柔壁风洞设计中的Elastica反问题

提出了计算柔壁风洞设计中大挠度反问题的分段线性化方法。将风洞的柔性壁简化为一端固支、一端可自由滑动的梁,其受到气压分布力、自重以及作动筒集中力的作用,需要通过离散分布的作动筒控制柔壁形状。柔壁在多种马赫数条件下的形状和气压沿长度方向变化规律已知,而要求解所需作动筒集中力的大小。通过对简单梁理论的修正,提出了分段线性化方法计算方法,得到了梁的变形方程组,并求得问题的近似解。然后采用非线性迭代方法得到在近似解作用下变形曲线,与气动设计曲线进行比较。

Inverse Problem of Elastica in the Design of Flexible-walled Wind Tunnel

This paper presents a method of segmented linearization to solve the inverse problem of elastica in the design of flexible-walled wind tunnels The flexible wall whose configuration is controlled by some actuating cylinders is subjected to air pressure,gravity and several forces,and simplified to be a beam which is fixed at one end and can slide freely over a hinge at the other end The configurations of the flexible wall under certain Mach numbers, the air pressure and gravity,as well as the position of the controlled points are given,while the values of the forces are to be determined.Through the amendment of simple beam theory,the segmented linearization method is suggested.Then a group of equations about deformation are established,and the approximate results are obtained.Furthermore,several deformation curves are obtained by an accurate nonlinear method,and then compared with the design curves.