Acoustic impedance sensitivity analysis and design optimization using the wave based method

In a weakly coupled structural-acoustic problem, the boundary conditions may be composed by two conditions. One is a velocity boundary condition, which can be obtained from a dynamic structural analysis and the other is an acoustic impedance boundary condition. The acoustic impedance boundary condition is used for modeling acoustic absorbent behavior at boundaries proportional to the velocity difference between structural and fluid velocity. This paper introduces an acoustic impedance design sensitivity analysis and optimization for designing an absorbent material layout on a vibrating panel using the wave based method. The velocity boundary condition of a simple-shaped structure is obtained from a dynamic analysis with the finite element method (FEM) and the acoustic response is computed with the wave based method (WBM). The thickness of the absorbing material on each structural element is considered as a design variable. The sensitivity of acoustic pressure with respect to the impedance is analytically derived using the wave based system equations. Then the final sensitivity is derived through the chain rule by considering the curve fitting equation for describing the impedance variance with respect to the thickness of the absorbing material. The design sensitivity results are used in a sizing design optimization of the absorbing panel layout of the vibrating plate with good results.