# Dynamic analysis of a cracked bar by the method of characteristics

Dynamic analysis of a cracked bar by the method of characteristics The purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem.Design/methodology/approachThe bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations.FindingsIn this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack.Originality/valueA numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Structural Integrity Emerald Publishing

# Dynamic analysis of a cracked bar by the method of characteristics

, Volume 10 (4): 16 – Aug 7, 2019
16 pages

/lp/emerald-publishing/dynamic-analysis-of-a-cracked-bar-by-the-method-of-characteristics-6EfCSgXzCx
Publisher
Emerald Publishing
ISSN
1757-9864
DOI
10.1108/ijsi-01-2018-0001
Publisher site
See Article on Publisher Site

### Abstract

The purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem.Design/methodology/approachThe bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations.FindingsIn this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack.Originality/valueA numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar.

### Journal

International Journal of Structural IntegrityEmerald Publishing

Published: Aug 7, 2019

Keywords: Wave propagation; Crack; Method of characteristics; Impulse forces; Longitudinal spring

### References

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