Modeling and Analysis of Bandgap Optimization for Periodic Thin-Walled Stiffened Coupled Structures Based on Null-Space Method and Kirchhoff Thin-Plate Theory

Aiming at the problems of cumbersome parameter tuning and low computational efficiency in traditional methods for the bandgap optimization of periodic thin-walled stiffened coupled structures, this paper integrates the null-space method with the Kirchhoff thin-plate theory to establish an efficient model for bandgap analysis. The proposed method realizes matrix-based construction of coupled and periodic boundary conditions, decouples boundary constraints from displacement shape functions, avoids the limitations of virtual spring stiffness, and requires no remeshing during parameter variation. Comparisons with the finite element method verify its convergence and accuracy: the average deviation of bandgap widths in the 0–250 Hz range is 0.37 Hz, and the computational efficiency is about 2.5 times that of FEM(Finite Element Method). This paper also systematically analyzes the effects of four key parameters, including thin-wall thickness, stiffener thickness, stiffener height and stiffener spacing, on the number and width of bandgaps and proposes targeted optimization strategies for different engineering scenarios. The results provide a new method for vibration and noise reduction design of such structures and lay a foundation for future bandgap modeling and optimization of advanced lightweight periodic structures.