Nonlinear wind-induced aerodynamic stability of orthotropic saddle membrane structures

The galloping of a tensioned orthotropic saddle closed membrane structure is theoretically investigated in this paper. The aerodynamic force acting on the membrane surface is determined by the potential flow theory of fluid mechanics and the thin airfoil theory of aerodynamics. Based on the von Kármán's large amplitude theory and the D'Alembert's principle, the interaction governing equations of wind-structure coupling are established. Then, by applying the Bubnov-Galerkin method, the complicated interaction equations are transformed into second order nonlinear differential equation with constant coefficients. Through judging the stability of the second order nonlinear differential equation, the critical wind velocity is obtained. By parametric analysis of analytical examples, we can conclude that it's of great significance to consider the orthotropy and geometrical nonlinearity to prevent the aerodynamic instability of saddle membrane structures; the arch-to-span ratio ε and span ratio λ are the main control parameters of the critical wind velocity. The formula for critical wind velocity obtained in this paper provides a more accurate theoretical solution for the aerodynamic stability of the saddle membrane structures than the previous studies.