Numerical simulation of passive–active cells with microperforated plates or porous veils

The main goal of this work consists in the numerical simulation of a multichannel passive–active noise control system based on devices involving a particular kind of cell. Each cell consists of a parallelepipedic box with all their faces rigid, except one of them, where a porous veil or a rigid micro-perforated plate (MPP) is placed. Firstly, the frequency response of a single passive cell is computed, when it is surrounded by an unbounded air domain (an anechoic room) and harmonic excitations are imposed. For the numerical solution of this three-dimensional problem, the original unbounded domain is truncated by using exact perfectly matched layers (PML) and the resulting partial differential equation (PDE) is discretized with a standard finite element method. Secondly, the passive cells are transformed into active by assuming that the opposite face to the passive one may vibrate like a piston in order to reduce noise. The corresponding multichannel active control problem is stated and analyzed in the framework of the optimal control theory. A numerical method is proposed to assess and compare different control configurations.