Reformulation of Frequency Based Substructuring Method Considering Elastic Joints According to Sherman-Morrison-Woodbury Formula

Abstract

The frequency based substructuring method considering elastic joints (FBSM-CEJ) is reformulated according to Sherman-Morrison-Woodbury Formula (SMWF) in this paper, the derivation process of which is more concise and the order of the matrix that requires inversion in the corresponding derivation result is lower comparing to the existing FBSM-CEJ. Meanwhile, the reformulated FBSM-CEJ possesses more applicability and operability that can be used to directly and efficiently calculate the frequency response function (FRF) matrix of complex structure no matter the impedance matrix of the elastic joints is singular or not. Last but not least, via using none-mass spatial beam element to simulate the dynamic properties of elastic joints, the performance of the reformulated FBSM-CEJ is verified through numerical simulation. All the achievements obtained from this work will provide a theoretical basis for analysing the dynamic properties of a complex structure considering elastic joints.

Keywords

• elastic joints
• frequency based substructuring method
• frequency response function
• Sherman-Morrison-Woodbury Formula
• spatial beam element