A linearised Hybrid FE-SEA analysis method for complex systems with nonlinearities under random excitation

Within complex structures it is not uncommon for localised nonlinearities to be present, this renders conventional linear mid-high frequency analysis techniques such as the Hybrid Finite Element (FE) - Statistical Energy Analysis (SEA) method inapplicable. The development of a linearisation procedure applicable to an ensemble of random systems featuring deterministic nonlinearity is initially considered in this work, which is centred around the technique of Equivalent Linearisation. Constraining the linearisation to remain invariant across the whole ensemble, key to the linearised hybrid formulation developed, produced a relation between the order of both nonlinearity and the required statistical response moment when considered for Gaussian excitation. From the linearisation derived, an extension to hybrid variance theory was necessary to determine the variance of a frequency integrated response of the master system. A numerical study is then used to demonstrate the linearised Hybrid FE-SEA method against a series of Monte Carlo benchmark simulations adopting a Lagrange Rayleigh-Ritz model. The benchmark simulations feature different treatments of the nonlinearity from the linearisation developed to the full nonlinear solution.