Identification of in-plane force in outer-clamped annular plates by using modal parameters

Abstract

The vibration and stability of center-clamped annular plates are much of interest to designers in the past. Recently the problems associated with outer-clamped thin annular plates have attracted the attention of researchers in the course of investigating the dynamic characteristics of structures such as a wafer cutting machine. Unlike the center-clamped disks, centrifugal force due to rotation tends to make the outer-clamped disks unstable. In addition, thin disks may experience large deflection due to relatively small bending stiffness. To overcome such problems, uniform in-plane tension, which can stabilize or strengthen thin annular plates during rotation, is normally required. However, in the process of imposing uniform in-plane tension on a thin annular plate, undesired nonuniform in-plane force is likely to be accompanied in practice. Nonuniform in-plane force may make the plate unstable and induce the inaccuracies in cutting process. Thus the check of uniformity in in-plane force is required for the good installation of thin annular plates before initial operation and for the estimation of looseness after a long period of operation. Vibration analysis for outer-clamped annular plates under arbitrary in-plane force is formulated to investigate the influence of in-plane force on transverse vibration of the plates. The arbitrary in-plane force along the outer edge of an annular plate is expressed as Fourier series, and, the perturbation and Galerkin``s methods are employed to obtain modal parameters and responses. In particular, it is shown that the perturbation method not only reduces the computational effort but allows clear physical insight into the effect of uniform and nonuniform in-plane force on the modal parameters of an annular plate. Through numerical examples, both methods are compared, and the effectiveness of the perturbation method is discussed. During numerical simulations, particular phenomenon, so-called curve veering, was found in ei...