Edge effect on radiation efficiency of a baffled beam below the critical frequency

Abstract

The radiation efficiency of a beam is theoretically determined from the total acoustic power radiated from the vibrating surface. The beam is supported in an infinite baffle, with edges constrained by either rotational or translational springs. Asymptotic solutions are derived for frequencies well below the critical frequency (KL≪1). In the range of KL<1, the asymptotic solutions are validated by numerical evaluation. For comparison, the low‐frequency solutions are normalized by dividing them by the radiation efficiency of a beam with hinged supports. Numerical results show that a beam with edges constrained by soft springs may generate higher radiation efficiency than one with edges constrained by stiff springs. For a beam with edges constrained by translational springs, the maximum value of normalized efficiency ratio asymptotically approaches 2 as the mode number tends to infinity. For a beam with edges constrained by rotational springs, the radiation may be higher than that of a clamped beam. This phenomenon exists only for low‐order modes.