矩形平面双曲抛物面薄膜屋盖的动力失稳临界风速  

CRITICAL WIND VELOCITY OF HYPERBOLIC PARABOLOID MEMBRANE ROOFS WITH RECTANGULAR PLANE

作　　者：刘瑞霞[1] 杨庆山[1] 李作为[1] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044

出　　处：《工程力学》2005年第5期105-110,共6页Engineering Mechanics

基　　金：国家自然科学基金九五重大项目(59895410);教育部高等学校优秀青年教师教学科研奖励计划资助项目

摘　　要：由于薄膜结构质量轻、刚度小、自振频率低,对风的作用非常敏感,一般认为在风荷载作用下会产生较大的位移和加速度反应,并可能引起局部流场的变化甚至诱发气弹失稳,所以应在考虑风与结构的耦合作用基础上分析结构的风振反应。失稳临界风速的确定是其主要内容之一。研究了均匀的理想势流作用下小垂度矩形双曲抛物面薄膜屋盖的失稳临界风速。首先建立薄膜屋盖的平衡方程,然后应用流体力学中的势流理论确定作用于薄膜表面上的气动力,从而建立起风与薄膜结构的耦合作用方程,并利用Bubnov-Galerkin方法将用带有积分的微分方程表示的耦合作用方程转化为一组常系数二阶微分方程,根据Routh-Hurwitz稳定性准则确定薄膜的失稳临界风速。由临界风速公式可以看出,临界风速与膜材参数、薄膜屋盖本身的几何尺寸和形状及两个方向上的预张力有关。With light mass, small stiffness and low natural vibration frequency, membrane roofs are sensitive to wind. Generally, wind loading may induce large displacement and acceleration, of membrane roofs which may result in the change of local flow field around the structure and even induce the aeroelastic instability. So the wind-induced vibration of such structures should be analyzed considering the wind-structure interaction. The determination of the critical wind velocity is one of the main targets. The critical wind velocity of a hyperbolic paraboloid membrane roof with rectangular plane under the action of uniform ideal potential flow is studied. The equilibrium equation of the membrane roof is obtained. The potential flow theory in fluid mechanics is adopted to define the aerodynamic forces on the membrane roof and the equation of wind-structure interaction is obtained. The Bubnov-Galerkin method is applied to transform this complicated interaction equation into a system of second order linear differential equations with constant coefficients. Finally, Routh-Hurwitz stability criterion is used to determine the critical wind velocity. The formula shows that the critical wind velocity depends on the material parameters, the scale and the shape of the structure, and the pretension forces in two principal directions.

关 键 词：薄膜屋盖 失稳 风与结构的耦合作用 势流 临界风速 

分 类 号：TU312[建筑科学—结构工程]