Abstract
Basic equations are expressed with physical consideration for flow around roofs. These equations are deduced from velocity potential and oscillations of roofs with initial tension as restoring force considering strong interaction between roofs and flow. Modal approach to oscillations decides total circulation together with velocity condition at trailing edge. Then, roof's oscillation is rewritten as a nonlinear differential equation. A periodic solution is obtained by asymptotic expansion method and the existence of solution and its uniqueness condition are examined. A frequency equation is given from condition that roofs and flow are equal in period of oscillations. Its solutions are decided in different domains depending mainly on wind velocity and roof's weight. Two critical velocities are induced on the basis of total potential energy, which is dependent on wind velocity using the solution of frequency equation. The first is a critical velocity where amplitudes become infinite. The second corresponds to velocity of division between two domain, where oscillations alter modes and enegy at a jump. Accuracies of these velocities are examined. Frequency and damping of structure, especially its weight have maked influence on these velocities. There is not the first critical in case of remarkably heavy roofs. Partly using experimental values, these critical velocities are made to correspond to those which reveal the phenomena.
