Abstract
of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. 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 in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
| Original language | English |
|---|---|
| Pages (from-to) | 87-96 |
| Number of pages | 10 |
| Journal | Applied Mathematics and Mechanics |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2010 |
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Keywords
- flow-induced vibration
- fluid-structure interaction
- generalized variational principle
- numerical methods
- generalized minumum residual (GMRES) method
Cite this
Fully coupled flow-induced vibration of structures under small deformation with GMRES method. / Zhang, Li-xiang; Guo, Yakun; Zhang, Hong-ming.
In: Applied Mathematics and Mechanics, Vol. 31, No. 1, 01.2010, p. 87-96.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fully coupled flow-induced vibration of structures under small deformation with GMRES method
AU - Zhang, Li-xiang
AU - Guo, Yakun
AU - Zhang, Hong-ming
PY - 2010/1
Y1 - 2010/1
N2 - Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. 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 in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
AB - Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. 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 in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
KW - flow-induced vibration
KW - fluid-structure interaction
KW - generalized variational principle
KW - numerical methods
KW - generalized minumum residual (GMRES) method
U2 - 10.1007/s10483-010-0109-z
DO - 10.1007/s10483-010-0109-z
M3 - Article
VL - 31
SP - 87
EP - 96
JO - Applied Mathematics and Mechanics
JF - Applied Mathematics and Mechanics
SN - 0253-4827
IS - 1
ER -