Formulation of the boundary element method in the wavenumber–frequency domain based on the thin layer method

• The boundary element method is formulated based on the thin-layer method.
• The procedure avoids numerical evaluation of boundary integrals.
• The procedure circumvents the singularities of the fundamental solutions.
• Fundamental solutions are calculated via modal superposition.
• Procedure is validated against finite element results.

This paper links the boundary element method (BEM) and the thin-layer method (TLM) in the context of structures that are invariant in one direction and for which the equations of motion can be formulated in the wavenumber–frequency domain (2.5D domain). The proposed combination differs from previous formulations in that one of the inverse Fourier transforms and the Green’s functions (GF) integrals are obtained in closed form. This strategy is not only supremely efficient, but also avoids singularities when the collocation point belongs to the integrating boundary element, and provides accurate evaluations of the coefficients of the boundary element matrices.