Numerical Study on a Model of Transverse Vibrations of a Beam
Keywords:
Calculus of variation, Partial differential equation, Finite difference method
Abstract
In this study, we apply finite difference method (explicit and implicit methods), for solving transverse vibrations of beam equations linearly and nonlinearly. We discuss two equations; the first equation is obtain by assuming that the deflection is very small ''first derivative of the dependent variable is equal to zero ''. Then Euler Lagrange equation is used. The second equation is obtain by using the Euler Lagrange equation without assumption that the deflection is very small ''first derivative of the dependent variable is not equal to zero ''.
References
Barari A., Ganjavi B., Ghanbari M. Jeloudar, and Domairry G., (2010) Assessment of two analytical methods in solving the linear and nonlinear elastic beam deformation problems. Journal of Engineering, Design and Technology, 2010, 8(2):127–145.
Dennis G. Zill and Micheal R. Cullen, (2009), Differential Equations with Boundary Value Problems, 2009.
Ghiocel Groza, Ana – Maria Mitu, Nicolae Pop and Tudor Sireteam, (2018). Transverse vibrations analysis of a beam with degrading hysteretic beam model. Doi: 10.2478/auom-2018-0008, Vol. 26(26) 2018,125 – 139.
Khaled Abdalla Ishag. (2019 a). A Solution of Nonlinear Models for Concrete Beam. Sudan University of Science and Technology, 2019.
Khaled Abdalla, Faris Azhari Okasha (2019 b) Homotopy Perturbation Transform Method for Extensible Beam Equations, FES Journal of Engineering Scinces, Vol. 8, No. 1(2019) , pp 15 – 20.
Khaled Abdalla, Mohamed Ali Osman and Faris Azhari Okasha, (2020) Numerical Solution and Stabilty for Model of Extensible Beam,Journal of Engineering and Computer Science. VOL. 21, No 3 (2020). http://journal.sustech.edu/index.php/JECS/issue/view/24
Lokenath Debnath, (2007) Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition, 2007.
Randall J. Leveque (2007), Finite Difference Methods for Ordinary and Partial Differential Equations, 2007.
Roncen T., Sinou J-J., and Lambelin J-P. (2017), Expriments and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions and uncertainties, X internatianl conference on structural dynamics, EURODYN 2017.
Dennis G. Zill and Micheal R. Cullen, (2009), Differential Equations with Boundary Value Problems, 2009.
Ghiocel Groza, Ana – Maria Mitu, Nicolae Pop and Tudor Sireteam, (2018). Transverse vibrations analysis of a beam with degrading hysteretic beam model. Doi: 10.2478/auom-2018-0008, Vol. 26(26) 2018,125 – 139.
Khaled Abdalla Ishag. (2019 a). A Solution of Nonlinear Models for Concrete Beam. Sudan University of Science and Technology, 2019.
Khaled Abdalla, Faris Azhari Okasha (2019 b) Homotopy Perturbation Transform Method for Extensible Beam Equations, FES Journal of Engineering Scinces, Vol. 8, No. 1(2019) , pp 15 – 20.
Khaled Abdalla, Mohamed Ali Osman and Faris Azhari Okasha, (2020) Numerical Solution and Stabilty for Model of Extensible Beam,Journal of Engineering and Computer Science. VOL. 21, No 3 (2020). http://journal.sustech.edu/index.php/JECS/issue/view/24
Lokenath Debnath, (2007) Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition, 2007.
Randall J. Leveque (2007), Finite Difference Methods for Ordinary and Partial Differential Equations, 2007.
Roncen T., Sinou J-J., and Lambelin J-P. (2017), Expriments and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions and uncertainties, X internatianl conference on structural dynamics, EURODYN 2017.
Published
2022-12-29
How to Cite
Khaled Abdalla Ishag, Abulfida Mohamed Ahmed, & Asmaa Eltayeb. (2022). Numerical Study on a Model of Transverse Vibrations of a Beam. Journal of The Faculty of Science and Technology, (9 (2), 79 -. https://doi.org/10.52981/jfst.vi9 (2).2884
Section
Articles
