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On Aerodynamic Stability of Membrane Structures

The aerodynamic instability critical wind velocity of three-dimensional membrane structures is studied by combining the non-moment theory of thin shallow shells and the potential flow theory in fluids. The dynamic equilibrium equation of the structure is established by applying the non-moment theory of thin shells, with the assumption that the coming flow is uniform ideal potential flow. The aerodynamic interaction equations of the membrane structure in two cases, i.e., the wind is in the structural arch or sag direction, are obtained based on the aerodynamic forces being determined by applying the potential flow theory and the thin airfoils theory in which the wind-structure interaction is taken into account. Bubnov-Galerkin approximate method is applied to transform the interaction equation into a second order linear ordinary differential equation; and the instability critical wind velocity is obtained from Routh-Hurwitz stability criterion.