An analytical dynamic stiffness method for efficient broadband vibro-acoustic analysis of complex built-up structures

An analytical modelling technique is presented, combining the dynamic stiffness method (DSM) with the spectral DSM (SDSM) for the broadband vibro-acoustic analysis of complex built-up structures. In particular, the structures are modelled exactly by the DSM based on particular solutions tailored for general acoustic or distributed force excitations; whereas the acoustic cavities are modelled by the SDSM where the boundary conditions are described by modified Fourier series with a rapid convergence rate. The vibro-acoustic coupling along the interfaces between the structures and the cavities is achieved by applying the normal velocity continuity condition, leading to a coupling matrix in an analytical manner. Both structural and acoustic cavity elements are assembled directly to model complex vibro-acoustic systems and no extra element discretization is required for both structural and acoustic domains. Consequently, the proposed method uses very few degrees of freedom (DoFs) but describes the broadband vibro-acoustic behaviour highly accurately. It is demonstrated that the proposed method exhibits a predominant advantage over the finite element package COMSOL in terms of accuracy and computational efficiency. This approach also has the potential to serve as the benchmark for a wide range of vibro-acoustic problems.