Journal of Fluids and Structures 22 (2006) ??–?? www.elsevier.com/locate/jfs Riser Modal Identification in CFD and Full-Scale Experiments D. Lucor a , H. Mukundan b , M.S. Triantafyllou b,* a Laboratoire de Mod´ elisation en M´ ecanique, Universit´ e Pierre et Marie Curie, 4 place Jussieu, Paris, France b Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge MA, USA Abstract A systematic methodology is presented to obtain the vortex induced vibrational modes of a riser, based on data from CFD coupled to a long beam under tension and placed in sheared cross-flow; two profiles were tested: (a) linear, and (b) exponential. The modes we estimate are in fact nonlinear equilibria between the flow-induced excitation forces and the structural dynamics and are characterized by varying amplitude and phase along the span; these are complex modes, mixtures of traveling and standing waves. Simplifying procedures to represent the VIV response in terms of a few clusters of modes have been applied successfully, reducing substantially the data needed to represent the VIV response. c  2006 Elsevier Ltd. All rights reserved. 1. Introduction Vortex induced vibrations (VIV) of bluff, flexibly-mounted rigid structures and long flexible structures with bluff cross-section, placed within a transverse oncoming flow, constitute a self-excited, self-limiting process. Indeed, excitation forces are caused by an instability of the wake flow, but once the structure starts vibrating, the forces change and eventually become resistive, beyond an amplitude of vibration typically around one transverse body dimension (Sarpkaya, 1979; Zdravkovich, 1997; Govardhan and Williamson, 2000). The wake instability has a preferred frequency, the Strouhal frequency fS ; if the structural natural frequency is close to fS , then vibrations are excited at a frequency near the natural and Strouhal frequency, as determined by the added mass of the structure, which is frequency- and amplitude-dependent. Hence, within a uniform current the spectrum of the excitation forces, as well as the spectrum of the system response, is found to have a large peak, often the only peak, within a narrow frequency range relatively close to its natural frequency (Triantafyllou et al., 2003). In the case of a flexible structure, such as a uniform taut string, or a uniform tensioned beam, placed in a uniform current, a narrow-band response may be observed, resulting in apparently standing waves, such as one would expect from free vibrations of such structures. However, these are self-excited vibrations whose amplitude is limited by either the structural damping or the self-limiting nature of the fluid forces; hence they can be thought of as nonlinear dynamic equilibria of the fluid-structure interaction process. Since they result from a resonant matching between fluid excitation and small-amplitude (hence linearizable) structural response, the nonlinearity is almost entirely due to the fluid. We will call these flow-structure interaction monochromatic, or narrow-band responses modes, recognizing that they may bear no resemblance to free vibration structural modes. In the case of non-uniform current, the excitation is not at a single frequency, since the Strouhal frequency depends linearly on the spatially variable speed of flow (Stansby, 1976). As a result, a wide-band excitation is obtained, resulting in excitation of a single natural frequency, if the natural frequencies are spaced far apart from * Corresponding author. Tel.: +1 617 253 4335; fax: + 1 617 253 8125. E-mail address: mistetri@mit.edu (M.S.Triantafyllou). Preprint submitted to the Journal of Fluids and Structures 25 January 2006