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Dynamic analysis of a cracked bar by the method of characteristics

Hillal Ayas (Department of Structures and Materials, University of Sciences and Technology Houari Boumediene, Algiers, Algeria)
Mohamed Chabaat (Department of Structures and Materials, University of Sciences and Technology Houari Boumediene, Algiers, Algeria)
Lyes Amara (Department of Civil Engineering and Hydraulics, University of Jijel, Jijel, Algeria)

International Journal of Structural Integrity

ISSN: 1757-9864

Article publication date: 12 April 2019

Issue publication date: 7 August 2019

Abstract

Purpose

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/approach

The 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.

Findings

In 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/value

A 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.

Keywords

Citation

Ayas, H., Chabaat, M. and Amara, L. (2019), "Dynamic analysis of a cracked bar by the method of characteristics", International Journal of Structural Integrity, Vol. 10 No. 4, pp. 438-453. https://doi.org/10.1108/IJSI-01-2018-0001

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited