An investigation of transmission coefficients for finite and semi-infinite coupled plate structures

This paper introduces a method for determining the transmission coefficient for finite coupled plates using an analytical waveguide model combined with a scattering matrix. In the scattering matrix method, the amplitudes of the structural waves impinging on a junction are separated into incident, reflected, and transmitted components. The energy flow due to each of these waves is obtained using a wave impedance method, which is subsequently used to determine the transmission coefficient. Transmission coefficients for semi-infinite and finite L-shaped plates are investigated for single and multiple point force excitations, and for controlled incident wave sources. It is shown that the transmission coefficients can also be calculated from details of the modal transmission coefficients and the modal composition of the energy incident on the junction. Results show that the modal transmission coefficients are largely independent of whether the plates have finite or semi-infinite boundary conditions, and are only dependent on the details of the coupling. Finally, frequency averaged transmission coefficients are compared for semi-infinite and finite structures. In the cases considered, it is found that the semi-infinite system is a good approximation for finite systems after frequency averaging, especially if the system is excited with multiple point force excitation.