Effect of distributed follower loads on instability of simply supported pipes conveying fluid

In this study, divergence and flutter instabilities of a simply supported pipe conveying fluid under distributed follower loads are investigated. The governing equation is derived by extended Hamilton's principle. The Galerkin method is used to discretize the equation of motion, and then the instability analysis is evaluated by solving a quadratic eigenvalue problem. Generalized differential quadrature (GDQ) method is used to validate the results are obtained by Galerkin method. In Galerkin's method, a very important issue is to make sure that a sufficient number of pipe-modes are used in discretizing to obtain reliable results. This problem is solved by L.Wang [۱] by using two pipe-modes todiscretize the governing equation but, in present work we will show the results that he obtained is not valid and predict incorrectly the limitation of divergence and flutter instabilities and also critical flow velocities, especially when the viscoelastic coefficient of pipe is small. We used more pipe-modes to solve the problem and showed that with increasing the pipe-modes the results are different from those obtained by L.Wang [۱] and the present results converge with increasing number of pipe-modes. There is an excellent agreement with the present results obtained by Galerkin method with those obtained by GDQ method.

Keywords:

Divergence and Flutter Instabilities , Simply Supported Pipe Conveying Fluid , Distributed Follower Loads , Galerkin Method , Generalized Differential Quadrature (GDQ) Method