Flow Induced Vibration
FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH
IVAN GRANT
Bachelor of Science in Mechanical Engineering Nagpur University Nagpur, India June, 2006
submitted in partial fulfillment of requirements for the degree MASTERS OF SCIENCE IN MECHANICAL ENGINEERING at the CLEVELAND STATE UNIVERSITY May, 2010
This thesis has been approved for the department of MECHANICAL ENGINEERING and the College of Graduate Studies by:
Thesis Chairperson, Majid Rashidi, Ph.D.
Department & Date
Asuquo B.Ebiana, Ph.D.
Department & Date
Rama S.Gorla, Ph.D.
Department & Date
ACKNOWLEDGMENTS
I would like to thank my advisor Dr.Majid Rashidi and Dr.Paul Bellini, who provided essential support and assistance throughout my graduate career, and also for their guidance which immensely contributed towards the completion of this thesis. This thesis would not have been realized without their support. I would also like to thank Dr.Asuquo.B.Ebiana and Dr.Rama.S.Gorla for being in my thesis committee. Thanks are also due to my parents,my brother and friends who have encouraged, supported and inspired me.
FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH
IVAN GRANT ABSTRACT 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
IVAN GRANT
Bachelor of Science in Mechanical Engineering Nagpur University Nagpur, India June, 2006
submitted in partial fulfillment of requirements for the degree MASTERS OF SCIENCE IN MECHANICAL ENGINEERING at the CLEVELAND STATE UNIVERSITY May, 2010
This thesis has been approved for the department of MECHANICAL ENGINEERING and the College of Graduate Studies by:
Thesis Chairperson, Majid Rashidi, Ph.D.
Department & Date
Asuquo B.Ebiana, Ph.D.
Department & Date
Rama S.Gorla, Ph.D.
Department & Date
ACKNOWLEDGMENTS
I would like to thank my advisor Dr.Majid Rashidi and Dr.Paul Bellini, who provided essential support and assistance throughout my graduate career, and also for their guidance which immensely contributed towards the completion of this thesis. This thesis would not have been realized without their support. I would also like to thank Dr.Asuquo.B.Ebiana and Dr.Rama.S.Gorla for being in my thesis committee. Thanks are also due to my parents,my brother and friends who have encouraged, supported and inspired me.
FLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH
IVAN GRANT ABSTRACT 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