ORIGINALS G. Alonso Æ J. Meseguer Æ I. Pe´ rez-Grande Galloping instabilities of two-dimensional triangular cross-section bodies Received: 3 November 2004 / Revised: 4 March 2005 / Accepted: 5 March 2005 / Published online: 29 April 2005 Ó Springer-Verlag 2005 Abstract Galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations. It normally appears in bodies with small stiffness and structural damping when they are placed in a flow and the incident velocity is high enough. In this paper a systematic approach for the analysis of galloping of triangular cross-section bodies is reported. Wind tunnel experiments have been conducted aiming at establishing the unstable characteristics of isosceles tri- angular cross-section bodies when subjected to a uni- form flow with angles of attack ranging from 0 to 180°. The results have been summarized in a stability map, where galloping instability zones in the angle of at- tack—main vertex angle plane—are identified. 1 Introduction Aeroelastic phenomena are becoming more and more important from the point of view of its application po- tential to modern structural design. Among these phe- nomena, one can consider vortex shedding, translational galloping, wake galloping, torsional divergence, flutter and buffeting. This paper is focused on the experimental analysis of translational galloping. Let us consider the case of a body within a fluid at rest. If for any reason the body begins to oscillate, the structural damping and eventu- ally the viscosity of the surrounding fluid dissipate en- ergy and damp the oscillations. When the same body is placed within a flow, aerodynamic forces produced by the relative movement between the body and the fluid may get the amplitude of those oscillations to decrease, remain stable, or increase, depending on the ratio be- tween the energy that the aerodynamic forces transmit to the oscillating body and the energy that the system is able to dissipate. Because of the body displacement the aerodynamic forces are modified by the movement of the structure, and when this movement is slow enough to consider the aerodynamic forces to be quasi-steady, the phenomenon is called galloping. In a body reference frame, across- wind oscillation of the structure periodically changes the angle of attack of the incident wind, and such variation in the angle of attack produces variation in the aero- dynamic forces acting on the structure, which in turn affects the dynamic response of the structure. Galloping is a typical instability of flexible, lightly damped structures with special and non-symmetric cross-sections. Under certain conditions these structures may have large amplitude, normal to wind oscillations at much lower frequencies than those of vortex shedding found in the Ka´rma´n vortex street. Theoretical foundations of galloping are well estab- lished and understood, very often supported by experi- ments such as in Parkinson and Smith (1964), Novak (1969, 1972) and Simiu and Scanlan (1996). As it is well known, galloping can be explained by taking into ac- count that although the incident velocity U is uniform and constant, because of the lateral oscillation of the body, in a body reference system the total velocity changes both magnitude and direction with time. Therefore, the structure angle of attack also changes with time, hence the aerodynamic forces acting on the body. Let us consider a structure at rest that is oriented at given angle of attack a 0 with respect to the incident flow. Assuming a structure oscillating along the z-axis within a uniform flow with velocity U, the relative velocity between the fluid and the body is U r =[U 2 +(dz/ dt) 2 ] 0.5 , and the angle of attack due to oscillation is a = (dz/dt)/U. Therefore, drag d(a) and lift l(a) are: d ðaÞ¼ 12qU 2 r bc d ðaÞ; and lðaÞ¼ 12qU 2 r bc l ðaÞ; G. Alonso (&) Æ J. Meseguer Æ I. Pe´rez-Grande IDR/UPM, E.T.S.I. Aerona´uticos, Universidad Polite´cnica de Madrid, 28040 Madrid, Spain E-mail: galonso@idr.upm.es Tel.: +34 91 33 66 353 Fax: +34 91 33 66 363 Experiments in Fluids (2005) 38: 789–795 DOI 10.1007/s00348-005-0974-8