An analytical study of the across-wind response of cylinders due to vortex shedding

The across-wind response of tapering cylinder-like structures, such as chimneys, due to periodic shedding of vortices is obtained under lock-in conditions. The method of analysis incorporates aerodynamic effects and describes the lift forces by a linear model monoharmonic in nature. Under lock-in conditions, the critical wind speed and the lift and aerodynamic coefficients are assumed to be uniform throughout the height of the chimney, although its outside diameter varies. The aerodynamic and lift coefficients are derived from a lift oscillator model which adequately describes the experimental results of the vortex-induced oscillation (at lock-in) of an elastically-supported cylinder. With the help of an example problem, the paper shows how the response of the chimney is sensitive to the choice of the critical diameter used for the determination of critical wind velocity and the lift and aerodynamic coefficients. It also emphasizes the importance of the lock-in condition in the second mode in relation to bending stresses.