Shock and Vibration

Shock and Vibration / 2012 / Article

Open Access

Volume 19 |Article ID 579287 | 18 pages | https://doi.org/10.3233/SAV-2012-0665

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

Received19 Apr 2011
Revised20 Oct 2011

Abstract

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.

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

458 Views | 1693 Downloads | 10 Citations
 PDF  Download Citation  Citation
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.