Sound radiation of a line source moving above an absorbing plane with a frequency-dependent admittance

Abstract

This paper is concerned with the derivation of an analytical solution for the acoustic pressure field generated by a line source moving at a constant speed and height above an absorbing plane and summarizes the results obtained in a recent article [Dragna and Blanc-Benon, J. Sound Vib. 349, 259-275, 2015]. As an extension of previous studies, the frequency dependence of the admittance is accounted for. First, a Lorentz transformation is used to obtain an equivalent stationary problem. A special attention is paid to the translation of the admittance boundary condition in the Lorentz space. An analytical solution is obtained as a Fourier transform. Excitation of surface waves is investigated depending on the Mach number. In the far field, an asymptotic expression is sought using the modified saddle point method. The solution is expressed under the form of a Weyl-Van der Pol formula, in which the admittance is evaluated at the Doppler frequency. Comparison of the pressure field obtained with the analytical s...