Transverse vibrations of a clamped elliptical plate carrying a concentrated mass at an arbitrary position

Free vibrations of clamped, thin elliptical plates carrying a concentrated mass at an arbitrary position are studied in order to analyze the mass effect on the natural frequencies and mode shapes of the plate. A variational approach, the well-known Ritz method, is used, where the displacement amplitude is approximated by polynomial expressions in the Cartesian coordinates. The present proposal exhibits excellent agreement with particular cases of the problem available in the literature and also with an independent solution obtained by means of the finite element method. Some new results are presented for the natural frequencies and modes of clamped elliptical plates with a concentrated mass.