Fully coupled flow-induced vibration of structures under small deformation with GMRES method

Li-xiang Zhang, Yakun Guo, Hong-ming Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)87-96
Number of pages10
JournalApplied Mathematics and Mechanics
Volume31
Issue number1
DOIs
Publication statusPublished - Jan 2010

Fingerprint

Vibration
Fluids
Fluid structure interaction
Nonlinear equations
Turbomachine blades
Flow of fluids
Turbines
Fluid
Finite element method
Geometry
Trapezoidal Rule
Formulation
Complex Geometry
Viscous Flow
Turbine
Blade
Viscous Fluid
Incompressible Fluid
Fluid Flow
Linear equation

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 journalArticle

Zhang, Li-xiang ; Guo, Yakun ; Zhang, Hong-ming. / Fully coupled flow-induced vibration of structures under small deformation with GMRES method. In: Applied Mathematics and Mechanics. 2010 ; Vol. 31, No. 1. pp. 87-96.
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