Power flow through dynamically coupled subsystems

Abstract

In practical applications of the statistical energy analysis (SEA) or other power flow techniques, the calculation of the power flow between subsystems is of fundamental concern. When the subsystems are connected by multimodal structures, for instance, vibration mounts, values for the coupling loss factors as found in the literature are not suitable. In this paper we present a general theoretical framework for calculating the coupling loss factor when the coupler is numerically modeled by classical dynamics, notably by means of a finite element analysis (FEA). After presenting some pertinent results and definitions from SEA, FEA, and structural dynamical theory, an expression for the “coupling” impedance matrix, which relates the forces and free velocities at nodes along the subsystem/coupler boundaries, is derived. This impedance is formed from the admittance matrix of the coupler, calculated using FEA, and input impedances for the systems, analytically calculated. From the coupling impedance, expressions for the coupling loss factors are derived for the cases where the SEA subsystems are plates or beams and include flexural, longitudinal, and torsional forms of energy transmission. Finally, numerical examples are given for the application of this technique to structures consisting of two beams or plates connected by a multimodal coupler.