Aerodynamic Stability of Orthotropic Tensile Membrane

Tensile membranes are increasingly finding their applications in stadiums, community centers, airports, and public spaces due to a variety of attributes. Apart from civil structures, they are also common in mechanical and aerospace systems. The membrane flexibility enhances their susceptibility to wind. Beyond a threshold wind speed, membranes demonstrate dynamic instability either in the form of flutter or divergence. Analysis of aerodynamic instability is presented for a planar, prestressed, orthotropic rectangular membrane. The differential equation of motion is derived, including von Kármán’s nonlinear strain and orthotropic material. The aerodynamic loading is described by the thin airfoil aerodynamics following the potential flow framework. The nonlinear differential equations are solved using the Bubnov–Galerkin method, accommodating the higher modes in the analysis. Linearized stability (eigen) analysis is performed to obtain the critical wind speed and is verified with the unsteady responses from the nonlinear analysis. Modal parameters are also compared with the ones from the finite element analysis. Parametric studies are conducted to examine the influence of key parameters (e.g. along-wind span, membrane pretension, and pretension ratio) on the critical wind speed. Significance of membrane prestress and aspect ratio is demonstrated on the stability behavior. The higher, unsymmetric modes are shown to result in complex aeroelastic behavior.