Applied Mathematics and Mechanics

, Volume 31, Issue 1, pp 87–96

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

• Li-xiang Zhang (张立翔)
• Ya-kun Guo (郭亚昆)
• Hong-ming Zhang (张洪明)
Article

## 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.

## Key words

flow-induced vibration fluid-structure interaction generalized variational principle numerical methods generalized minimum residual (GMRES) method

O332

74F10

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© Shanghai University and Springer Berlin Heidelberg 2010

## Authors and Affiliations

• Li-xiang Zhang (张立翔)
• 1
Email author
• Ya-kun Guo (郭亚昆)
• 2
• Hong-ming Zhang (张洪明)
• 1
1. 1.Department of Engineering MechanicsKunming University of Science and TechnologyKunmingP. R. China
2. 2.School of EngineeringUniversity of AberdeenAberdeenUK