基于GMRES算法的弹性结构强耦合小变形流激振动分析

Analysis of Fully Coupled Flow-Induced Vibration of Structure Under Small Deformation With GMRES

使用混合广义变分原理,将基于Lagrange表述的小位移变形结构振动问题与基于Euler描述的不可压缩粘性流动问题,统一在功率平衡的框架下建立流固系统的耦合控制方程.用有限元格式做空间离散后,再用广义梯形法将有限元控制方程转化为增量型的线性方程组,该方程组的系数矩阵具有非对称性,其中元素含对流效应和时间因子.将GMRES算法与振动分析的Newmark法和流动分析的Hughes预测多修正法结合,发展成一种基于GMRES-Hughes-Newmark的稳定算法,用于计算具有复杂几何边界的强耦合流激振动问题.以混流式水轮机叶道为数值算例的计算表明,模拟结果与试验实测结果吻合较好.

Lagrangian-Eulerian formulations, based on a generalized variational principle of coupling fluid and solid dynamics, was established to describe flow-induced vibration of a structure under small deformation in incompressible viscous fluid flow. The spatial discretization of the formulations was on multi-linear interpolating functions using the finite element method for both the fluid and solid structure. The generalized trapezoidal rule was used to obtain apparently nonsymmetric linear equations in incremental form for the variables of the flow and vibra- tion. The nonlinear convective term and time factors were contained in nonsymmetric coeffi- cient matrix of the equations. Generalized minimum residual method （GMRES） was used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark was de- veloped to deal with flow-induced vibration with dynamical fluid-structure interaction in complex geometry. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented was suitable for dealing with the flowinduced vibration of structures under small deformation.