It is known that by linearly filtering the outputs of a dense set of accelerometers, sensing the motion of the boundary of an acoustically radiating object, a relatively small set of quantities is obtained, from which the far field (FF) can be identified. Key properties of the spatial filters are: a) the filters are purely combinatorial (i.e. non-dispersive) and, b) the filtering functions are algorithmically identified from the geometry of the radiator boundary and the highest frequency of the disturbance exciting the system. Abating the acoustic radiation does not require to stop the boundary vibration motion, being sufficient instead to actively modify the boundary normal velocity with the objective of nulling, or practically, substantially reducing the outputs of the radiation filters. The shell here considered has rotational symmetry and the disturbance, modeled as a ring force excited by either a single tone or by a broadband process, is also assumed to be axisymmetric. The radiation filter outputs constitute the signals fed back to the multivariate controller that drives a set of uniform ring force actuators. The number of actuators is the minimum possible (or close to it) for the given boundary geometry and the highest frequency of the disturbance. The controller includes a compensating network subtracting electronically the effect of the actuators from the outputs of the sensors. With this scheme the system becomes essentially feedforward, and therefore is inherently stable. The controller and the compensating network are causally implemented via finite impulse response (FIR) matrix filters. The identification of the FIR matrix coefficients of the controller is obtained by minimizing the average residual power which is radiated when the controller is acting. A highly efficient optimization algorithm is established. Several numerical examples for different disturbance configurations show the effectiveness of the approach here presented for radiating noise cancellation. The simulation was performed by using the well known NASHUA computer model for a shell in water.

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