A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions

A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions

The purpose of the present paper is the development of a physically discrete model for free transverse constrained vibrations of beams. The discrete model consists on an N-degree of freedom system made of masses placed at the end of solid bars connected with spiral springs. The calculations made inv...

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Main Authors: Rahmouni A., Beidouri Z., Benamar R.
Format: Article
Language:English
Published: EDP Sciences 2012-07-01
Series:MATEC Web of Conferences
Online Access:http://dx.doi.org/10.1051/matecconf/20120110015
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spelling doaj-de50b078e93f497c8462ebeeb350e0c82021-02-02T00:04:27ZengEDP SciencesMATEC Web of Conferences2261-236X2012-07-0111001510.1051/matecconf/20120110015A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary ConditionsRahmouni A.Beidouri Z.Benamar R.The purpose of the present paper is the development of a physically discrete model for free transverse constrained vibrations of beams. The discrete model consists on an N-degree of freedom system made of masses placed at the end of solid bars connected with spiral springs. The calculations made involve two tensors, namely the mass tensor [mij] and the linear rigidity tensor [kij]. The results obtained by the physically discrete model show a good agreement and a quick convergence to the equivalent continuous beam for various end conditions for both the natural frequencies and the corresponding mode shapes. The model proposed in the present paper, which has been validated here using classical cases, may be easily applied to the flexural vibration of beams with various types of discontinuities, and to beams carrying concentrated masses. http://dx.doi.org/10.1051/matecconf/20120110015
collection DOAJ
language English
format Article
sources DOAJ
author Rahmouni A.
Beidouri Z.
Benamar R.
spellingShingle Rahmouni A.
Beidouri Z.
Benamar R.
A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
MATEC Web of Conferences
author_facet Rahmouni A.
Beidouri Z.
Benamar R.
author_sort Rahmouni A.
title A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
title_short A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
title_full A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
title_fullStr A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
title_full_unstemmed A Discrete Model for the Natural Frequencies and Mode Shapes of Constrained Vibrations of Beams with Various Boundary Conditions
title_sort discrete model for the natural frequencies and mode shapes of constrained vibrations of beams with various boundary conditions
publisher EDP Sciences
series MATEC Web of Conferences
issn 2261-236X
publishDate 2012-07-01
description The purpose of the present paper is the development of a physically discrete model for free transverse constrained vibrations of beams. The discrete model consists on an N-degree of freedom system made of masses placed at the end of solid bars connected with spiral springs. The calculations made involve two tensors, namely the mass tensor [mij] and the linear rigidity tensor [kij]. The results obtained by the physically discrete model show a good agreement and a quick convergence to the equivalent continuous beam for various end conditions for both the natural frequencies and the corresponding mode shapes. The model proposed in the present paper, which has been validated here using classical cases, may be easily applied to the flexural vibration of beams with various types of discontinuities, and to beams carrying concentrated masses.
url http://dx.doi.org/10.1051/matecconf/20120110015
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