A new method for solving parameter mutation analysis in periodic structure bandgap calculation

This study introduces a bandgap solution method that combines the domain decomposition method with the linear expression method based on the principle of the energy method to solve problems related to detailed geometric construction, physical parameter mutation in multi-period structures, and high-frequency calculation from a new perspective. Moreover, it derives the vibration dispersion curve of the periodic structure using AB-type periodic beams and periodic row pile structures as examples by decomposing the calculation domain into multiple sub-domains for independent solutions. Subsequently, it proposed the linear expression method to manage boundary displacement constraints. The accuracy and effectiveness of the proposed method are confirmed by comparing the numerical results with those from the finite element method. The study results have shown that in contrast to traditional modeling methods and finite element methods, the proposed method can enhance computational efficiency by more than 30 times. Furthermore, as the parameter difference grows, the efficiency improvement becomes even more pronounced. By increasing the number of segmented structures within the cell, the challenges of function fitting in addressing high-frequency problems using traditional energy methods are effectively mitigated. Additionally, an optimal number of segments exists to maximize computational efficiency for varying computational frequency requirements.