A virtual joints based transfer matrix method for dynamic performance analysis of periodic beams

Abstract

An updated Transfer Matrix (TM) method involving spatial discretization through the introduction of virtual joints is proposed for the dynamic analysis of periodic structures with long transfer distances. The root cause of numerical issues in the TM method arising from long transfer distances is identified. This issue is effectively addressed by discretizing the original beam segments with virtual joints. The Joint Coupling Matrix (JCM) method is used to universally describe the restraints and interactions at all joints, leading to the closed-form solutions for the dynamic responses of periodic beams. To validate the updated TM method, the natural frequencies and forced vibration responses calculated from the updated TM method are compared with those from Finite Element Method (FEM). Then, the updated TM method is used to investigate the vibration mitigation performance of periodic structures. Results from both free and forced vibration analyses reveal the variation characteristics of natural frequencies with structural periodic parameters and elucidate the relationship between the vibration mitigation performance of periodic beams and the loading frequencies. Furthermore, through Frequency Response Function (FRF) analysis, the vibration mitigation mechanism of periodic beams is examined in depth from a vibration perspective. This work provides valuable guidance for the optimal parameter configuration of periodic structures to achieve enhanced vibration mitigation performance.