Spatial Behaviour for the Harmonic Vibrations in Plates of Kirchhoff Type

Volume 4, Issue 4, 2003

Article 65

SPATIAL BEHAVIOUR FOR THE HARMONIC VIBRATIONS IN PLATES OF KIRCHHOFF TYPE

CIRO D'APICE AND STAN CHIRITA

DIIMA, UNIVERSITY OF SALERNO,
VIA PONTE DON MELILLO,
84084 FISCIANO (SA), ITALY.
E-Mail: dapice@diima.unisa.it

FACULTY OF MATHEMATICS,
UNIVERSITY OF IASI,
6600-IASI, ROMANIA.

Received 20 February, 2003; Accepted 08 April, 2003.
Communicated by: A. Fiorenza

ABSTRACT. In this paper the spatial behaviour of the steady-state solutions for an equation of Kirchhoff type describing the motion of thin plates is investigated. Growth and decay estimates are established associating some appropriate cross-sectional line and area integral measures with the amplitude of the harmonic vibrations, provided the excited frequency is lower than a certain critical value. The method of proof is based on a second-order differential inequality leading to an alternative of Phragmèn-Lindelöf type in terms of an area measure of the amplitude in question. The critical frequency is individuated by using some Wirtinger and Knowles inequalities.

Key words:
Kirchhoff plates, Spatial behaviour, Harmonic vibrations.

2000 Mathematics Subject Classification:
74K20, 74H45.

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