Wake-induced vibration of tandem and staggered cylinders with two degrees of freedom Gustavo R.S. Assi Department of Naval Architecture & Ocean Engineering, University of São Paulo, NDF, Escola Politécnica, 05508-030 São Paulo, Brazil article info Article history: Received 3 February 2014 Accepted 2 July 2014 Available online 22 August 2014 Keywords: Wake-induced vibration Circular cylinders Vortex wake Flow interference abstract The wake-induced vibration (WIV) of two staggered cylinder with two degrees of freedom (2-dof) has been investigated by experiments in a water channel for Reynolds number between 2000 and 25 000. The streamwise separation was fixed to 4 diameters and the lateral separation varied between 0 and 3 diameters for tandem and staggered config- urations. Results are presented in the form of trajectories of motion and dynamic response curves of displacements, frequencies and force coefficients. Excitation caused by the WIV mechanism is found to get weaker as the initial position of the downstream cylinder is increased from the centreline of the wake (tandem arrangement) towards the sides. For a lateral separation of 3 diameters wake interference was already found to be negligible. Evidence of a type of wake-stiffness concept is also observed to occur for 2-dof WIV in tandem arrangement, especially for higher reduced velocities. A similar mechanism may also be occurring for staggered arrangements around the centreline. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction The topic of wake-induced vibration (WIV) of a pair of interfering cylinders is a fundamental subject in fluid–structure interaction that still draws the attention of many researches. In a few words, WIV is a fluid–elastic mechanism able to excite into oscillatory motion a bluff body immersed in the wake generated from another body positioned upstream. At first sight it appears to be a very simple phenomenon, but careful investigations have uncovered complex mechanisms that can only be understood through the lenses of unsteady fluid–elasticity. In the present study we are concerned with the WIV of the downstream cylinder of a pair arranged in tandem and staggered configurations, i.e. in staggered arrangements the cylinders are not aligned with the flow but offset from the centreline. WIV differs from the well studied phenomenon of vortex-induced vibration (VIV)—reviewed by Bearman (1984), Williamson and Govardhan (2004) and others—in the sense that the excitation is not generated in the vortex shedding mechanism of the body itself, but it comes from the interaction of the body with a wake developed further upstream. It is not difficult to be carried away by the apparent simplicity of the problem and plan or design experiments without considering the number of parameters involved. For example, take two cylinders modelled as rigid bodies with two degrees of freedom (2-dof) each. To start with geometric parameters, there will be two diameters and a streamwise and a cross-flow separation, which will distinguish the tandem from the staggered arrangements. On the structural properties side, there will be different parameters of mass for each cylinder as well as damping and stiffness regarding each direction of motion. After all, a pair of rigid cylinders oscillating in 2-dof will present a dozen of different possible combinations of geometric and Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jfs Journal of Fluids and Structures http://dx.doi.org/10.1016/j.jfluidstructs.2014.07.002 0889-9746/& 2014 Elsevier Ltd. All rights reserved. E-mail address: g.assi@usp.br Journal of Fluids and Structures 50 (2014) 340–357