This paper presents the development of an implicit partitioned numerical framework for predicting the nonlinear aeroelastic response of a curved panel backed by an acoustic cavity in supersonic flow. This coupled fluid–structure–acoustic system consists of the unsteady compressible Navier–Stokes equations, solved using a finite volume method within an Arbitrary Lagrangian-Eulerian (ALE) formulation to describe the supersonic airflow, a geometrically nonlinear structural model incorporating a coordinate transformation matrix to characterize the curved panel dynamics, and a nonlinear wave equation to capture finite-amplitude sound wave propagation within the cavity. The accuracy of the proposed method is validated through comparisons with reference results. The study reveals a range of complex nonlinear aeroelastic phenomena under specific combinations of panel stiffness, curvature, and cavity pressure, including chaotic dynamics and acoustic resonance.