Conversion of an acoustically hard body into an acoustically transparent one in an initial-value problem

An algorithm for the real-time suppression of the fields scattered and radiated by a vibrating smooth closed surface of an arbitrarily shaped elastic body is developed and examined analytically. The surface of the protected body is assumed to be hard relative to the surrounding compressible medium. The active quenching system under consideration is composed of (a) a subsystem that rapidly forms a given distribution of normal particle velocities on the protected surface and (b) a subsystem that detects the incident waves with the use of a one-layer network of acoustic microphones surrounding the protected surface. It is shown that an acoustically hard body equipped with the proposed active system can be transparent for a certain class of incident wave fields. The statement of an initial-value problem allows a considerable decrease in the number of microphones in the active system for a chosen class of incident waves and, as a consequence, reduces the noise in the control system. The control algorithm includes logical and nonlinear operations, which rules out the conventional description of the quenching system in terms of a combination of linear electric circuits with constant parameters.