Free vibration of two identical circular cylinders in staggered arrangement

An investigation on flow-induced response characteristics of two identical circular cylinders in staggered arrangement is conducted in the fluid mechanics laboratory of Kitami Institute of Technology, Japan. Each cylinder was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Measurements were conducted at stagger angle alpha = 5 degrees, 10 degrees, 15 degrees, 25 degrees, 45 degrees and 60 degrees L/D ranging from 0.1 to 3.2, with Delta L/D = 0.1, where L is the gap width between the cylinders, and D is the diameter of a cylinder. At each position (alpha, L/D) of the cylinders, dependence of vibration-amplitude-to-diameter ratio alpha/D on reduced velocity U(r) (= U(infinity)/(f(n)D)) is examined, where U(infinity) is the free-stream velocity and f(n) is the natural frequency of the cylinder. There are seven cylinder-response patterns, depending on whether vortex-excited and/or galloping vibrations of the cylinders are generated, in the range alpha = 5 degrees-60 degrees, L/D = 0.1-3.2 and U(r) = 1.5-26. Pattern I corresponds to no generation of vortex-excited or galloping vibration of either cylinder. In Pattern II the upstream cylinder does not experience vortex-excited or galloping vibration, but the downstream one experiences a galloping vibration. Pattern III involves both vortex-excited and galloping vibrations of the downstream cylinder and only galloping vibration of the upstream cylinder. Pattern IV is associated with generation of vortex-excited vibration of both cylinders at the same Ur range. Pattern V refers to the case where the downstream cylinder experiences vortex-excited vibration, but the upstream cylinder does not. Pattern VI is characterized by vortex-excited vibration of the downstream cylinder in two regimes of Ur, whereas that of the upstream cylinder occurs in one regime only. In Pattern VII the upstream and downstream cylinders experience vortex-excited vibration at two different U(r) regimes, respectively. The L/D regime of the vibration patterns generated at each alpha is identified.