Static and Dynamic Bifurcations Analysis of a Fluid-Conveying Pipe with Axially Moving Supports Surrounded by an External Fluid

Author:

Fasihi Ali1,Shahgholi Majid2ORCID,Kudra Grzegorz1ORCID,Awrejcewicz Jan1ORCID

Affiliation:

1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Stefanowski St. 1/15, 90-924 Lodz, Poland

2. Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

Abstract

In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed.

Funder

Narodowe Centrum Nauki

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering

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