Impedance of Pistons on a Two–Layer Medium with Inviscid Homogeneous Flow

An integral transform technique is used to develop a general solution for the impedance of two-dimensional pistons acting on a two-layer medium. The medium consists of a semi-infinite fluid with homogeneous subsonic flow above a viscoelastic layer in a rigid infinite baffle. The stresses acting on the planar baffle and piston, as a result of piston motion, are determined using linear elasticity theory and the pressures in the fluid are determined using the convected wave equation. The case of a rigid piston of length L is considered. The derived expression for impedance is evaluated by direct numerical integration of the wavenumber transformed solution. Numerical results over a range of flow speeds and layer thicknesses are compared with classical impedance functions. At low frequencies (k₀L < 2), the impedances vary significantly from the classical piston impedance functions due to the shear properties of the viscoelastic medium and flow Mach number. These deviations from the classical piston impedance occur for both resistance and reactance. It was also found that with increasing Mach number, the reactive component of impedance transitions from negative (spring-like) to positive (mass-like) in the low frequency range. At higher frequencies, the influence of Mach number is secondary to layer thickness.