A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses
type: Item
instance of: scholarly article
title: A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses
zbMATH Open document ID: 1003.74037
DOI: 10.1016/S0020-7403(99)00049-1
published in: International Journal of Mechanical Sciences
publication date: 2003-01-27T00:00:00Z
review text: The author presents a frequency analysis for Euler-Bernoulli beams carring multiple masses with different boundary conditions. The location of concentrated masses on a uniform beam is arbitrary. The exact frequency equations for classical boundary conditions (fixed, free, pinned, guided ends) are derived by using differential equations and boundary and compatibility conditions of the corresponding eigenvalue problems. Then the author derives the frequency equation in ``determinant'' form by the application of Maple. The main purpose is to investigate the validity of Dunkerley formula for uniform Euler-Bernoulli beams carring multiple masses. The author discuss a modification of Dunkerley formula, and the results obtained by the modified Dunkerley formula are compared to those obtained from the ``exact'' frequency equations. An error parameter is introduced to characterize the efficiency of Dunkerley's formula. The author establishes that the modified Dunkerley expression can generally yield good approximation of natural frequencies. The computational time saved due to Dunkerley method is illustrated by several examples.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1488703
zbMATH Keywords: eigenfrequencies
zbMATH Keywords: Euler-Bernoulli beams
zbMATH Keywords: concentrated masses
zbMATH Keywords: frequency equations
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: modified Dunkerley formula
zbMATH Keywords: error parameter
author: K. H. Low
reviewed by: István Ecsedi
describes a project that uses: Maple
MaRDI profile type: Publication
Wikidata QID: Q127633390
full work available at URL: s0020-7403(99)00049-1
OpenAlex ID: W1966325099
description: scientific article; zbMATH DE number 1488703