Transmission loss of plates with internal resonators modelled by harmonic oscillators with frequency dependent complex mass and spring stiffness

Sound transmission loss measurements on an epoxy plate containing lead spheres with a silicon-rubber coating show remarkable improvements over the mass law. The reasons for this behavior are basically understood, however, previous modelling attempts failed to achieve satisfactory agreement with the experimental result. In particular, the description of the coated sphere as a harmonic oscillator with frequency-independent parameters needs to be improved. Both spring constant and mass of the harmonic oscillator are now considered complex functions of frequency. If the internal resonator is enclosed in a rigid frame, the whole structure is even more simply described by a frequency-dependent complex mass. In general, these quantities can be determined experimentally or theoretically via elementary relations. Results have been obtained from the analytical solution of the corresponding elastodynamic problem for two examples: the above epoxy plate and a layer sequence 'elastic