Thermal Circuit Approach to Vibrations in Coupled Systems and the Noise Reduction of a Rectangular Box

Abstract

Stationary, wide-band vibrations of complex dynamic systems are treated in terms of energy quantities, neglecting details of structure and excitation. Approximate relations between the average energies in loosely and conservatively coupled systems are obtained in terms of modal densities, internal losses, and coupling losses. It is shown that the products of modal density and coupling-loss factor are equal within each pair of subsystems. The general theory is applied to study the noise reduction of a rectangular box, and experimental results are compared with theoretical predictions with generally good agreement. The transmission behavior of a box at a given frequency is shown to depend on the relation of this frequency to the lowest mechanical- and acoustic-resonance frequencies and the critical frequency of the walls. Theory and experiment show that near the lowest mechanical resonances the pressure in the box may considerably exceed that in the incident sound field.