol. 3 (2008), No. 9, 1675–1693

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.

spatial behavior, harmonic vibrations, linear elasticity, strongly elliptic elasticity tensor
Received: 8 May 2008
Revised: 22 September 2008
Accepted: 23 September 2008
Published: 1 November 2008
Stan Chiriţă
Faculty of Mathematics
Al.I. Cuza University of Iaşi
Blvd. Carol I, nr. 11
700506 - Iaşi
Michele Ciarletta
Dipartimento di Ingegneria dell’Informazione e Matematica Applicata (DIIMA)
Università di Salerno
Via Ponte Don Melillo
84084 Fisciano (SA)