FINITE FREQUENCY BAND AVERAGING EFFECTS IN THE STATISTICAL ENERGY ANALYSIS OF TWO CONTINUOUS ONE-DIMENSIONAL SUBSYSTEMS

Abstract

The differences between frequency average powers and energies and their ensemble averages as used in SEA are examined with reference to a system comprising two dynamically one-dimensional subsystems. This system was analyzed by using a wave approach in references [1–4], where expressions for time harmonic coupling and input powers, their ensemble averages and the coupling loss factor were derived. The SEA equations are stated and results from references [1–4] reviewed. The process of frequency averaging is discussed. It is then assumed that all the parameters describing the system response are frequency independent except for the subsystem phases, which are then related to the (constant) subsystem modal densities. Three frequency averaging effects are seen to occur and the standard deviations of the frequency average coupling and input powers, subsystems energies and coupling loss factor evaluated. First, fractional mode count effects are significant when only a few uncoupled modes of vibration lie in the frequency band, and decrease in inverse proportion to this number. Secondly, modal line-up effects occur when the ratio of the modal densities of the subsystem is rational. These effects persist over arbitrarily large frequency bands and are particularly strong when the modal densities are equal or when one is zero, rather less so when one is twice the other. Thirdly, near-line-up effects are important, even over frequency bands which contain many uncoupled modes, when the modal density ratio is close to one of those values which gives large modal line-up effects. The application to the case of two coupled beams is discussed.