Approximation of Power Flow Between Two Coupled Beams Using Statistical Energy Methods

In this work, an investigation is performed into developing a general framework for predicting the power flow between coupled component structures with uncertain system parameters. A specific example of two coupled beams is considered, in which a torsional spring is attached at the coupling point to adjust the coupling strength. The power flow in the nominal system is formulated using component mode synthesis (CMS). First, the parameter-based statistical energy method, which employs free-interface component modes, is applied to obtain approximations for the ensemble-averaged power flow with each beam length having a uniformly-distributed random perturbation. Then, using fixed-interface component modes and constraint modes, the Craig-Bampton method of CMS is employed to formulate the nominal power flow equation in terms of the constraint-mode degrees of freedom. This fixed-interface CMS method is seen to provide a systematic and efficient platform for power flow analysis. Using this CMS basis, a general approximation for the ensemble-averaged power flow is formulated regardless of the probability distribution of the random parameters or the coupling strengths between the substructures. This approximation is derived using Galerkin’s method, in which each modal response is expanded in locally linear interpolation functions in the random system parameters. The proposed general framework is numerically validated by comparisons with wave approximations from the literature for this two-coupled-beam system.