Shape determination of wind-resistant wings attached to an oscillating bridge using adjoint equation method
Shape determination of wind-resistant wings attached to an oscillating bridge using adjoint equation method
复制标题
利用伴随方程法确定悬桥抗风翼的形状
DOI：
10.1016/j.cma.2012.08.022
复制
发表时间：
2013
影响因子：
7.2
通讯作者：
M. Kawahara
中科院分区：
文献类型：
--
作者：
Hisaki Sawanobori;M. Kawahara
应用任意拉格朗日-欧拉(ALE)有限元方法和最优控制理论(性能函数由桥梁的位移表示)，确定了在不可压缩的瞬变粘性流动中，摆动桥梁上安装的机翼的角度。目前，一些桥梁上安装了机翼，以防止风流引起的振动。当机翼的角度改变时，振动状态也会改变。因此，机翼倾角是考虑桥梁振动最小化的一个非常重要的参数。在本研究中，机翼的角度是基于最优控制理论确定的。为了最小化桥梁的振动，引入了性能函数作为最小化指标。性能函数由桥梁位移的平方和定义。利用拉格朗日乘子法将该问题转化为无约束极小化问题。利用扩展性能函数的定常条件，可以得到伴随方程。用于更新机翼角度的梯度可以通过求解伴随方程和状态方程来得到。采用加权梯度法作为极小化技术。在这项研究中，提出了用该理论来确定使桥梁振动最小的角度。用ALE形式描述的Navier-Stokes方程作为状态方程来描述流体绕桥的运动。利用弹簧支承体的位移和转角，用运动方程表示桥梁的运动。作为数值研究，给出了低雷诺数流动时机翼倾角的最优控制。因此，可以确定使桥梁振动变得最小的机翼角度。得到的数值结果与实际桥梁翼面的角度相对应。
The purpose of this study is to determine the angle of a wing that is attached to an oscillating bridge located in transient incompressible viscous flows, using the arbitrary Lagrangian–Eulerian (ALE) finite element method and optimal control theory, in which a performance function is expressed by the displacement of the bridge. Currently, some bridges have wings attached to them to prevent oscillation caused by wind flows. When the angle of the wing changes, the state of oscillation also changes. Therefore, the angle of the wing is a very important parameter to consider the minimization of the oscillation of the bridge. In this research, the angle of the wing is determined based on optimal control theory. To minimize the oscillation of a bridge, the performance function is introduced as the minimization index. The performance function is defined by the square sum of the displacements of a bridge. This problem can be transformed into a unconstrained minimization problem by the Lagrange multiplier method. The adjoint equations can be obtained by using the stationary condition of the extended performance function. The gradient used for updating the angle of the wing can be derived by solving the adjoint and state equations. The weighted gradient method is applied as a minimization technique. In this study, the determination of the angle at which the oscillation of the bridge is minimized is presented using this theory. To express the motion of fluids around a bridge, the Navier–Stokes equations described in the ALE form are employed as the state equations. The motion of the bridge is expressed by the motion equations by using the displacements and rotational angle of the body supported by springs. As a numerical study, the optimal control of the angle of the wing is demonstrated at low Reynolds number flows. Thus, the angle of the wing at which the oscillation of the bridge becomes minimum can be determined. Numerical results obtained correspond to the angle of actual bridge wing.