Modal characteristics of in-plane vibration of circular plates clamped at the outer edge

The equations of in-plane vibration in thin flat plates are solved for free vibration in circular plates clamped at the outer edge. The mode shapes are represented by trigonometric functions in the circumferential direction and by series summation of Bessel functions in the radial direction. Accuracy of the predictions of natural frequencies and mode shapes is assessed by comparisons with finite-element predictions and with previously reported results. The present solution gives very accurate predictions. The work also highlights the nature of coupling between the different circumferential and radial modes and the response of different vibrational modes at the center of the plate. It is shown that the center point of the plate vibrates only for modes with unity circumferential wave number (number of nodal diameters). Nondimensional frequency parameters are listed and the radial mode shapes of natural vibration are depicted to illustrate the free-vibration behavior in the frequency range of practical interest.