Sound transmission through periodically inhomogeneous plates

This paper completes a series of articles on the calculation of sound transmission through periodically inhomogeneous infinite plates. Whereas the two preceding articles treat the special cases of low frequencies and thin plates, respectively, the problem is now solved without these restrictions within the framework of linearised elasticity theory. A variational formulation leads to an infinite system of linear equations for the expansion coefficients of the displacement field inside the inhomogeneous plate. In a self-consistent manner these coefficients also determine the transmission coefficients for the diffracted waves and thus the transmission loss. Several simple examples have been successfully evaluated by a numerical implementation called GENERAL. More realistic applications require more effective numerical solvers or the use of supercomputers.