基于特征正交分解的三维壁板非线性颤振分析

THREE-DIMENSIONAL PANEL NONLINEAR FLUTTER ANALYSIS BASED ON PROPER ORTHOGONAL DECOMPOSITION METHOD

基于von Karman大变形理论及活塞理论建立超音速流中壁板的气动弹性方程。采用特征正交分解法(POD)结合向伽辽金法(Galerkin)的映射这样一种半解析法建立降阶模型(ROM)求解三维壁板的非线性气动弹性问题,并与传统的Galerkin法对比。发现并证明了POD数值模态与伽辽金法简谐基函数之间转换矩阵的正交性,从而简化了POD降阶模型的建立过程。通过数值算例考察了POD法的准确性、收敛性及高效性。结果表明POD降阶模型能够以更少的模态,更高的计算效率达到与Galerkin法同样的精度。以长宽比4为例,POD法以2个模态,3s的时间计算了壁板的振动响应;而Galerkin法需要16个模态,900s的时间。

A semi-analytical approach based on the proper orthogonal decomposition(POD) method with a Galerkin projection scheme is adopted to construct a reduced order model(ROM) to solve three-dimensional panel nonlinear aeroelasticity problem in supersonic flow, using von Karman large deflection theory and piston theory. Orthogonality of the transform matrix between the numerical POD modes and harmonic basis functions of the Galerkin method is proved, which simplifies the construction of POD/ROM. The accuracy, convergence and efficiency of the POD method are verified through numerical examples. It reveals that the POD/ROM can recover the Galerkin solutions with the same accuracy and computational efficiency, using fewer modes. When considering an example with a length-to-width ratio of 4, 2 modes and 3 seconds are required in the POD method to describe panel oscillation, while 16 modes and 900 seconds are required in the Galerkin method.