A geometrical approach to estimate the modal radiation efficiency of complex structures

The radiation efficiency of plates has been the study of many works. The rectangular simply supported plate is the most studied case, followed by the circular one. Analytical formulas and approximations for multiple boundary conditions, baffled and unbaffled cases have been the subject of study for decades. For a structure with a complex shape, numerical methods are appropriated such as FEM and BEM approaches. Semi-analytical based on Rayleigh’s integral also appear in the literature to calculate the radiation, mixed with the surface velocity calculated by FEM; they are easy to implement but they are resource consuming as large matrices are presented. In this work, we present a method for estimating the modal radiation efficiency of simply supported and clamped complex plates, based on the theory of Greenspan for circular radiators and with a geometrical approach.