Simplified equations for natural frequencies of pipes on elastic foundation conveying gases

Abstract

Pipelines are commonly subjected to harmonic forces induced by reciprocating centrifugal pumps and compressors, unbalanced moments and forces in turbomachinery, pressure surge, and momentum changes due to valve operation. To guard resonance and fatigue failure, the natural frequencies of pipelines need to be accurately characterized. The present study introduces two sets of simplified equations to compute the natural frequencies of pipes conveying gases resting on uniform elastic foundation for different boundary conditions. While the first set is analytically derived by solving the differential equation, the second set is obtained based on a decoupling approach. A finite element code is built to verify the results computed using both sets of equations and excellent agreement is obtained.