Free Vibration Analysis of Multiply Connected Plates Using the Method of Fundamental Solutions

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of multiply connected plates is proposed. The coefficients of influence matrices are easily determined when the fundamental solution is known. True and spurious eigensolutions appear at the same time. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary where the fictitious sources are distributed. To verify this finding, mathematical analysis for the appearance of spurious eigenequations using degenerate kernels and circulants is done by demonstrating an annular plate with a discrete model. In order to obtain the true eigensolution, the Burton & Miller method is utilized to filter out the spurious eigensolutions. One example is demonstrated analytically and numerically to see the validity of the present method.