We address acoustic transmission loss through doubly-periodic elastic panels separating two semi-infinite fluid half-spaces. This involves the computation of the transmitted and reflected sound fields due to an incident plane wave. The elastic panel may have complex internal structures, for example, a sandwiched honeycomb core. Our computations are based on using high order (p-version) finite element discretization. The semi-infinite fluid half-spaces on either side of the elastic panel are truncated using perfectly matched layer (PML) approximations. We verify our model using data for transmission loss for thin and thick homogeneous elastic plates using analytic solutions based on 3D elasticity as well as thin and thick plate theory. This is followed by a study of transmission loss though sandwiched honeycomb panel for a range of frequencies and incident angles.

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