Additional Mass: Orthotropic Membrane Material with Four Sides Fixed in Air Flow

When the membrane material in the air field vibrates, it will drive the movement of the surrounding air. The aerodynamic force generated by the moving air will act on the membrane material in turn, resulting in the change of dynamic characteristics such as membrane vibration frequency. In this paper, the additional air mass produced by membrane vibration in air is studied. Firstly, under the assumption that the incoming flow is uniform and incompressible ideal potential flow, the additional air mass acting on the surface is derived by using the thin airfoil theory and potential flow theory respectively. Then, according to the first law of thermodynamics and the principle of aeroelasticity, the analytical expression of the additional air mass is derived. Finally, through a specific example, the variation of the additional air mass with the membrane material parameters and pretension, as well as the influence of the aerodynamic force on the vibration frequency and amplitude of the membrane is obtained.