Abstract: Due to the limitations of traditional locally resonant metamaterial plates under classical boundary assumptions and the strong dependence of linear design approaches on the attached mass ratio, this study establishes a unified dynamic model for Euler-buckled beam-type nonlinear metamaterial plates under elastic boundary conditions using the Fourier series expansion and a semi-analytical energy method, and systematically investigates the nonlinear bandgap behavior. An improved two-dimensional Fourier series is adopted as the admissible function for the transverse displacement of the plate, which eliminates the constraints imposed by classical boundaries and enables the model to accommodate various boundary constraints. Hamilton's principle is employed to derive the governing dynamic equations of the nonlinear metamaterial plate. The energy method is utilized to compute the dispersion surfaces of the infinite nonlinear metamaterial plate, thereby clarifying the frequency band characteristics of both linear and nonlinear bandgaps. The harmonic average approach and the numerical integration method are respectively applied to solve the frequency-domain responses, and the accuracy of the proposed model is validated through cross-verification between the two approaches. Furthermore, the nonlinear bandgap behavior and vibration response characteristics are comprehensively investigated from both time-domain and frequency-domain perspectives. The regulation mechanisms of the Euler-buckled beam structural parameters on the equivalent stiffness and bandgap are revealed, and the effects of boundary conditions and excitation amplitude on the bandgap characteristics are discussed in detail. The results indicate that adjusting structural parameters can effectively tune the resonant frequency and bandgap. Boundary conditions cause significant variations in the bandgap. When the excitation amplitude exceeds a critical value, the system exhibits complex chaotic responses. Finally, experimental validation of the proposed theoretical model is carried out using a prototype of the Euler-buckled beam-type nonlinear metamaterial plate. The experimental results confirm the effectiveness of the present model. The theoretical modeling and analytical results presented in this work provide a theoretical foundation and technical support for the vibration attenuation analysis of nonlinear metamaterial plates under complex boundary conditions.