First-Order, Quasi-Linear Equations and The Method of Characteristics

1997 ◽  
pp. 111-133
Author(s):  
Lokenath Debnath
Keyword(s):  
Method Of Characteristics ◽  
Linear Equations ◽  
First Order ◽  
The Method Of Characteristics

Dynamic analysis of a cracked bar by the method of characteristics

2019 ◽  
Vol 10 (4) ◽  
pp. 438-453 ◽  
Author(s):  
Hillal Ayas ◽  
Mohamed Chabaat ◽  
Lyes Amara
Keyword(s):  
Design Methodology ◽  
Method Of Characteristics ◽  
Numerical Approach ◽  
Crack Size ◽  
Equation Of Motion ◽  
Content Type ◽  
Reflected Waves ◽  
First Order ◽  
The Method Of Characteristics ◽  
The Difference

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.

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