Coupling rod energy models using local energy density

Abstract

To couple medium‐ and high‐frequency models of rod vibration in terms of energy density and intensity, relationships that enforce continuity of power flow and compatibility of energy density are required at the joint. The continuity relationship for local power flow at a joint between two rods is straightforward. However, for joints of rods with different properties, there is a jump discontinuity of local energy density at the joint. An exact relationship for the power flow can be found using the receptance method. A good frequency‐averaged approximation of the power flow can be found using the so‐called wave transmission method commonly used in statistical energy analysis. In this investigation, a relationship for the jump discontinuity of the local energy density, which uses the ratio of the local kinetic energy density to the total density, is examined. The technique is capable of deterministic or statistical prediction of energy in the coupled rods. [This investigation was supported by the NASA Langley Research Center.]