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Volume 4, Issue 4, Article 65 |
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Spatial Behaviour for the Harmonic Vibrations in Plates of Kirchhoff Type
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Authors: |
Ciro D Apice, Stan Chirita, |
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Keywords:
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Kirchhoff plates, Spatial behaviour, Harmonic vibrations. |
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Date Received:
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20/02/03 |
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Date Accepted:
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08/04/03 |
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Subject Codes: |
74K20,74H45.
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Editors: |
Alberto Fiorenza, |
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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.
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