Asymptotic Solution for Axial Stiffness for Supports of Pipes Conveying Fluids

Piping systems conveying fluids are frequently subjected to harmonic excitations from various sources such as unbalanced forces in turbomachinery and pulsations from reciprocating compressors and pumps, etc. These systems are typically longitudinally supported by discrete flexible steel frames placed at regular intervals to mitigate the induced axial vibrations. In order to effectively control these vibrations, it is critical to establish the minimum axial stiffness provided by pipe supports to achieve a desired fundamental natural frequency for the system. The present study proposes an asymptotic solution to determine the minimum axial stiffness of pipe supports necessary to meet a specific axial natural frequency target. Starting with the Hamilton’s principle, the governing differential equation of motion is derived for fluid-conveying pipes supported by continuous longitudinal springs. The solution is then obtained for the cases of continuous and discrete pipe supports. The predictions of the proposed solution are compared against the predictions from the commercial finite element software. The study provides a robust analytical framework for designing pipeline support systems to mitigate their longitudinal vibrations and improve the overall system stability.