Active structural acoustic control of transmitted sound through a double panel partition by weighted sum of spatial gradients

Abstract

Active control of harmonic sound transmission through an acoustically baffled, rectangular, simply supported double panel partition has been analytically studied. Velocity potential method is used for the vibro-acoustic modeling unlike the commonly used cavity mode method. It is very well-known that at high frequencies uncontrolled double panel partition mostly radiates sound due to the dipole-type motion of the radiating panel, which the volume velocity method can't be able to detect, therefore, weighted sum of spatial gradients is used to control these modes and achieves sound attenuation in a broad frequency band. A piezoceramic actuator (lead zirconate titanate) is attached on one side of the panel surface, and the optimal magnitude and phase of the voltage supplied to the lead zirconate titanate for minimizing the weighted sum of spatial gradients and volume velocity at the error sensor locations are calculated using a simple-gradient based algorithm. Numerical results of sound power transmission ratio and averaged quadratic velocity of panels indicate that lead zirconate titanate should be placed on the incident panel and minimization of the control quantities should be done on the radiating panel to achieve better sound attenuation. The acoustic radiation mode analysis shows that the weighted sum of spatial gradients is able to control multiple acoustic radiation modes and, thereby, accomplishes better reduction of sound power transmission compared to volume velocity.