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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 9/2016

13-04-2016 | Original

A close-form solution applied to the free vibration of the Euler–Bernoulli beam with edge cracks

Authors: Yang Yan, Qingwen Ren, Ning Xia, Linfei Zhang

Published in: Archive of Applied Mechanics | Issue 9/2016

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Abstract

This paper investigates the free vibration of a homogeneous Euler–Bernoulli beam with multiple transverse cracks under non-symmetric boundary conditions. The differential equation is formulated by introducing Dirac’s delta function into the uniform flexural stiffness, and the close-form solution of mode shapes is then derived by applying the Laplace transform technique. The proposed method is validated against existing experimental method for damaged cantilever beams. With the validated method, a parametric study is performed to study the effect of crack numbers, damage parameters and crack locations on the natural frequencies and mode shapes for three non-symmetric boundary conditions (pinned–clamped, clamped–free shear and pinned–free shear).
previous article Nonlinear dynamic behaviors of circumferential rod fastening rotor under unbalanced pre-tightening force
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Appendix
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Metadata
Title
A close-form solution applied to the free vibration of the Euler–Bernoulli beam with edge cracks
Authors
Yang Yan
Qingwen Ren
Ning Xia
Linfei Zhang
Publication date
13-04-2016
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 9/2016
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-016-1140-x

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