Two-dimensional Coupling Vibration Analysis of Fluid and Structure Using an FEM Displacement Method. 2nd Report. Extraction Method of Spurious Modes.

Abstract

There are many structural vibration problems which include fluid motion; one example is that of an oil-filled power transformer tank. In fluid vibration analysis, the wave equation is commonly solved using the velocity potentials or pressures as unknown variables in FEM, FDM and BEM. On the other hand, for structural vibration analysis, displacements are generally used as unknown variables. However, it is difficult to solve problems involving vibrations of fluid and structure simultaneously by taking into account fluid-structure interactions, except by using added masses instead of fluid, or Herrmann's special variational principle. These approaches include special and complex techniques which are unfamiliar to most engineers. In this paper, a new vibration calculation method which can treat fluid and structure simultaneously is proposed; it uses an FEM displacement method which is familiar to most engineers. When the displacement method is applied to two-or three-dimensional fluid vibrations, spurious vibration modes caused by excessive degrees of freedom are observed. These modes are not only bothersome, but also hinder analysis accuracy. In a previous paper, a rejection technique, in which natural frequencies of spurious modes are made to be 0 Hz, was developed. But, matrix size is unchanged, because spurious modes are still contained in the matrix. As a result, a large memory and long calculation time are needed to solve the matrix. In this paper, an extraction method is developed for them and the matrix size is reduced. Then, the new calculation method is applied to solve coupled vibrations of fluid and structure. The method is judged to be applicable to actual vibration analysis.