Date of Award
Pipe -- Fluid dynamics, Finite element method, Structural dynamics, Vibration, Finite element analysis, Flow induced vibrations, Matlab programming, Numerical methods, Flow through pipes
Flow induced vibrations of pipes with internal fluid flow is studied in this work. Finite Element Analysis methodology is used to determine the critical fluid velocity that induces the threshold of pipe instability. The partial differential equation of motion governing the lateral vibrations of the pipe is employed to develop the stiffness and inertia matrices corresponding to two of the terms of the equations of motion. The equation of motion further includes a mixed-derivative term that was treated as a source for a dissipative function. The corresponding matrix with this dissipative function was developed and recognized as the potentially destabilizing factor for the lateral vibrations of the fluid carrying pipe. Two types of boundary conditions, namely simply-supported and cantilevered were considered for the pipe. The appropriate mass, stiffness, and dissipative matrices were developed at an elemental level for the fluid carrying pipe. These matrices were then assembled to form the overall mass, stiffness, and dissipative matrices of the entire system. Employing the finite element model developed in this work two series of parametric studies were conducted. First, a pipe with a constant wall thickness of 1 mm was analyzed. Then, the parametric studies were extended to a pipe with variable wall thickness. In this case, the wall thickness of the pipe was modeled to taper down from 2.54 mm to 0.01 mm. This study shows that the critical velocity of a pipe carrying fluid can be increased by a factor of six as the result of tapering the wall thickness
Grant, Ivan, "Flow Induced Vibrations in Pipes: a Finite Element Approach" (2010). ETD Archive. 633.