Approximation of power flow between two coupled beams using statistical energy methods

In this work, an investigation is performed into developing a general frame work, for predicting the power flow, between coupled component structures w ith uncertain system parameters. A specific, example of two coupled beams i s 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 f ormulated 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, wit h each beam length having a uniformly-distributed random perturbation. Then , using fixed-interface component modes and constraint modes, the Craig-Bam pton method of CMS is of constraint-mode employed to formulate the nominal power flow, equation in terms of the degrees of freedom. This fixed-interfa ce CMS method is seen to provide a systematic and efficient platform for po wer flow, analysis. Using this CMS basis, a general approximation for the e nsemble-averaged power flow, is formulated regardless of the probability di stribution of the random parameters or the coupling strengths between the s ubstructures. This approximation is derived using Galerkin's method, in whi ch each modal response is expanded in locally linear interpolation function s in the random system parameters. The proposed general framework is numeri cally validated by comparisons with wave approximations from the literature for this two-coupled-beam system.