This paper presents the analysis of a system of articulated pipes hanging vertically under the influence of gravity. The liquid, driven by a slightly fluctuating pressure, circulates through the pipes. Similar systems have been analysed in the past by numerous authors but a common feature of their work is that the behavior of the fluid flow is prescribed, rather than left to be determined by the laws of motion. This leads to a linear formulation of the problem which can not predict the behavior of the system for finite amplitudes of motion. A circumstance in which this behavior is important arises in the stability analysis of the system in the neighbourhood of critical velocities, that is, flow velocities at which the system starts to flutter. Hence, the purpose of the present study was to investigate in greater detail the region close to critical velocities in order to find by how much these critical velocities would be affected by the amplitudes of motion. This led to a set of three coupled-nonlinear equations, one of which represents the motion of the fluid. In the mathematical development, use is made of a scheme which permits the uncoupling of the modes of motion of damped nonconservative dynamic systems. Results are presented showing the importance of the nonlinearities considered.
Unified Linear Stability Analysis for Thermal Convections in Spherical Shells Under Different Boundary Conditions and Heating Modes