弹性支承对三维曲壁板颤振特性的影响

摘要

A method for increasing the flutter dynamic pressure of curved panels with a concentrated elastic support was proposed and the effects of the concentrated elastic support position and its stiffness on the flutter velocity of curved panels were studied.The nonlinear aeroelastic model of a curved panel with a concentrated elastic support in supersonic air flow was established using the virtual work principle and the finite element method.The large deformation of the curved panel was described by using Von Karman large deformation strain-displacement relationship.The quasi-steady first order piston theory was used to calculate the aerodynamic force acting on the surface of the curved panel.The eigenvalue solution was then utilized to determine the flutter dynamic pressure of the curved panel.The dynamic characteristics of the curved panel were analyzed by changing the stiffness and position of the concentrated elastic support based on the frequency coalescence theory.Results showed that the elastic support located in different positions has significantly different effects on the flutter dynamic pressure;the elastic support located in the central region of the curved panel or in the chordwise middle line leads to a drop of the flutter dynamic pressure,and the flutter dynamic pressure decreases with increase in elastic support stiffness;if the elastic support is located in the center of the curved panel,the flutter dynamic pressure has a maximum drop;when the elastic support position changes along the line perpendicular to the flow stream and is far away from the chordwise middle line,there is an increasing of the flutter dynamic pressure,and the flutter dynamic pressure increases with increase in elastic support stiffness;while the elastic support position changes in the area near leading edge and trailing edge and along the flow stream,the flutter dynamic pressure increase;the method of adding a concentrated elastic support to increase flutter dynamic pressure can be applied as a measure to control the flutter of a curved panel,and the elastic support should be located on the spanwise midline with a distance of 20%chord length from the boundary.%提出了一种在四边简支曲壁板上附加一个弹性支承来提高曲壁板颤振临界动压的方法，研究了弹性支承的位置和刚度对曲壁板颤振速度的影响规律。应用von Karman大变形应变-位移关系来描述曲壁板的结构大变形，用一阶活塞气动力理论计算曲壁板的气动力，采用虚功原理和有限元方法，建立起带弹性支承的圆柱壳曲壁板在超音速气流中的颤振方程。通过求解曲壁板系统的特征方程获得其颤振临界动压。运用频率重合理论分别分析了改变弹性支承刚度和位置对曲壁板颤振特性的影响。结果表明，与不带弹性支承的曲壁板颤振特性相比，弹性支承位于不同位置时，会对曲壁板的颤振动压产生明显不同的影响：①弹性支承位于曲壁板中心点附近区域或位于弦向中线上时，都会导致曲壁板颤振动压降低且随着支承刚度的增大而减小；在曲壁板中心点处，颤振动压降低幅度最大；②弹性支承位置沿垂直于气流方向且远离弦向中线变化时，都会使颤振动压提高，且随着支承刚度的增大而增大；③当支承位置在前缘和后缘部位顺气流方向变化时，颤振动压都会提高；④采用附加弹性支承的方法来提高曲壁板颤振动压时，应将弹性支承布置在曲壁板展向中线距边界20％弦长处。