Efficient reduced order modeling of low- to mid-frequency vibration and power flow in complex structures

In this paper, a methodology is presented for generating low order models of vibration and power flow from a finite element model (FEM) of arbitrary size and complexity, as well as for accurately predicting power flow statistics due to uncertainties. The modeling method is based on component mode synthesis, but a novel secondary modal analysis reduction technique is used to further reduce the number of degrees of freedom. In particular, this technique results in characteristic constraint (CC) modes, a highly-reduced order basis for capturing the motion of the interface between components - and thus the power flow. Then the nominal power flow is computed using these CC modes of the component structures. Furthermore, a multi-level substructuring technique is presented for handling large FEMs. This technique can efficiently construct a low-order model for calculating vibration response and power flow for an entire vehicle structure. Considering the variation of system parameters of this low-order model, the ensemble-averaged power flow is then calculated. Each modal response is expanded in a series of globally orthogonal polynomials or locally linear interpolation functions in these parameters. Then the system equations are derived using Galerkin's method. This statistical treatment provides efficient and accurate modeling of parameter uncertainties, which is critical for mid-frequency vibration analysis.