Re-examination of natural frequencies of marine risers by variational iteration method

2015 ◽  
Vol 94 ◽  
pp. 132-139 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang ◽  
Xin Li ◽  
Jing Zhou
Keyword(s):  
Iteration Method ◽  
Natural Frequencies ◽  
Variational Iteration Method ◽  
Marine Risers ◽  
Variational Iteration

Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method

2016 ◽  
Vol 23 (2) ◽  
pp. 220-234 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Accurate Determination ◽  
Variational Iteration Method ◽  
Mode Shapes ◽  
Engineering Practice ◽  
Timoshenko Beams ◽  
Variational Iteration

Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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