Active Shielding and Control of Environmental Noise

In the framework of the research project supported by NASA under grant # NAG-1-01064, we have studied the mathematical aspects of the problem of active control of sound, i.e., time-harmonic acoustic disturbances. The foundations of the methodology are described in our paper [1]. Unlike. many other existing techniques, the approach of [1] provides for the exact volumetric cancellation of the unwanted noise on a given predetermined region airspace, while leaving unaltered those components of the total acoustic field that are deemed as friendly. The key finding of the work is that for eliminating the unwanted component of the acoustic field in a given area, one needs to know relatively little; in particular, neither the locations nor structure nor strength of the exterior noise sources need to be known. Likewise, there is no need to know the volumetric properties of the supporting medium across which the acoustic signals propagate, except, maybe, in a narrow area of space near the perimeter of the protected region. The controls are built based solely on the measurements performed on the perimeter of the domain to be shielded; moreover, the controls themselves (i.e., additional sources) are concentrated also only on or near this perimeter. Perhaps as important, the measured quantities can refer to the total acoustic field rather than to its unwanted component only, and the methodology can automatically distinguish between the two. In [1], we have constructed the general solution for controls. The apparatus used for deriving this general solution is closely connected to the concepts of generalized potentials and boundary projections of Calderon's type. For a given total wave field, the application of a Calderon's projection allows one to definitively tell between its incoming and outgoing components with respect to a particular domain of interest, which may have arbitrary shape. Then, the controls are designed so that they suppress the incoming component for the domain to be shielded or alternatively, the outgoing component for the domain, which is complementary to the one to be shielded.