rspa.royalsocietypublishing.org Research Cite this article: Konstantinidis E. 2013 Added mass of a circular cylinder oscillating in a free stream. Proc R Soc A 469: 20130135. http://dx.doi.org/10.1098/rspa.2013.0135 Received: 25 February 2013 Accepted: 9 May 2013 Subject Areas: fuid mechanics Keywords: fuid mechanics, fuid–structure interaction, potential fow Author for correspondence: Efstathios Konstantinidis e-mail: ekonstantinidis@uowm.gr Added mass of a circular cylinder oscillating in a free stream Efstathios Konstantinidis Department of Mechanical Engineering, University of Western Macedonia, Bakola and Sialvera, Kozani 50100, Greece The fundamental understanding of the added mass phenomenon associated with the motion of a solid body relative to a fluid is revisited. This paper focuses on the two-dimensional flow around a circular cylinder oscillating transversely in a free stream. A virtual experiment reveals that the classical approach to this problem leads to a paradox. The inertial force is derived afresh based on analysis of the motion in a frame of reference attached to the cylinder centroid, which overcomes the paradox in the classical formulation. It is shown that the inertial force depends not only on the acceleration of the cylinder per se, but also on the relative motion between body and fluid embodied in a parameter called alpha, α, which represents the ratio of the maximum transverse velocity of the cylinder to the free-stream velocity; the induced inertial force is directionally varying and non-harmonic in time depended on the alpha parameter. It is further shown that the component of the inertial force in the transverse direction is negligible for α< 0.1, increases quadratically for α< 0.5, and tends asymptotically to the classical result as α →∞, i.e. in still fluid. 1. Introduction Whenever acceleration is imposed on a fluid by acceleration of a body moving through the fluid, or acceleration of the fluid relative to the body, additional inertial forces act on the body due to the ‘added mass’ effect. The calculation of these inertial forces has been of fundamental interest in fluid mechanics for more than a century. It can also be of considerable significance in some engineering applications involving lightweight structures submerged in dense fluids. One such example is the ‘vortex-induced vibration’ of offshore structures encountered in exploration and extraction of petroleum from sea beds; marine cables, pipelines, risers, platforms, 2013 The Author(s) Published by the Royal Society. All rights reserved.