The minimum multimodal radiation efficiency of baffled finite beams

Abstract

A technique for deriving the optimal surface velocity distribution on the surface of a finite baffled beam has been developed. The optimal velocity distribution minimizes the radiation efficiency of the beam for a specified maximum permissible mode and frequency. A modal expansion of the surface velocity in terms of unknown modal amplitude coefficients, the Rayleigh integral, and a far-field intensity integration are employed to obtain a quadratic expression for the radiation efficiency of the beam. Application of a suitable constraint to avoid trivial solutions leads to an eigenvalue problem identical in form to the Rayleigh quotient employed in dynamic mechanical systems. The eigenvector of modal amplitude coefficients corresponding to the lowest eigenvalue yields the minimum radiation efficiency, while the eigenvalue itself is the actual value of the minimum radiation efficiency. Near and below coincidence, the optimal eigenvector of modal amplitude coefficients yields a radiation efficiency significantly less than the radiation efficiency of any single modal component acting alone. Simply supported and clamped–clamped boundary conditions are considered, and numerical examples are presented for each.