Abstract:

Modal densities are parameters that participate in the specification of a statistical energy analysis (SEA) model of a complex composed of a number of coupled dynamic systems. The modal density n((omega)) of a dynamic system in this context, is defined by the equation: ((Delta)(omega))n((omega))=N((omega)), where a frequency band {(omega),(Delta)(omega)} is identified by the bandwidth ((Delta)(omega)) centered at the frequency ((omega)) and N((omega)) is the number of resonant modes, in this dynamic system, for which the resonance frequencies lie within this frequency band. Usually, it is assumed that the modal density n((omega)) is a continuous and/or a monotonic function of the frequency ((omega)). Moreover, it is often argued that the modal densities are identical for dynamic systems that possess the same propagation speeds and the same spatial extents, i.e., the same volumes, areas, or lengths. The implication that the assumption and the argument are particularly valid for the higher frequency range, has designated SEA suitable for ``a high-frequency analysis only.'' The modal densities are examined, for a few simple dynamic systems, in an attempt to reassess the assumption, the argument, and the designation.