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

Abstract

A new, computational approach provides a methodology for specifying how the acoustic power radiated from a complex, three-dimensional vibrating structure may be controlled. The method uses a superposition principle to transform the surface of a vibrating structure into a discrete distribution of acoustic sources interior to the boundary surface of the structure. The transformation is carried out by requiring that the interior sources produce the same or nearly the same normal velocities as those prescribed on the surface of the vibrating structure. 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 equivalent sources. To control the radiated acoustic power, one or more secondary point sources is then placed on or near the surface of the vibrating structure. By using the total power radiated from the vibrating structure and the secondary sources as an objective function for an optimization operation, the optimal strengths and locations of the secondary sources are found that lead to a maximum reduction in the acoustic power radiated from the vibrating structure. The significance of this approach is that it provides design guidelines for applying active control techniques to complex vibrating structures.