Active Structural Acoustic Control of Clamped Flat Plates Using a Weighted Sum of Spatial Gradients

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.