Dynamic behavior of tubes subjected to internal and external cross flows

This article presents a method for thoroughly examining the dynamic characteristics of a tube under the influence of either the internal flow or the external cross flow. The tube is modeled as a thin cylindrical shell whose governing equations are derived from an energy method. The effects due to internal flow are introduced into the system through initial stress. Galerkin's method in conjunction with the method of multiple scales is employed for obtaining the stability of the tube vibration. According to the results, instability can occur under certain conditions of resonance. Regarding the effects of the external cross flow, a numerical approach is initially employed to interpolate the experimental data of the pressure distributions due to the flow. The dynamic characteristics of the tube under steady flows and flows with small time variation are then investigated. Stability of the solution is also discussed.