Josip Loncaric
Institute for Computer Applications in Science and Engineering
NASA Langley Research Center
Active Shielding and Control of Environmental Noise
We present a mathematical framework for the active control of time-harmonic acoustic disturbances. Our approach provides for the exact volumetric cancellation of unwanted noise in a given predetermined region of space while leaving the rest of the total acoustic field unaffected. For eliminating the unwanted component, one needs to know neither the actual noise sources nor properties of the supporting medium. The controls are built based solely on the measurements performed on the perimeter of the region to be shielded; moreover, the controls themselves are concentrated also only near this perimeter. The measured quantities can refer to the total acoustic field, and the methodology automatically distinguishes between its adverse and friendly components. We construct a closed form general solution to the aforementioned noise control problem. The apparatus used for deriving this general solution is closely connected to the concepts of generalized potentials and boundaray projects of Calderon's type. For a given total wave field, the application of the Calderon's projection allows us to decompose it into the incoming and outgoing components with respect to a particular domain of interest, which may have arbitrary shape. Then, the controls are designed so that to 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. To demonstrate that the new noise control technique is appropriate, we analyze a simple two-dimensional model example that allows full analytical consideration.