| Summary |
Aerodynamic stability of long-span flat roofs has been investigated on the basis of the computational fluid dynamics with a large eddy simulation. The span to eaves-height ratio (L/H) of the building was changed from 3 to 9 to understand the effect of the separated flow and the separation bubble, which are strongly affected by L/H, on the unsteady aerodynamic forces acting on the vibrating roof in the first antisymmetric mode. First, the distributions of mean and RMS fluctuating wind pressure coefficients on the rigid and vibrating roofs were examined, in which the vibration mode was assumed to be the first anti-symmetric mode. The results on the mean and fluctuating wind pressure distributions on the rigid roofs indicate that the eaves height is one of the most important factors to evaluate the wind pressure distributions. It is also found that the distributions of RMS fluctuating wind pressure coefficients on the vibrating roof is characterized by the vibration mode. To understand the characteristics of fluctuating wind pressures in detail, the power spectral densities and phase differences of fluctuating wind pressures were examined. The general shape of the power spectral densities for the vibrating roof was found to be similar to that for the rigid roof. The results indicate that the fluctuating component of wind pressures at the forced vibration frequency is related to the roof’s vibration significantly. However, the roof’s vibration affects the phase differences of fluctuating wind pressures only a little. The unsteady aerodynamic forces at the location of anti-nodes of vibration mode are affected by the separation bubble generated by the flow separation from the leading edge of the roof. However, the generalized unsteady aerodynamic forces are minutely affected by L/H. Finally, a formula for the critical wind velocity that induces the aerodynamically unstable vibration is proposed on the basis of the generalized aerodynamic damping.The critical reduced wind velocity, defined by the velocity at the eaves height, the span and the natural frequency of the first anti-symmetric mode, are 1.27 and 1.47 for the uniform flow and the turbulent boundary layer, respectively.
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