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

In this paper, the weighted sum of spatial gradients, or WSSG (formerly known as composite velocity) is developed for use in active structural acoustic control (ASAC) on clamped flat rectangular plates. In previous work, WSSG was developed on a simply-supported flat rectangular plate\cite{pseudo}, 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 found to provide improved control compared to volume velocity. Sensitivity analysis has also shown that comparable control, regardless of the sensor location, can be achieved using WSSG as an objective function. Experimental results have demonstrated that this control metric works effectively in practice, with results similar to the simulations. The results show that WSSG can be used as an effective control metric on clamped rectangular plates.