Random response analysis with the amplitude error correction for acoustic cavities via generalized coordinates

This paper investigates the stationary random response of enclosed acoustic cavities and proposes a numerical method for correcting the amplitude error. Acoustic modal truncation improves computational efficiency but can introduce substantial amplitude errors. Firstly, the Pseudo Excitation Method (PEM) is introduced to transform the random acoustic response into a deterministic harmonic formulation. Secondly, the pseudo sound pressure is projected onto generalized coordinates to construct a positive definite system, thereby avoiding the difficulty caused by the uniform pressure mode under the Neumann boundary condition. Then, inspired by the fast dynamic flexibility matrix algorithm, the pseudo generalized sound pressure is approximated by retaining only a few modes in the high-order term, and the corrected response spectral matrix is recovered in physical space. Numerical examples demonstrate that the proposed method converges rapidly, improves accuracy over the conventional modal superposition method, and performs frequency sweeps more efficiently than the full-order finite element model. The source correlation is also shown to significantly affect both the frequency response and spatial distribution of the random acoustic field.