Complex retraction equivalent source method for solving external acoustic problems

In order to overcome the non-unique solution problem of the conventional equivalent source method at the corresponding eigenfrequency, the basic guidelines of adding virtual damping into the equivalent source method is proposed according to the damping characteristics of the imaginary part of the coordinates of the equivalent source point. The complex source point constructed by complex retraction is used to add virtual damping to the equivalent source system, and a complex retractive equivalent source method with unique solution in full wavenumber domain is proposed. The mechanism of the complex retraction equivalent source method in overcoming the non-unique solution problem is described in accordance with the zero-point characteristic of the characteristic indicator function, involving the theory, modeling method and selection of damping parameter. The simulation and analysis of typical acoustic radiation and acoustic scattering problems indicate that the present method can obtain the unique solution in the entire frequency domain simply and effectively for arbitrarily shaped acoustic source. Its computational accuracy and efficiency are equivalent to the conventional equivalent source method, which solves the problem of poor adaptability of the complex radius vector method.