Transverse Vibrations of a Free Circular Plate Carrying Concentrated Mass

The plate under consideration carries a concentrated mass at its center, which is struck impulsively in a direction perpendicular to the undisturbed plate face. Only circularly symmetric vibrations are considered. The solution is carried out by the use of the Laplace transform method, treating the concentrated mass as a plate-density impulse. The first four natural frequencies are displayed as functions of mass ratio, and the first mode shape is displayed for three mass ratios. The natural frequencies, particularly the higher, are shown to be very sensitive to changes in mass ratio at small values of the concentrated mass.