Elucidation of the relationship between complex acoustic power and radiation efficiency for vibrating bodies

Abstract

This investigation examines the physical meaning of surface complex acoustic power and its relationship to acoustic radiation efficiency. It is shown that the radiated power is the power radiating out of a far-field surface where the plane wave relationship between pressure and particle velocity holds. Meanwhile, the reactive power pertains to the difference between kinetic energy and potential energy. A stationary condition of the ratio between the radiated power to the reactive power yields an eigenvalue problem, subsequently decomposing the surface acoustics into a modal representation. Doing so further allows the examination of the relationship between acoustic radiation efficiency and power factor of the complex power. According to the results, the radiation efficiency of the first radiation mode is nearly equal to the square of the first modal power factor. The modes beyond the first of the modal radiation efficiencies are relatively larger than the corresponding squared modal power factors. Numerical examples of elastic structures subjected to external forces illustrate the relationship between radiation efficiencies and power factors of complex powers.