Analysis of periodic acoustic problems with double-sided impedance condition

The modeling of unequal impedance on either side of a vibrating structure is important in many engineering applications. Although the boundary element method is well suited for the analysis of periodic acoustic problems, the modeling of the double-sided impedance condition is not possible in the conventional boundary-element method. In particular, the indirect boundary-element method allows the simultaneous modeling of acoustic domains separated by thin vibrating structures. Thus a facility to model the double-sided impedance condition is very useful in the solution of realistic engineering problems using the indirect boundary-element method. The indirect boundary-element method models the jump of the acoustic pressure and the acoustic velocity between the two sides of the vibrating surface. The impedance relationship that relates the acoustic pressure to the velocity is not reducible to a single relationship between the jump of pressure and velocity. Since the relationship is expressed by two equations, the solution of the equations requires the generation of two sets of integral equations at the impedance surface. The application of this newly developed formulation for the solution of the double-sided impedance condition will be demonstrated by solving a number of example problems. An additional feature of this development is that this formulation can be used to eliminate the irregular frequencies that are associated with the solution of periodic exterior acoustic problems using the boundary element method. The application of this formulation for the elimination of irregular frequencies will also be demonstrated through example problems. [See NOISE-CON Proceedings for full paper.]