Abstract Summary
The influence of uncertainties arising from material properties and manufacture in engineering structures leads to increasing variation in the response characteristics with frequency. This is in combination with the likelihood that within a complex system, localised nonlinearities can also present themselves, rendering commonplace linear high frequency techniques such as the Hybrid Finite Element (FE) - Statistical Energy Analysis (SEA) method inapplicable. The alternative being to run vastly expensive huge degree of freedom Monte Carlo simulations in the time domain in order to fully capture the nonlinear dynamics, becomes prohibitive for large built-up systems. The development of a linearisation procedure applicable to an ensemble of random systems featuring deterministic nonlinearity is firstly considered in this work, which is centred around the technique of Equivalent Linearisation. This presents a relation between the order of both the nonlinearity in the system and response moment required to determine linearised parameters. With the proposed linearisation being developed around deterministic nonlinearity it is exploited by the Hybrid FE-SEA method by describing the nonlinearity as part of the master system, but for this an extension to hybrid variance theory is necessary. The linearised Hybrid FE-SEA method is then assessed against a series of Monte Carlo benchmark simulations adopting a Lagrange Rayleigh-Ritz model that employ different linearisation procedures including that developed for the hybrid method but also the full nonlinear solution.
