Frequency Solution of Structures Coupled with Inviscid Fluids
In many dynamic analyses of fully coupled fluid structure systems, the fluid can be assumed to be inviscid. In such cases, it can be effective to perform a frequency solution and mode superposition analysis for the dynamic response.
The major expense is then in solving for the frequencies and mode shapes, which requires the solution of the quadratic eigenvalue problem:
(K  λ ^{2}M  λ C) φ = 0
where K and M correspond to the stiffness and inertia effects of the fluid and structure, and the full coupling is expressed in C. The vector φ contains the nodal structural displacements and fluid potentials (see Finite Element Procedures, by K.J. Bathe, Prentice Hall 1996).
In ADINA version 8.3, the Lanczos method can be used for the solution of this eigenvalue problem. The animations below show two vibration modes of a reactor vessel with piping analysed using ADINA. The table gives the number of degrees of freedom of the system, the total number of frequencies calculated and the corresponding solution times using ADINA on an IBM Linux machine with four processors.
Degrees of freedom

Number of frequencies

Total solution time

593,496

1000

7.43 h

593,496

100

0.74 h

