Exact expressions for numerical evaluation of high order modes of vibration in uniform Euler-Bernoulli beams

Document Type

Article

Source of Publication

Applied Acoustics

Publication Date

12-1-2018

Abstract

© 2018 Elsevier Ltd In the literature, expressions can be found for the mode shape functions of uniform Euler-Bernoulli beams. However, these expressions permit the evaluation of only the first 12 modes or so due to numerical issues associated with the evaluation of near field waves that increase exponentially with frequency. To overcome this problem, approximate expressions have been developed that avoid the evaluation of these waves. This article presents in tabular form alternative, exact expressions of beam mode shape functions that are numerically stable. These formulations have not been reported in the literature before and they are of special interest for researchers working in the area of structural acoustics and vibration. Beams with combinations of the classical boundary conditions of clamped, free, pinned, and sliding are considered.

ISSN

0003-682X

Publisher

Elsevier Ltd

Volume

141

First Page

371

Last Page

373

Disciplines

Life Sciences

Keywords

Architectural acoustics, Approximate expressions, High order mode, Mode shape function, Near fields, Structural acoustics and vibration, Uniform Euler-Bernoulli beams, Function evaluation

Scopus ID

85050818335

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Green: A manuscript of this publication is openly available in a repository

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