Free Vibration and Stability Analysis of a Spinning Annular Circular Plate

In this paper, Rayleigh Ritz method has been applied to investigate free vibration behavior and stability of a rotating annular plate with an attached point mass. The classical thin plate theory assumptions have been used to calculate the strain energy and kinetic energy. The coordinate functions are combinations of polynomials which satisfy boundary conditions at the outer boundary. The frequency speed diagram is obtained for (0, 0) vibration mode. The plate is assumed to be spinning and the initial stress fields in the plate are derived assuming the plane stress condition. The problem is of practical importance in many engineering applications, e. g., silicon wafers used for LSI chips are produced by slicing the cylindrical crystal ingot with a disk like tool which is free along the inside hole and clamped at the outer radius. It has been shown that mode (0, 0) correspond to two modes at frequencies f1 and f2. Mode f2 experiences a flutter type of instability after the critical speeds. The critical speeds are independent of attached point masses but depend upon the inner radius and bending rigidity of the plate. With increase in bending rigidity, critical speeds increase. For a plate i.e., for D = 0.18e4, f2 mode meets f1 mode and makes the f1 mode unstable and the corresponding rotational speed of the plate is dependent on inner radius. With increase in inner radius, this rotational speed decreases.