Exact solutions of in-plane natural vibration of a circular plate with outer edge restrained elastically

We solve exactly the equations of in-plane natural vibration for a circular plate whose outer edge is restrained elastically. The mode shapes are represented by trigonometric functions with a number of nodal diameters in the circumferential direction and mode functions in the radial direction. We present the exact frequency equations and mode functions and tabulate the frequency parameters satisfying the frequency equations. The corresponding mode functions and two-dimensional mode shapes are illustrated when both radial and tangential stiffness are zero (free edge), infinity (clamped edge), or medium. Comparisons with previous reported results confirm the accuracy of the present work.

► Mode shapes are represented by trigonometric functions in circumferential direction and mode functions in radial direction. ► Exact frequency equations and mode functions are presented. ► Frequency parameters satisfying frequency equations are tabulated. ► Corresponding mode functions and two-dimensional mode shapes are illustrated.