Chebyshev-fourier forced vibration analysis of laminated annular plates coupled with periodically distributed dynamic vibration absorbers

Abstract This study established a dynamic analysis model for laminated annular plates coupled with periodically distributed dynamic vibration absorbers (DVAs). Based on the first-order shear deformation theory (FSDT), the kinetic energy, strain energy, external work, and boundary spring potential energy of the structure were derived using the energy method and penalty function approach, and the Lagrangian energy functional of the structure was constructed. According to the model simplification principle, the DVAs were simplified into basic elements consisting of mass blocks coupled with spring-damper systems. The displacement functions of the structure were described using the Chebyshev-Fourier method (CFM). The Rayleigh-Ritz method and the implicit Newmark method were applied to solve the energy functional for free and forced vibrations, yielding the natural frequencies, vibration responses under external forces, and vibrational energy of the structure. A series of comparative analyses were conducted, comparing the SGM results with published data and finite element method (FEM) results, which verified the validity of the proposed method. Based on this, the effects of material parameters, annular plate dimensions, boundary constraints, and DVA installation parameters on the vibration characteristics of the structure were investigated. The findings demonstrated that the installation of distributed DVAs can effectively suppress the vibration of the structure.