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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。
Aeroelasticity equation of supersonic flow inwall based on von Karman theory of large deformation and piston theory. A reduced-order model (ROM) was established by semi-analytic method of feature orthogonal decomposition (POD) combined with Galerkin mapping to solve the nonlinear aeroelasticity problem of three-dimensional panel. Compared with the traditional Galerkin method Compared. The orthogonality of the transition matrix between the POD norm and the Galerkin harmonic basis function was found and proved, which simplified the establishment of the POD reduction model. Numerical examples are used to investigate the accuracy, convergence and efficiency of POD method. The results show that the POD reduction model can achieve the same accuracy as the Galerkin method with fewer modalities and higher computational efficiency. Taking the aspect ratio 4 as an example, the POD method calculates the vibration response of the siding with 2 modalities and 3 s time, while the Galerkin method requires 16 modalities and 900 s time.