Active control of the acoustic radiation of a vibrating structure using a superposition formulation

In this paper, optimal control theory is applied to the problem of reducing the acoustic power radiated from a complex, three-dimensional, vibrating structure. Using the principle of wave superposition, a vibrating structure's acoustic field can be shown to be approximately equivalent to the sum of the fields due to a finite number of acoustic sources located in the interior of the radiating body. Based on this transformation, the total time-averaged, acoustic power output from the vibrating structure can be expressed in terms of the strengths of the interior point sources. Two methods are then used to optimally reduce the acoustic power output from the vibrating body. The first method consists of placing a secondary source outside the structure and, by optimizing its source strength, minimizing the total, time-averaged acoustic power output of the entire system. The second method assumes that the vibrating structure's normal surface velocity can be altered such that the total power radiated from the vibrating structure is minimized. The optimum surface velocity distribution produced by this method is shown to be dependent on the number and location of the surface nodes defining the geometry of the structure.