Boundary Element Method for Fast Solution of Acoustic Problems: Active and Passive Noise Control

Abstract

This thesis presents boundary element formulations for three-dimensional acoustic problems of active (ANC) and passive (PNC) noise control. A new boundary element strategy, referred to as RABEM (Rapid Acoustic Boundary Element Method), has been formulated and implemented for acoustic problems. The assembly time for both the system matrix and the right hand side vector is accelerated using a Hierarchical-matrix approach based on the Adaptive Cross Approximation (ACA). Two different H-matrix-GMRES solvers (one without preconditioners and one with a block diagonal preconditioner) are developed and tested for low and high frequency problems including noise emanated by aircraft approaching an airport. A new formulation for solving the ANC based on attenuating the unwanted sound in a control volume (CV) rather than cancelling it at a single point is presented. The noise attenuation is obtained by minimising the square modules of two acoustic quantities - the potential and one component of the particle velocity - within the CV. The two formulations presented include a single and a double secondary source, respectively. Several examples are presented to demonstrate the e fficiency of the proposed technique. A new approach, based on sensitivity analysis, for determining the optimum locations of the CV and the optimum location/orientation of the secondary source is presented. The optimisation procedure is based upon a first order method and minimises a suitable cost function by using its gradient. The procedure to calculate the cost function gradients is explained in detail. Finally, a PNC strategy applied to the interior of an aircraft cabin is investigated. A lower noise level is achieved through the introduction of a new textile with a higher noise absorbing coe cient than a conventional textile, especially at low frequencies. The so-called "bubble concept", which consists of adding cap insertions at the sides of the passenger head, is also investigated.