Active structural acoustic control of turbulent boundary layer induced energy transmission into a double-wall backed enclosure system

Abstract An active structural-acoustic control (ASAC) algorithm based on Stochastic Linear Quadratic Regulator (LQR) is developed and implemented numerically in the present work for attenuating turbulent boundary layer (TBL) induced energy transmission through a double-wall panel into an acoustic enclosure. Goody's single point wall-pressure spectrum and combined Corcos-Mellen's spatial correlation function are used to generate the TBL cross power spectra on the exterior panel. Mindlin's first order shear deformation theory is used to model the deformation behavior of the structural panels, classical wave equation is used to model the two acoustic enclosures and finally Green's Theorem is used to couple the structure-acoustic model. Necessary governing equations for surface mounted collocated PVDF sensors and IDE-PFC actuators connected using a stochastic LQR feedback algorithm are appended with the structural model. The developed governing equations are then computed using finite element (FE) codes developed in-house to predict the acoustic power level inside the enclosure, with and without control. The structural model developed is generic in nature capable to incorporate orthotropic laminates, functionally graded materials, frequency-dependent structural damping, and variable stiffener orientation, if any, in predicting the energy transmission into a double-wall backed enclosure. Hence, the developed numerical model enables the designers for precise quantification of transmitted sound with and without ASAC and greater flexibility in terms of the number of panel leaves, boundary, and stiffening condition of the aircraft panel-cavity-panel-enclosure system, made of isotropic or orthotropic laminates.