Summary
In the mid-high frequency range, system uncertainties that may arise from manufacture, the environment, or material properties have a far greater influence on the structural response than in the low frequency range. As a result, obtaining estimates of ensemble response statistics become severely expensive when using conventional deterministic methods employing a Monte Carlo analysis. The Hybrid Finite Element - Statistical Energy Analysis (FE-SEA) method, is an alternative approach that employs a statistical description of components to efficiently yield response statistics. A limitation of this technique is that it was developed for linear systems which restricts the applications, since localised nonlinearities are likely to present themselves within practical engineering systems. In this work, a linearisation scheme is developed for an ensemble of random systems with localised deterministic nonlinearities that is based around the technique of Equivalent Linearisation (EL). This accounts for the randomness present in both an ensemble of random structures and the random response exhibited by a deterministic structure under random loading, for which EL was developed. Although the linearisation is completely general, it is used as part of a Hybrid FE-SEA analysis requiring significant extension of existing theory to evaluate statistical distributions of the response concerning the nonlinearity. Benchmark studies are conducted using Monte Carlo simulations with a Lagrange Rayleigh-Ritz model, and this is assessed against the linearised Hybrid FE-SEA method considered for different linearisation techniques.
