Petites oscillations d'un liquide dans un vase fermé par une membrane élastique. (Small oscillations of a liquid in a rigid container closed by an elastic membrane)
type: Item
instance of: scholarly article
title: Petites oscillations d'un liquide dans un vase fermé par une membrane élastique. (Small oscillations of a liquid in a rigid container closed by an elastic membrane)
zbMATH Open document ID: 0663.76004
DOI: 10.1007/BF00945121
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: The problem of the small oscillations of a liquid in a rigid container closed by an elastic membrane is investigated. In the first part, the container is fixed. In the general case, the existence of the eigenfrequencies of the system is proved by means of the methods of the functional analysis. An analytic solution is given in the case of a circular cylindrical container. The second part deals with a moving container. The equations of motion are obtained by means of a variational principle and are written in the form of an operational equation in a suitable Hilbert space. The existence of the eigenfrequencies arises from the theory of the completely continuous self-adjoint operators in an Hilbert space.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 47B99
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35P99
zbMATH DE Number: 4085205
zbMATH Keywords: small oscillations
zbMATH Keywords: elastic membrane
zbMATH Keywords: eigenfrequencies
zbMATH Keywords: analytic solution
zbMATH Keywords: circular cylindrical container
zbMATH Keywords: moving container
zbMATH Keywords: Hilbert space
zbMATH Keywords: completely continuous self-adjoint operators
author: P. Capodanno
MaRDI profile type: Publication
cites work: Q4068312
cites work: Sur les petites oscillations d'un pendule élastique contenant un liquide. (Small oscillations of an elastic pendulum containing a liquid)
cites work: Q3789190
cites work: Q5820721
cites work: Q5732873
cites work: Q5599957
cites work: Q5557046
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full work available at URL: https://doi.org/10.1007/bf00945121
OpenAlex ID: W2253499217
description: scientific article; zbMATH DE number 4085205