An exact model reduction technique for beam structures: Combination of transfer and dynamic stiffness matrices

An exact and direct modelling technique is presented in this paper for modelling beam structures. This technique is based on the combination of transfer and dynamic stiffness matrices. In this technique, the whole structure is first divided into substructures based on the required master degrees-of-freedom. For each substructure, the global dynamic stiffness matrix (DSM) is obtained directly by rearranging the corresponding global transfer matrix. In this way, the internal degrees-of-freedom of each substructure are not used in the model. Therefore, the order of the model is greatly reduced. The efficiency and simplicity of the method is demonstrated by two numerical examples. The results are compared with those obtained by other model reduction methods such as static and dynamic reduction methods and with experimental results. It is shown that the method presented in this paper can predict accurately all the eigensolutions in a large frequency range in terms of a low dimension dynamic stiffness matrix.