Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements

In the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET) but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine...

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Main Author: Yusuf Yesilce
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.3233/SAV-2012-0665
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author Yusuf Yesilce
author_facet Yusuf Yesilce
author_sort Yusuf Yesilce
collection DOAJ
description In the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET) but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine the exact frequency-response amplitudes of the axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements (including point masses, rotary inertias, linear springs and rotational springs) and subjected to a harmonic concentrated force and the exact natural frequencies and mode shapes of the beam for the free vibration analysis. The model allows analyzing the influence of the shear and axial force and harmonic concentrated force effects and intermediate concentrated elements on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate concentrated elements, an intermediate pinned support, applied harmonic force, left-end support and right-end support of Timoshenko beam are derived. After the derivation of the coefficient matrices, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, solving the equations associated with the last overall coefficient matrix one determines the exact dynamic response amplitudes of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force. Equating the determinant of the overall coefficient matrix to zero one determines the natural frequencies of the free vibrating system (the case of zero harmonic force) and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. The calculated vibration amplitudes of the forced vibrating systems and the natural frequencies of the free vibrating systems are given in tables for different values of the axial force. The dynamic response amplitudes and the mode shapes are presented in graphs. The effects of axial force and harmonic concentrated force on the vibration analysis of Timoshenko multi-span beam are also investigated.
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spelling doaj-art-14181118ee884850845c42680c9c538f2025-02-03T01:03:42ZengWileyShock and Vibration1070-96221875-92032012-01-0119473575210.3233/SAV-2012-0665Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated ElementsYusuf Yesilce0Civil Engineering Department, Engineering Faculty, Dokuz Eylul University, Izmir, TurkeyIn the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET) but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine the exact frequency-response amplitudes of the axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements (including point masses, rotary inertias, linear springs and rotational springs) and subjected to a harmonic concentrated force and the exact natural frequencies and mode shapes of the beam for the free vibration analysis. The model allows analyzing the influence of the shear and axial force and harmonic concentrated force effects and intermediate concentrated elements on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate concentrated elements, an intermediate pinned support, applied harmonic force, left-end support and right-end support of Timoshenko beam are derived. After the derivation of the coefficient matrices, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, solving the equations associated with the last overall coefficient matrix one determines the exact dynamic response amplitudes of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force. Equating the determinant of the overall coefficient matrix to zero one determines the natural frequencies of the free vibrating system (the case of zero harmonic force) and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. The calculated vibration amplitudes of the forced vibrating systems and the natural frequencies of the free vibrating systems are given in tables for different values of the axial force. The dynamic response amplitudes and the mode shapes are presented in graphs. The effects of axial force and harmonic concentrated force on the vibration analysis of Timoshenko multi-span beam are also investigated.http://dx.doi.org/10.3233/SAV-2012-0665
spellingShingle Yusuf Yesilce
Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
Shock and Vibration
title Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
title_full Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
title_fullStr Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
title_full_unstemmed Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
title_short Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements
title_sort free and forced vibrations of an axially loaded timoshenko multi span beam carrying a number of various concentrated elements
url http://dx.doi.org/10.3233/SAV-2012-0665
work_keys_str_mv AT yusufyesilce freeandforcedvibrationsofanaxiallyloadedtimoshenkomultispanbeamcarryinganumberofvariousconcentratedelements