Numerical research on the focusing characteristics of steady state sound field in finite space by combining finite element and phase conjugation methods

The research on sound source identification in an infinite free sound field has been relatively in-depth, but there is relatively little research on sound source identification and localization in limited spaces, especially those with sound absorption and insulation materials. The identification and reconstruction of the acoustical steady propagation field radiated from a single frequency finite space are studied numerically using discrete elements based on the phase conjugation method by FEM. Two different kinds of array forms of phase conjugation arrays are studied for sound source localization such as the planar array and the linear array. In addition, the influences of the existence of sound-absorbing material on the wall on the focusing properties are also discussed. The numerical results show that: The phase conjugation method can completely achieve the identification and location of the acoustical source finite space no matter using the planar array form or the linear array according to FEM. The linear array form can obtain the subwavelength focusing with fewer elements. The optimal distance between the array and the sound source is 0.5 [Formula: see text] and 2 [Formula: see text] to get the best reconstruction results. The smaller the absorption coefficient, the more to meet the multi-path phase compensation principle, the better reconstruction of the sound source.