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Numerical solution and stability for model of extensible beam
Joint Authors
Ishaq, Khalid A.
Ukashah, Faris al-Azhari
Source
Journal of Science and Technology : in Engineering and Computer Sciences
Issue
Vol. 21, Issue 3 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Sudan University of Science and Technology Deanship of Scientific Research
Publication Date
2020-12-31
Country of Publication
Sudan
No. of Pages
10
Main Subjects
Abstract EN
In this paper, numerical methods (finite differences methods for explicit and implicit) has been applied, to solve nonlinear partial differential equations.
In methodology, the beam was divided into very smaller squares, then the study discussed three partial differential equations generating from model.
The first equation called longitudinal vibrations of a beam, second equation known as transverse vibrations of a beam and then the third equation considered the extensible beam.
The equation of extensible beam was defined by Woiniwsky- Krieger as a model for transverse deflection of an extensible beam of natural length.
The study discussed the stability of these models (longitudinal vibrations, transverse vibrations and extensible beams).
The stability solution has been counted and considered unconditionally for implicit method, but it's conditional for an explicit method.
Obtaining the stability and convergent solution for longitudinal vibrations of a beam if width divisions is less than length divisions (R<2), and for transverse vibrations of a beam if width divisions less than the square length divisions (R<0.25), as well as for extensible beam if width divisions less than the square length divisions, the study recommended to use an implicit method.
But in case of using an explicit method, the divisions must be adhered for a stable and convergent solution.-
American Psychological Association (APA)
Ishaq, Khalid A.& Muhammad Ali Uthman& Ukashah, Faris al-Azhari. 2020. Numerical solution and stability for model of extensible beam. Journal of Science and Technology : in Engineering and Computer Sciences،Vol. 21, no. 3, pp.1-10.
https://search.emarefa.net/detail/BIM-1275081
Modern Language Association (MLA)
Muhammad Ali Uthman…[et al.]. Numerical solution and stability for model of extensible beam. Journal of Science and Technology : in Engineering and Computer Sciences Vol. 21, no. 3 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1275081
American Medical Association (AMA)
Ishaq, Khalid A.& Muhammad Ali Uthman& Ukashah, Faris al-Azhari. Numerical solution and stability for model of extensible beam. Journal of Science and Technology : in Engineering and Computer Sciences. 2020. Vol. 21, no. 3, pp.1-10.
https://search.emarefa.net/detail/BIM-1275081
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 10
Record ID
BIM-1275081