Parametric Resonance of Suspension Roofs in Wind

Since suspension roofs or curved membrane roofs are usually flexible, there are two important problems with regard to dynamic instability in wind-induced vibration of these roofs; one is flutter and the other is a resonance due to the periodical character of wind velocity fluctuations in atmospheric turbulence. The latter problem is undertaken here. If wind is assumed as inviscid potential flow, and if vorticities are introduced to represent the difference of velocities of wind and roofs in order to take into consideration wind-roof interaction effect, the latter problem can be analyzed as that of parametric resonance in antisymmetric deflection modes. Possibility of the occurrence of this resonance is confirmed under some conditions in atmospheric turbulence, where wind velocity fluctuation was revealed into spectral density function by Davenport. Analytic solution and numerical results, e.g., are presented concerning the several important factors which govern the prevention of parametric resonance.