Degrees of Freedom Reduction Technique for Free interface Substructure Based on Nodal Force Interpolation

Abstract:

According to the nodal displacement interpolation formulation in the finite element method, the interface degrees of freedom reduction technique for a free interface substructure was developed. Based on the basic transformation of the free interface modal synthesis method, the second coordinate transformation of the interface was completed, which effectively reduced the generalized degrees of freedom of the system, and the computation efficiency was improved. The modal analysis for a beam fixed at two ends was constructed as a numerical example, and the first ten main frequencies of the beam before and after the interface degrees of freedom reduction were compared. The result demonstrates that the proposed interface degrees of freedom reduction technique for the free interface substructure is reasonable and effective. In comparison with the modal reduction method for the interface degrees, the precision of the main computed frequencies obtained by these two methods are the same. However, the proposed method is more efficient and convenient when used in the engineering, though the latter has a better accuracy. Meanwhile, the influence on the calculation accuracy of the way to choose interpolation nodes was also discussed. The numerical results show that, the more the interpolation nodes involve in the modal analysis, the higher the calculation accuracy is. And when the interpolation nodes uniformly distribute on the interface, the accuracy is the highest.

Key words:free interface substructure; modal synthesis method; interpolation formulation; coordinate transformation matrix; degrees of freedom reduction