A mode-based approach for the mid-frequency vibration analysis of coupled long- and short-wavelength structures

A mode-based approach is described for the mid-frequency vibration analysis of a complex structure built-up from a long-wavelength source and a short-wavelength receiver. The source and the receiver respectively have low and high modal densities and modal overlaps. Each substructure is described in terms of its uncoupled, free-interface natural modes. The interface forces and displacements are decomposed in terms of a set of interface basis functions. Enforcing equilibrium and continuity conditions along the interface hence yields an analytical solution for the vibration response of the built-up structure. Expressions for the frequency response of the source and the power transmitted to the receiver are found. The correlations between the modal properties of the source and the receiver along the interface are derived. These modify the dynamic stiffness matrix of the structure. The flexible receiver is seen to add effective mass and damping to the source. The modes of the short-wavelength receiver are then described statistically in terms of a simple standing wave model. This approximation avoids the need for a modal analysis of the receiver. The results are compared with those of other methods including fuzzy structure theory. Numerical and experimental examples for beam-stiffened plate models are presented.