The acoustic-vortical wave equation is derived describing the propagation of sound in (i) a unidirectional shear flow with a linear velocity profile upon which is superimposed (ii) a uniform cross flow; together with an impedance wall boundary condition representing the effect of a locally reacting acoustic liner in the presence of bias and shear flow. This leads to a third-order differential equation in the presence of cross flow, and in its absence simplifies to the Pridmore-Brown equation (second-order); also the singularity of the Pridmore-Brown equation for zero Doppler-shifted frequency is removed by the cross flow. Because the third-order wave equation has no singularities (except at the sonic condition), its general solution is a linear combination of three linearly independent MacLaurin series in powers of the distance from the wall. The acoustic field in the boundary layer is matched through the pressure and horizontal and vertical velocity components to the acoustic field in a uniform free stream consisting of incident and reflected waves. The scattering coefficients are plotted for several values of the five parameters of the problem, namely the angle of incidence, free stream and cross-flow Mach numbers, specific wall impedance and Helmholtz number using the boundary layer thickness.

In this article, a dynamical model of the vibrations and acoustic radiation of a circular clamped plate excited by a voice coil and two annular piezoelectric patches is derived. This model is used to perform an optimization of the geometries with the objective to minimize the vibration of the plate along its second and third modes, so that the plate's radiation is equilibrated between its first and fourth eigenfrequencies. Experiments are then performed and show a good agreement with the model. Radiation of the designed system presents improvements when compared to a system when only a voice coil is used.

Inside micro cavities, specific dissipative mechanisms influencing acoustic wave propagation occur due to viscous and heat-conducting nature of the fluid. This work focuses on a possible extension of the so called “Low Reduced Frequency” model for acoustic wave propagation in a thermoviscous fluid. This extension is built starting from geometrical and physical assumptions (boundary layer theory, straight waveguides) and consists in the incorporation of a stationary laminar and subsonic mean flow. The resulting equivalent fluid model provides a new damping coefficient which depends on the Mach number, the shear and thermal wave numbers and the cross-sectional profiles of axial velocity and temperature. The main application area is the study of acoustic attenuation within automotive catalytic converters or also thin fluid layers like cooling systems in small electronic devices. This formulation has been implemented for a simple one dimensional thin tube. Convergence to the original model in the absence of mean flow has been reached and comparisons with variational solutions given by Peat show good agreements.