Time-domain techniques in the singularity expansion method

New methods of determining the natural frequencies and natural modes of a structure as characterized in the singularity expansion method (SEM) are presented. The method is based on the time-domain scattering equation which can be east in the form of a matrix difference equation. The homogeneous solution of the difference equation is a series of exponentials as found in the SEM representation. The natural frequency and mode solutions may be obtained either from the determinant of a matrix sum, which is similar to the current frequency-domain search method, or by an eigenvalue approach as in systems theory. The latter has shown promise for efficient SEM computations. An example of each approach is presented.