Background/Introduction <p>Modeling the nonlinear dynamic behavior of annular plates requires a careful balance between computational simplicity and high accuracy. A streamlined approach is needed to effectively capture these complex dynamics without excessive computational cost.</p> Purpose <p>This study aims to comprehensively investigate the nonlinear dynamic behavior of annular plates under various boundary conditions by developing a novel, simplified formulation.</p> Methods <p>The governing equations of motion are derived utilizing the first-order shear deformation theory (FSDT) alongside nonlinear Von–Karman strain-displacement assumptions. The partial differential equations (PDEs) are transformed into a set of ordinary differential equations (ODEs) using the Galerkin method. The method of multiple scales is then applied to analyze the system across three main phases: linear free vibration, nonlinear free vibration, and nonlinear forced vibration. Finally, the proposed model is validated through comparison with existing research and numerical simulations.</p> Results <p>The linear and nonlinear natural frequencies of both annular and circular plates were successfully obtained. Parametric analysis shows that increasing the ratio of inner to outer radius, as well as the ratio of thickness to outer radius, leads to more linear dynamic behavior. Additionally, boundary conditions strongly affect the degree of non-linearity. The model also reveals pronounced hardening behavior under external excitation, particularly for clamped and simply supported edges.</p> Conclusions <p>The proposed simplified formulation based on FSDT accurately captures both linear and nonlinear vibrations of annular plates with significantly reduced complexity. The findings provide important insights into the transition from linear to nonlinear regimes, demonstrating the high effectiveness and efficiency of the proposed modeling approach</p>