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Experimental investigation of the aeroelastic instability of bluff two-dimensional cylinders Brooks, Peter Noel Hamilton

Abstract

Aerodynamically bluff elastic structures such as suspension bridges and industrial smokestacks have been observed to vibrate violently in the presence of a low speed wind. Although a number of theories such as Den Hartog's quasi-steady instability criterion and the vortex resonance theory have been proposed to explain the phenomenon, the problem is still not completely solved nor yet fully understood. The purpose of this research was to dynamically test a number of two-dimensional cylinders of simple cross-section and to observe whether or not the results correlated with either of the two theories mentioned above. Necessary aerodynamic coefficients were obtained by the graphical integration of measured surface pressure distributions. Tests were performed on models mounted elastically with six degrees of freedom. Generally only one of two modes of vibration was excited at a given airspeed. Dynamic response curves are presented for several lightly damped cylinders. For cylinders with rectangular cross-section of length/width (b/h/ greater than 0.75, vibration occurred at any airspeed above a certain minimum which depended on the structural damping (galloping). Cylinders with b/h less than 0.683 were found to vibrate over a limited range of airspeeds which always included the critical velocity for resonance with the periodic formation of vortices in the wakes. Using quasi-steady theory, it was found that the D-section and rectangles with b/h less than 0.683 have zero aerodynamic damping to large relative angles of attack, due to the symmetry of the wake pressures at angles of attack greater than zero. Because of this the D-section is subject to galloping only when given a substantial initial amplitude. Vortex resonance was observed for all the cylinders tested with two exceptions; the reversed D-section and the D-section with the flat face initially at an angle of attack greater than 40°, both of which appear to be completely stable. Measurements of the frequency of vortex formation for stationary cylinders gave Strouhal numbers which showed only slight variation over the speed range used in the tests, However, a strong variation with b/h was noted for the rectangles 1.0 < b/h < 3.0. During vibration of any kind, the frequency of vortex formation was controlled at the frequency of vibration which in all cases was a natural frequency of the system being tested. An energy balance based on quasi-steady theory and neglecting structural damping yields velocity-amplitude curves which give good agreement with the experimental data for the galloping D-section and the square section at various initial angles of attack. The test results indicate that the steady state aerodynamic coefficients provide a useful approximation to the dynamic values; they also indicate that any theory which will completely predict the behaviour of such systems must include the effects of both negative aerodynamic damping and vortex resonance.

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