<p>A multivariate analysis method that utilizes the time-domain response under harmonic excitation of the corresponding frequency and its displacement spectrum to assist in analyzing nonlinear amplitude-frequency responses is proposed, which is aimed at investigating the nonlinear characteristics of a honeycomb core sandwich circular plate with functionally graded graphene platelet-reinforced composite face (GRFHC) coupled with dynamic vibration absorber (DVA). Considering both geometric nonlinearity and the first-order shear deformation theory (FSDT), the Spectro-Geometric Method and incremental harmonic balance (IHB) are employed to obtain the nonlinear amplitude-frequency response, which is further analyzed in conjunction with the nonlinear time-domain response under harmonic excitation and its displacement spectrum, providing a comprehensive evaluation of the nonlinear behavior of the circular plate based on the computationally derived nonlinear resonance range and the amplitude of super-harmonic. On this basis, the paper reveals how positive and negative Poisson's ratios affect the impact absorption performance of honeycomb sandwich structures, quantifies the nonlinear suppression effect of DVA, summarizes the optimal graphene-platelet layering method, and investigates the influence of plate geometric parameters, boundary conditions on nonlinear amplitude-frequency responses, as well as the underlying mechanisms governing how parameters affect these responses.</p>