Here, I was the first to investigate the sound reduction of a chaotically vibrating curved panel with/without a cavity. A sound reduction formula was obtained by combining the homogeneous wave equation and nonlinear structural governing equation. The chaotic and nonlinear sound radiations were computed from the multi-mode coupled formulations using a numerical integration method. The results obtained from the proposed method and classical harmonic balance method were generally in reasonable agreement. A modal convergence study was also performed to check the proposed method. The effects of chaotic vibration on the sound reduction of a curved panel with/without a cavity were studied in detail.