The Analysis of Nonlinear Vibrations of Top-Tensioned Cantilever Pipes Conveying Pressurized Steady Two-Phase Flow under Thermal Loading

Abstract

This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.