Thermoacoustic approach for the cloaking of a vibrating surface

Abstract

A vibrating surface in a quiescent fluid transmits pressure fluctuations, which propagate into far-field sound. The vibroacoustic mechanism involved, coupling vibration and sound, is common in a large number of applications. Yet, there is a growing interest in developing means for achieving “acoustic cloaking” of an animated boundary. We suggest the heating of a surface, generating thermoacoustic perturbations, as a mechanism for monitoring vibroacoustic sound. Considering a setup of an infinite planar wall interacting with a semi-infinite expanse of an ideal gas, we investigate the system response to arbitrary (small-amplitude) vibro-thermal excitation of the confining wall. Analysis is based on continuum Navier-Stokes-Fourier and kinetic Boltzmann equations, and supported by stochastic direct simulation Monte Carlo calculations. Starting with a case of a sinusoidally excited boundary, a closed-form solution is derived in both continuum and collision-free limits. The results, found valid at a wide range ...