Semi-analytical modeling and analysis of vibration bandgap modulation in anisotropic laminated beams

In this study, a semi-analytical method is established to solve the band gaps and vibration characteristics of anisotropic laminated beam structures. The energy functional of the beam structure is formulated based on the first-order shear deformation theory, and an improved Fourier series is adopted to represent the displacement functions of the structure. Artificial spring techniques are introduced to simulate periodic boundary conditions and typical boundary conditions. The Rayleigh–Ritz method is adopted to solve the band gap characteristics of the anisotropic laminated beam. The effectiveness of the proposed method is verified by comparison with the Transfer matrix method and results from published literature. Further parametric studies are conducted to reveal the influence mechanism of structural parameters and material properties on the band gaps of the unit cell. In addition, the equivalent conditions of band gaps for finitely periodic beam arrays and the robustness of boundary conditions to the band gap range are investigated, providing a theoretical basis for the vibration reduction design of anisotropic laminated beam structures.