Numerical study of inverse extreme problems of active sound control in two-dimensional multimode waveguides

Linear and nonlinear problems of active sound control in waveguides have been much investigated in the last years. Computing experiments for inverse extreme problems were carried out for waveguides of small or average depth, where the number of normal modes is up to 5060. At the same time in practice it is necessary to deal with deep waveguides, where the number of propagating modes can be from several hundred to several thousand. Nonlinear approach is preferable for the problem of active sound control. However nonlinear problem in multimode waveguide requires a great deal of computation. In the present work the inverse linear problem of active sound control in two-dimentional multimode waveguide is considered. The problem consists in finding the complex intensities of the compensating antenna elements from the condition of minimal power of the total acoustic field in the far zone of the waveguide. The numerical algorithm based on the regularized quadratic algorithm for minimization with respect to complex intensities of desired sources is applied to the decision of linear problems in waveguide. Sound control problems employ compensating antenna arrays of two types: linear (vertical, inclined and horizontal) and curvilinear. Results of computing experiments are discussed. It is shown that full suppression of the power of the primary source can be achieved by solving the linear problem for the specified configurations of the compensating antenna.