Mathematical analysis and numerical study of true and spurious eigenequations for free vibration of plates using real-part BEM

In this paper, an imaginary-part BEM for solving the eigenfrequencies of plates is proposed for avoiding singularity and saving half effort in computation instead of using the complex-valued BEM. By employing the imaginary-part fundamental solution, the spurious eigenequations in conjunction with the true eigenequation are obtained for free vibration of plate. To verify this finding, the circulant is adopted to analytically derive the true and spurious eigenequations in the discrete system of a circular plate. In order to obtain the eigenvalues and boundary modes at the same time, the singular value decomposition (SVD) technique is utilized. The analytical solutions are derived in the discrete system. Three cases, clamped, simply-supported and free circular plates, are demonstrated analytically and numerically to see the validity of the present method. SVD updating technique is adopted to suppress the ocurrence of the spurious eigenvalues, and a clamped plate is demonstrated analytically for the discrete system in this paper