On the extended Kirchhoff integral formulations for moving surfaces.

Abstract

An overview of extended Kirchhoff integral formulations for vibrating surfaces in motion is given. In particular, it is shown that one can derive different extended Kirchhoff integral formulations depending upon whether the effect of turbulence induced by the source convectional motion is neglected at the outset or at the end. One major difference is the presence of extra terms in the resultant integral formulations when the turbulence effect is neglected at the outset. These extra terms represent the effects of the mass flux in the normal direction acting on fluid due to surface oscillations and the time rate of change of mass across the surface area in the normal direction due to source convection. Such extra terms do not appear in the integral formulation when the turbulence effect is accounted for in the derivation, because they are cancelled completely by those induced by the turbulent stress field. The sound fields thus predicted by these two different integral formulations differ from each other. The differences between these two predictions are negligible at low Mach numbers, but increase with the Mach number and the noncompactness of the source. Also discussed are the uniqueness of solutions given by the extended Kirchhoff integral formulations. [Work supported in part by ONR, NSF, and IMR of Wayne State Univ.]