An analytical dynamic stiffness formulation for highly accurate broadband vibro-acoustic response analysis

An analytical modelling technique is presented that integrates the dynamic stiffness method (DSM) with spectral DSM (SDSM) for broadband 2D vibro-acoustic response analysis. The method employs DSM to model beams with exact solutions specifically designed for general acoustic or distributed force excitations. Meanwhile, acoustic cavities are modelled using SDSM, where boundary conditions are described by the rapidly converging modified Fourier series. The vibro-acoustic coupling at beam-cavity interfaces is enforced via the normal velocity continuity condition, resulting in an explicitly formulated coupling matrix with concise analytical expressions. This ensures a more direct, accurate, and efficient representation of the structural-acoustic coupling effect. Both beam and acoustic cavity elements are assembled directly to model complex vibro-acoustic systems, without requiring extra element discretization in either the structural or acoustic domains. As a result, the method requires very few degrees of freedom (DoFs) while maintaining high accuracy in predicting broadband vibro-acoustic behaviour. Notably, the proposed approach achieves comparable accuracy to the finite element package COMSOL while using only 0.06% of the DoFs and 0.2% of the computational time. These advantages highlight the method's potential as a benchmark tool for various vibro-acoustic problems.