A two-stage approach to updating of mass, stiffness and damping matrices

Abstract

Model updating techniques are used to update a dynamic FE model of a structure so as to obtain its accurate representation in terms of mass, stiffness and damping matrices. Some of the existing updating methods update all the three matrices simultaneously using either complex FRFs or modal data. These methods, however, are faced with numerical problems in practical implementation due to large difference in the magnitudes of the elements of the stiffness and mass matrices on one end and of the damping matrix on the other.This paper proposes a two-stage approach for updating mass, stiffness and damping matrices and performs numerical and experimental investigations to assess the effectiveness of such an approach. The first stage of updating is based on the concept of normal FRFs, which represent the FRFs of a structure if the structure were undamped, to update the mass and stiffness matrices. In the second stage, the damping matrix is updated based on the difference of complex and normal FRFs, which represents the effect of damping in the structure on its frequency response.The numerical example of a fixed-fixed beam structure is first considered that allows investigating the impact of first stage of updating on the second stage. This is followed by an experimental example of an F shape structure. A new method called ‘hybrid’ method to deal with data incompleteness in the context of two-stage updating is suggested. Effectiveness of the two-stage method when updating parameters cannot be chosen correctly is also investigated. The two stage approach presented and the results of the investigations carried out would be helpful in proper implementation and application of the proposed updating method in practice.