Abstract

In the mid-frequency range, a systems vibrational response becomes sensitive to structural uncertainties. This in combination with the small length scale of deformation requires deterministic approaches such as the Finite Element (FE) method to run expensive high degree-of-freedom Monte-Carlo simulations. Coupling Statistical Energy Analysis (SEA), a well-established high frequency technique, to the FE method leads to far greater efficiency in predicting response statistics of built-up systems. This approach is known as the Hybrid FE-SEA method. A limitation of this technique is that it was developed for linear systems, this restricts the applications since in practical engineering systems nonlinearities are likely to be present. In this work, a linearisation scheme is developed for a general ensemble of nonlinear random systems under stochastic loading but which is applicable to the Hybrid FE-SEA method. This required significant extension of the Hybrid FE-SEA method, by introducing a framework for pre-averaged stochastic random loads developed in conjunction with broadband-averaging of response statistics. Although developed for nonlinear systems both extensions to the theory have applications to linear systems. A benchmark study with a Lagrange Rayleigh-Ritz model employing Monte Carlo simulations has been used to assess the linearised Hybrid FE-SEA method.