Coupling of numerical and statistical methods in acoustics

Problems in the field of vibroacoustics can be modelled in two fundamental ways. On the one hand, they can be addressed in a deterministic way, using numerical methods like the Finite Element Method. On the other hand, statistical methods such as SEA (Statistical Energy Analysis) can be used. Numerical methods are useful for cases with complex geometries but imply a high computational cost for the calculation at high frequencies, especially when working in large domains. They also provide detailed vibration and pressure fields, which are not required by acoustic regulations since they only consider averaged values. Statistical methods are suitable for high frequencies. They deal directly with averaged energies but require specific parameters of power transmission, like internal loss factors and coupling loss factors, whose values can not be calculated analytically for complex geometries. In this work both techniques are coupled so that necessary parameters for the SEA are obtained using a deterministic analysis. In the deterministic approach the Galerkin formulation is used to solve the dynamic problem in its weak form, with the eigenfunctions of the structural elements as the bases of functions used to express the vibration field. Then, a study of the different ways of estimating the coupling loss factor between two subsystems once the deterministic results are obtained is presented, with a discussion of their advantages and disadvantages. The described technique is applied to estimate the coupling loss factors in different configurations consisting of two plates connected with different devices. The obtained results are compared with existing approximated expressions and the good performance of the method is verified. Moreover, the estimated parameters are used to solve larger and more complex systems with SEA. Their results and computational costs are compared with those of the numerical solutions of the same problems. Obtained results differ slightly depending on the technique used for the estimation of the coupling loss factor but provide good trends in general. Therefore, this study shows the potential of combining the deterministic approach (and numerical methods) with the statistical approach in order to solve realistic vibroacoustic problems in the whole frequency range, stressing the differences between the various ways of estimating the coupling loss factor