Study on the Aerodynamic Stability of Tensioned Geometrically Nonlinear Orthotropic Membrane Structure
|Keywords||Tensioned Membrane Structure Orthotropy Geometrical Nonlinearity Aerodynamic Instability the Critical Wind Velocity|
Tensioned membrane structure, a flexible space system with elegant appearance, long span, good seismic performance and economy, etc., is strongly favoured by architects for the past few decades. However, with the low deadweight, long span, small lateral rigidity and low natural frequency, it is more sensitive to the wind load than traditional structures. Following wind-structure interaction, the self-excited aerodynamic instability phenomenon may occur as the wind velocity reaches a certain value. At present, the theoretical study on the aerodynamic instability of tensioned membrane structure is hysteretic for a further development of engineering practice. This paper studies the aerodynamic stability of tensioned geometrically nonlinear orthotropic membrane structure models with plane and hyperbolic paraboloid respectively. The wind is assumed to be uniform, non-viscous and incompressible flow during the analysis. Based on the large amplitude theory and the D’Alembert’s principle, the nonlinear interaction governing equations of wind-structure is established.According to the degree of wind-structure separation, the structural model is assumed to be a symmetric or bending thin airfoil, and combined with potential flow theory in fluid mechanics and thin airfoil theory in aerodynamics, the aerodynamic force acting on the membrane surface is determined. 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 equation with constant coefficients. Through judging the stability of periodic solution, the critical velocity of divergence instability is determined.Taking into account the geometric nonlinearity and orthotropy of membrane, the given examples show that the critical velocity is relevant to the membrane material, the amplitude, the sizes, the pretensions in two principal directions, the orders of vibration mode and the wind direction. From the analysis of each parameter, it can be conclude that the main way to enhance the aerodynamic stability is to rationalize the structural sizes and pretensions; simultaneously, it has positive significance to arrange the membrane’s warp and weft rationally according the local wind regime in order to prevent a destructive instability of the structure; the direction and order of instability are inconsistent at different span ratio. At last, some conclusions obtained from the examples may be referred for the engineering design and practice.