A generalized finite sine transform method (FSTM) is presented in this paper and applied to the eigenfrequency computation of a rectangular plate with arbitrarily distributed concentrated masses and translational springs. Compared with the analytical-and-numerical combined method (ANCM), FSTM keeps the same number of mode shapes in the system eigenfrequencies computation in order to have the convergence. However, unlike ANCM or the finite element method (FEM), whose eigenfrequency computation depends on the number of mode or element. The eigenfrequency computation by FSTM is mainly dependent on the total number of concentrated masses and springs. Therefore, the FSTM computation on the system eigenfrequencies is much faster when the total number of concentrated masses and springs is small.
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