Dynamics of arrays of cylinders with internal and external axial flow

Various aspects of the dynamics and stability of clusters of tubular cylinders containing internally flowing fluid and surrounded by a bounded external axial flow are examined. The general character of free motions is established by obtaining the eigenfrequencies of the system and studying their evolution with increasing flow, internal or external. Stability diagrams have been obtained for the critical flow velocities, beyond which the system would lose stability by buckling (divergence), under the combined effect of internal and external flow. Free vibration, following an initial disturbance of one of the cylinders, is studied, in order further to examine the effect of hydrodynamic coupling. It is found that beating phenomena may arise, implying energy transfer between cylinders and the possibility of transient amplitudes much larger than the initial disturbances. Also, the vibration of the system (in still fluid) when one cylinder is constrained to oscillate in a prescribed manner is examined, establishing that transmission of vibration from cylinder to cylinder can be very rapid; indeed, such constrained motion of one cylinder at certain frequencies may induce large amplified motions of others.