STUDY ON DYNAMIC STABILITY AND FREE VIBRATIONS OF MULTI-SPAN FLUID-CONVEYING PIPES IN WATER WITH VARIOUS END CONDITIONS
Journal Title: International Journal of Applied Engineering Research and Development (IJAERD) - Year 2017, Vol 7, Issue 1
Abstract
The literature regarding transverse vibrations of fluid-conveying pipes in air is plenty, however, most of them is for the stability of single-span clamped-free (C-F) pipes, and the reports relating to the critical flow velocities of the multi-span fluid-conveying pipes (either in air or in water) with various end supports are not found yet, thus, this paper tries to study the title problem by using the finite element method (FEM). First of all, the property matrices of an axial-loaded fluid-conveying pipe element in water are derived through application of the Lagrange’s equation. Next, the assembly technique is used to construct the overall mass, damping and stiffness matrices for the entire fluid-conveying pipe, and after imposing the total constrained degrees of freedom (DOFs), the equations of motion for the entire multi-span fluid-conveying pipe are obtained. Solution of the latter equations of motion will produce the complex eigenvalues and complex eigenvectors, with the imaginary part of each eigenvalue and the real part of each eigenvector denoting the damped natural frequency and damped mode shape, respectively. To confirm the reliability of the presented approach, the stability curve, the Argand diagrams for several complex eigenvalues and the associated dimensionless critical flow velocities of a single-span pipe with three (end) boundary conditions (BCs) are determined and compared with the existing literature, and good agreement is achieved. For a “q-span” pipe ( ) with equal span lengths and S end supports (or BCs), it has been found that, its first dimensionless critical flow velocity leading to buckling can easily be determined from the Argand diagram associated its 1st complex eigenvalue , and this is not true for a classical axial-loaded “q-span” beam on the basis of static-stability theory. Furthermore, for the last pipe with pinned-pinned (P-P) end supports, it has been found that the first dimensionless critical flow velocity is given by . In addition to the stability analyses, the determination of damped natural frequencies and damped mode shapes of a multi-span fluid-conveying pipe (with Coriolis effect considered) in three BCs is also illustrated. Since the information regarding the dynamic behaviors of the multi-span fluid-conveying pipes (either in air or in water) is rare, the presented approach and the obtained results will be useful in the practical applications.
Authors and Affiliations
JONG-SHYONG WU, DER-WEI CHEN, JEE-RAY WANG, CHING-AN HUANG
Keywords
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STUDY ON DYNAMIC STABILITY AND FREE VIBRATIONS OF MULTI-SPAN FLUID-CONVEYING PIPES IN WATER WITH VARIOUS END CONDITIONS
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