Active Control of Sound for Composite Regions

Abstract

We present a methodology for the active control of time-harmonic wave fields, e.g., acoustic disturbances, in composite regions. This methodology extends our previous approach developed for the case of arcwise connected regions. The overall objective is to eliminate the effect of all outside field sources on a given domain of interest, i.e., to shield this domain. In this context, active shielding means introducing additional field sources, called active controls, that generate the annihilating signal and cancel out the unwanted component of the field. As such, the problem of active shielding can be interpreted as a special inverse source problem for the governing differential equation or system. For a composite domain, not only do the controls prevent interference from all exterior sources, but they can also enforce a predetermined communication pattern between the individual subdomains (as many as desired). In other words, they either allow the subdomains to communicate freely with one another or otherwise have them shielded from their peers. In the paper, we obtain a general solution for the composite active shielding problem and show that it reduces to solving a collection of auxiliary problems for arcwise connected domains. The general solution is constructed in two stages. Namely, if a particular subdomain is not allowed to hear another subdomain, then the supplementary controls are employed first. They communicate the required data prior to building the final set of controls. The general solution can be obtained with only the knowledge of the acoustic signals propagating through the boundaries of the subdomains. No knowledge of the field sources is required, nor is any knowledge of the properties of the medium needed.

Broadband exterior cloaking

“…Here we also use active cloaking devices to achieve broadband exterior cloaking. The principle is similar to that of active sound control (see e.g [29,30]), with the fundamental novelty that we do not need a closed surface to suppress the incident field in a region while not radiating significantly. Another type of broadband exterior cloaking, using waveguides to guide waves around a "quiet zone", has recently been introduced and confirmed experimentally [31].…”

On the active manipulation of fields and applications: I. The quasistatic case

“…Regarding the active designs for the manipulation of fields we mention that this idea appeared first in the context of low-frequency acoustics where various techniques for the active control of low-frequency sound (or active noise cancellation) were proposed in the literature, and we could mention here the pioneer works of Leug [44] (feedforward control of sound) and Olson & May [45] (feedback control of sound). For a more detailed account of very interesting recent developments of the idea in the context of acoustics we mention the reviews [40], [42], [43], [38] [39] and the references therein.…”

The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes

“…This keeps the overall problem predominantly smooth. The method of difference potentials has previously been applied to multiple subregions in the context of active noise control, see [34]. Its application to solving the reflection/transmission problems for multiple scattering will be similar.…”