Abstract
It has been well known that some steel stacks with circular sections oscillate cousiderably perpendicular to the wind direction. Up to now, attentions seeme to have been paid only to the stability problems of determining the critical wind velocity for the aeroeastic instability of structures. From the point of view of structural design, however the oscillatory amplitude is of main interest so that the response problem shows be considered. The main assumptions employed in this paper are the following : i) The circular cylinder in a flowing fluid behaves as an nonlinear self-excited oscillator subjected to the external forcing with Strouhal frequency f(=SU/d), ii) Strouhal number S for the oscillating cylinder can approximately be expressed as a function of the amplitude X to be S=S(1+2X+βX^2), where S in Strouhal number for a stationary one. iii) The lift force coefficient C_L for the oscillating cylinder can de represented as a function of the amplitude to de C_L=C_L(1+a'X), where C_L is the lift force coefflcient for a stationary one. After the comparison the theoretical predictions based on the above assumptions and some exprimental results, the following conclusions are derived : i) The resonant curve obtained from this theory agrees fairly well with the experimental results. ii) The stability diagram based on this theory shows a general consensus with Scruton's experimental results. iii) Unlike a simple linear-forced system, the aerodynamic lift force induced on the oscillating cylinder has a non-linear character such that, the magnification factor m_f is proportional to λ^<-1/2> where λ is the logarithnic decrement of the structures. These results can explain the behavior observed in the field measurements of actual steel stacks.
