Aerodynamic Stability Analysis of Geometrically Nonlinear Orthotropic Membrane Structure with Hyperbolic Paraboloid

Abstract

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. The interaction governing the equation of wind-structure is established on the basis of large-amplitude theory and the D’Alembert principle. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second-order nonlinear differential equations with constant coefficients. Through judging the stability of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy and geometrical nonlinearity is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the planar model, there is a little inconsistency about the divergence instability regularities in the hyperbolic paraboloid model.