Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

•Free vibration of a multi-span pipe conveying fluid using VIM and TMM methods.•The current manuscript introduces novel multi-span analysis using VIM.•The pipe critical velocities are obtained using both methods.•VIM yields identical results to the exact method by adjusting number of iterations.•The...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2019-07, Vol.71, p.173-193
Main Authors: El-Sayed, T.A., El-Mongy, H.H.
Format: Article
Language:English
Subjects:
Boundary conditions
Conveying
Critical velocity
Dynamic stability
Elastic supports
Exact solution
Exact solutions
Free vibration
Internal flow pipe
Iterative methods
Mathematical analysis
Multi-span pipe
Pipes
Resonant frequencies
Stability analysis
Transfer matrix method
Variational iteration method
Vibration analysis
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Summary:•Free vibration of a multi-span pipe conveying fluid using VIM and TMM methods.•The current manuscript introduces novel multi-span analysis using VIM.•The pipe critical velocities are obtained using both methods.•VIM yields identical results to the exact method by adjusting number of iterations.•The use of VIM in solving the vibration of sophisticated structures is very promising. In this paper, a new formulation based on the variational iteration method (VIM) is applied to investigate the dynamic behavior and stability of a multi-span pipe conveying fluid. Transfer matrix method (TMM) is used to assemble the system of equations resulting from applying the boundary conditions. The natural frequencies of the pipe system are obtained for different flow velocities. Results from VIM are compared with those predicted by the exact solution method and also with published literature. The influence of the number of spans on the VIM convergence is investigated. Also, the effects induced by varying the value and location of an intermediate elastic support on the critical velocity and stability are studied. It is shown that using VIM yields highly accurate results that are in very well agreement with the exact solution. The main advantage of the VIM is that it successfully overcomes well-known computational difficulties that are usually encountered during complex root finding step maintaining high precision as well.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2019.02.006