An efficient analytical method for broadband vibro-acoustic analysis of coupled beam-cavity systems

Abstract

This paper presents an analytical approach that integrates the dynamic stiffness method (DSM) with the spectral dynamic stiffness method (SDSM) for broadband vibro-acoustic modelling of coupled beam-cavity systems. This combined method uses frequency-dependent shape functions to describe both the structural and the acoustic domains, while the interaction between them is analytically modelled by using the modified Fourier series (MFS). In particular, the DSM uses the particular solutions of beams expanded by the MFS to express analytically acoustic pressure loadings of cavities, eliminating extra fine domain discretizations; the SDSM, on the other hand, formulates the coupling conditions using the MFS in a strong sense by direct enforcement of velocity continuity conditions at the coupling boundaries, enabling more accurate boundary condition handling and physically meaningful solutions. Finally, based on the system matrix equation with very few degrees of freedom, the efficient Wittrick–Williams algorithm is extended to extract eigenvalues of the coupled systems while vibro-acoustic responses are evaluated with high accuracy. The proposed method, validated against benchmark and practical problems, achieves up to 18 times faster computation than COMSOL while maintaining comparable accuracy. This promising method can provide an efficient tool for vibration and noise prediction during early design phases.