Sound radiation from vibrating bodies in motion

Abstract

This paper presents an integral formulation for prediction of sound radiation from a vibrating body in motion. The formulation consists of volume and surface integrals. The volume integral represents the effect of the turbulent stress field induced by the motion of the vibrating body, while the surface integral represents the combined effects of the gradient of the turbulent stress field and the unsteady force exerted on the fluid by the surface, as well as the surface displacement effect. It is shown explicitly that source cancellations take place within the surface integral when turbulence effects are taken into account. Moreover, dimensional analysis demonstrates that the volume integral is negligible compared with the surface integral when the source is in rectilinear motion at low Mach numbers. If turbulence effects are neglected at the outset of the derivation, then there is no interaction between the turbulent stress field and the vibrating surface in motion and the resulting integral formulation is different. The fundamental difference is whether or not the effect of the gradient of the turbulent stress field is included in the integral formulation. Numerical examples of sound radiation from the dilating and transversely oscillating spheres moving rectilinearly in space at constant subsonic speeds are demonstrated.