A modal power balance approximation for point connected flexural beams

Abstract

In recent years, the application of power flow techniques to the analysis of beams and plates has led to an increased understanding of how noise is transmitted through structures. When applied in terms of mode-to-mode transmission, power flow evaluation has promise in modeling dynamic response at frequencies for which statistical energy analysis is not appropriate. Modal power flow calculations can, however, be computationally prohibitive. This paper introduces a modal power balance approach by which the computational effort can be reduced. The approach involves formulating the mode-to-mode power exchanged between two beams in terms of a set of modal power balance equations. These equations are analogous to the sub-system power balance equations of statistical energy analysis. By introducing suitable approximations, the equations can be integrated over frequency and length to express power flow relationships in terms of band-limited, modal mean-square values. The approach is applied to the configuration of two force and moment coupled flexural beams. The results are compared with a classical modal solution.