Active control of sound radiation from rib stiffened plate using the weighted sum of spatial gradients as the cost function

The active structural acoustic control of the rib stiffened plate highly improves the sound insulation performance in the low frequency range. This promotes the engineering relevance of the active control technic since the ribbed plate is a classical structural element widely applied in practical engineering. One of the key problems encountered when implementing such system is error sensing strategy. The traditional sensing strategy, such as sensing the radiation modes using distributed piezoelectric sensors, is difficult to implement due to the block of the ribs in the ribbed plate case. The pseudo-uniform structure quantity proposed recently, i.e., the weighted sum of spatial gradients (WSSG) is highly correlated with the radiated sound power of the radiating plate, which can be easily obtained by only sensing vibrating information of single point and is also less sensitive with the sensor location. Hence, WSSG is adopted in this paper to establish the error sensing strategy for the active structural acoustic control of the ribbed plate. The weights in WSSG directly impact the control performance, and should be chosen appropriately for the plates with different parameters. The parameter-based weights, which can be obtained conveniently according to the ratio of the flexural rigidity to the mass per unit area of the plate, are more preferable in real implementation for broadband frequency control. As for the ribbed plate case, due to the coupling effects of the ribs, the flexural rigidity of the ribbed plate is not uniform and varies for different kinds of rib arrangements. This is another parameter that will also affect the parameter-based weights. This paper compares the regions of the near-optimal weights for different locations of the ribs and summarizes the influence of this parameter on choosing the optimal weights. Combining the special resonant characteristics of the ribbed plate induced by the coupling effects of the ribs, the rule of the influence by the ribs are interpreted particularly. Then experiments are carried out to validate the conclusions. Results obtained can help for choosing the optimal weights of WSSG for the ribbed plate case.