Analysis of Vibration Characteristics of Periodic Structure Based on Modal Synthesis Transfer Matrix Method

With the continuous improvement of structural lightweight requirements, periodic structures are widely used in beams, plates, shells, and even entities in practical engineering. As an important part of structural design, the analysis of vibration characteristics of periodic structures has attracted much attention from engineering and scientific fields. Based on the transfer matrix method, the periodic structure is divided into multiple identical substructures. The Craig-Bampton modal synthesis method is used to reduce the stiffness matrix and mass matrix of the substructure, and the reduced-order substructure finite element transfer equation and transfer matrix are derived. A new method for efficiently assembling the transfer matrix of periodic structure system is proposed by using the self-similar characteristics of periodic structure. The natural frequency and vibration mode of the system can be obtained by combining the boundary conditions. Giving several numerical examples, the modal synthesis transfer matrix method, Craig-Bampton modal synthesis method and finite element method are used to numerically calculate its vibration characteristics. The results verify the correctness and effectiveness of the modal synthesis transfer matrix method. It shows that the proposed method system matrix order and calculation efficiency are high, which provides a new theoretical and technical support for the vibration characteristics analysis of periodic structures.