Defining the optimal number of actuators for active device noise reduction applications

It is possible to improve sound insulation of devices and machinery from the environment by appropriately controlling vibrations of their casings. When implementing this approach, there is a need to select efficient locations of actuators on each of the casing walls. A common solution is to employ an optimization algorithm to find favourable arrangement according to a given objective. One of the essential parameters of this process is a number of actuators to be optimized, but most often it is assumed a priori, without any proper considerations. The aim of this paper is to give an insight into the problem of defining the number of actuators for active noise reduction implementations. The optimal value depends on the particular application, its mechanical limitations, costs, considered frequency band to be controlled, etc. However, a general approach for analysis and decision making can be formulated. As an exemplary structure, a light-weight device casing is considered. The relationships between the number of actuators, the considered frequency band, and obtained values of the optimization index are given.