Acoustic impedance sensitivity approach for defining absorbing material layout using the wave based method

Abstract This study used the wave based method (WBM) to investigate the optimum layout of an absorbing material on a vibrating surface. The structural dynamic behavior was examined using the finite element model, and the acoustic response was computed using the WBM. The thickness of the absorbing material on each structural element was considered as the design variable. The sensitivity of the acoustic response to the acoustic impedance was derived using wave based system matrices, and a polynomial function was used to describe the impedance variation with respect to the thickness of the absorbing material. Thereafter, the final design sensitivity of a vibro-acoustic model was derived with respect to the thickness of the damping material using the chain rule. The design sensitivity results were found to be in good agreement with the results of the central finite difference methods. The design optimization of the absorbing material layout was applied to a vibrating surface using the design sensitivity results under various excitations, and the results of the optimization showed a layout similar to the active intensity plot of the vibrating surface. The proposed method can easily be applied to reduce the noise produced by a vibrating structure.