Acoustic modes in duct with parallel shear flow and vibrating walls

Abstract

Numerical and theoretical investigation of the influence of subsonic shear flow on the axisymmetric modes in a circular duct with vibrating walls are reported. The considered geometry is an elastic duct filled with fluid in shear motion, and surrounded by vacuum. Then, we solve the coupled problem in order to find the eigenmodes and the dispersion diagrams. In this first study, the problem is considered under axisymmetric assumption in order to simplify calculations in spite of the fact that, in real problems, the first vibration and acoustic modes are not axisymmetric. In the solid, i.e. the wall, exact axisymmetric elasticity equations are used to yield analytical expressions. In the fluid, the classical Pridmore-Brown equation governing transverse duct modes with shear flow is used. The boundary condition at the interface fluid/solid, responsible for the coupling, is chosen to be continuity of stress and normal displacement. In the solid, an approximate theory, called thin shell or Donnel theory, is also tried. Results show the influence of shear flow on dispersion diagram of acoustic modes in the duct. List of symbols