Development of a pseudo-uniform structural quantity for use in active structural acoustic control of simply supported plates: An analytical comparison

Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602, USA.
The Journal of the Acoustical Society of America (Impact Factor: 1.5). 05/2012; 131(5):3833-40. DOI: 10.1121/1.3699264
Source: PubMed


Active structural acoustic control has been an area of research and development for over two decades with an interest in searching for an "optimal" error quantity. Current error quantities typically require the use of either a large number of transducers distributed across the entire structure, or a distributed shaped sensor, such as polyvinylidene difluoride. The purpose of this paper is to investigate a control objective function for flat, simply-supported plates that is based on transverse and angular velocity components combined into a single composite structural velocity quantity, termed V(comp). Although multiple transducers are used, they are concentrated at a single location to eliminate the need for transducers spanning most or all of the structure. When used as the objective function in an active control situation, squared V(comp) attenuates the acoustic radiation over a large range of frequencies. The control of squared V(comp) is compared to other objective functions including squared velocity, volume velocity, and acoustic energy density. The analysis presented indicates that benefits of this objective function include control of radiation from numerous structural modes, control largely independent of sensor location, and need to measure V(comp) at a single location and not distributed measurements across the entire structure.

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    ABSTRACT: The weighted sum of spatial gradients (WSSG) control minimization parameter is developed for use in active structural acoustic control (ASAC) on a clamped flat rectangular plate. The WSSG minimization parameter is measured using four accelerometers grouped closely together on the test structure. In previous work, WSSG was developed on a simply supported flat rectangular plate and showed promise as a control metric. The displacement on the clamped plate has been modeled using an approximate analytical solution assuming shape functions corresponding to clamped-clamped beams. From the analytical formulation, weights, which were found to be the reciprocal of the wave number squared, have been derived to produce a uniform WSSG field across the plate. In active control simulations, this quantity has been shown to provide better global control of acoustic radiation than volume velocity. Analysis is presented which shows that comparable control, regardless of the sensor location, can be achieved using WSSG. Experimental results are presented which demonstrate that WSSG works effectively in practice, with results similar to the simulations. The results show that minimization of WSSG can be used as an effective control objective on clamped rectangular plates to achieve attenuation of acoustic radiation.
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