基于薄膜大挠度理论的张拉平面膜结构气动稳定性分析

Analysis on the aerodynamic instability of tensioned plane membrane structure based on the large deflection theory of membrane

基于冯·卡门薄膜大挠度理论,采用达朗贝尔原理,结合势流理论和薄翼型理论,建立了张拉平面膜结构在风荷载作用下的非线性气动耦合控制方程,并利用伽辽金法对其进行求解。对其解的稳定性进行判断,得到结构发散失稳的临界风速。通过算例,分析了结构各参数对失稳临界风速的影响。分析表明,张拉平面膜结构气动稳定性受多个参数共同控制,合理控制双向跨度和预张力是提高其气动稳定性的主要手段。

Based on Von Kármán＇s large deflection theory of membrane,the nonlinear aerodynamic coupling governing equations of tensioned plane membrane structure under wind load are established by D＇Alembert＇s principle combined with the potential flow theory and thin airfoil theory.The governing equations are solved by Bubnov-Galerkin method.Through judging the stability of its solution,the critical wind velocity of divergence instability is determined.In computational examples,the impacts of each structural parameter on the instability critical wind velocity are analyzed.The analysis shows that the aerodynamic stability of tensioned plane membrane structure is controlled by multiple parameters;to control the span and pretension reasonably is the main measure for improving its aerodynamic stability.