Session: SE-06-02 The T.H. Liu Memorial Symposium on the Seismic Analysis and Design of Piping Systems-2

Paper Number: 123190

123190 - Theoretical Analysis of Natural Frequencies and Mode Shapes of Piping Systems With Tees 

A theoretical analysis method for the natural frequencies and mode shapes of the piping system with tees is developed. In Vibrations of Continuous Systems, written by A. W. Leissa and M. S. Qatu, the characteristic equation for the two-span beam with a intermediate support is derived. The derivation utilizes the conditions of the continuity of the deflection angle and bending moments at the intermediate support. The author has extended this approach to a three-dimensional piping system with elbows in the paper presented at PVP2023. The piping system is decomposed into straight pipes and elbows. The straight pipes are assumed to permit longitudinal, bending, and torsional vibrations. To generalize the elbow's directions, the local coordinate system for each pipe and the unit vectors representing the elbow's directions have been introduced. In this paper, the proposed method is further extended to include tees. As well as the elbow, the tee's direction is generalized. At the tees, the displacements and deflection angles must be the same, and the resultant forces and moments must vanish. These connection conditions and the boundary conditions of the piping system yield the characteristic equation. The characteristic equation is solved numerically. The coefficients of the function representing the displacement are obtained as the eigenvector corresponding to the zero eigenvalue. A comparison with the FEM results shows the usefulness of the proposed method.

Presenting Author: Shinji Tamura Shimane University

Presenting Author Biography: Shinji Tamura was received a Dr. Eng. degree in engineering from Tokyo Institute of Technology, Japan, in 2000. He is an Associate Professor in the Department of Mechanical, Electrical and Electronic Engineering, Shimane University, Japan. His research interests include the vibration and reliability analysis of mechanical systems.

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