<p>The vibroacoustic behavior in plate-cavity coupling systems is prevalent across various engineering applications. Recently, metamaterials have emerged as a promising solution for vibration attenuation. Understanding the coupling mechanisms between nonlinear metamaterial plates and acoustic cavities is crucial for advancing nonlinear metamaterials in plate cavity coupling systems. A tunable nonlinear resonator based on Euler-buckled beams has been designed for suppressing vibroacoustic responses in plate-cavity coupled systems. A semi-analytical fluid–structure interaction framework is developed for analyzing the nonlinear metamaterial plate cavity coupling system (NLMPCCS), focusing on its nonlinear bandgap properties and vibroacoustic attenuation mechanisms. The governing equation of the NLMPCCS is derived using improved two-dimensional and three-dimensional Fourier series, with the coupled vibroacoustic responses solved through harmonic balance method and time integration method. Furthermore, an amplitude-dependent bandgap expression is developed to estimate nonlinear bandgaps. The proposed model is validated through finite element method and comparative studies. Based on the foundation, the bandgap behavior and vibroacoustic characteristics of the NLMPCCS are comprehensively analyzed in both time and frequency domains, elucidating the underlying mechanisms of nonlinear bandgap formation. Results demonstrate that the NLMPCCS achieves significantly enhanced vibration and sound pressure suppression compared to its linear counterpart. Finally, experimental validation has been conducted to verify the vibroacoustic characteristics of the proposed NLMPCCS based on Euler-buckled beam resonators.</p>