Equivalent linearisation in a hybrid FE-SEA approach for nonlinear vibro-acoustic modelling

Hybrid techniques, such as a Finite Element-Statistical Energy Analysis (FE-SEA), have been widely employed to model vibro-acoustic systems in order to estimate the ensemble averaged response due to external inputs, assuming that the governing equations of motion of the comprising structures and connections are linear. However, nonlinear behaviour can be found in the interfaces between the point where the input is applied and the system itself, resulting in the force being transmitted through a nonlinear path, that might affect the structural or acoustic response of the system depending on the amplitude of the input. With the aim of improving the estimation of the mean squared response of the system subjected to random inputs through a nonlinear interface, an equivalent linearisation approach has been adopted to linearise the equations of an existing FE-SEA method that supports prescribed displacements as inputs rather than forces. Results from numerical simulations of a nonlinear single degree of freedom system demonstrate the ability of the equivalent linearisation approach to estimate the mean square response with a minimum error, even for systems with strong nonlinearities. The method here developed has been validated against experimental data collected from a vibro-acoustic system excited through a nonlinear massless and undamped spring.