Vibration analysis of rotating cantilever plates

Abstract

A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components-one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.

Dynamics of Rectangular Plates Undergoing Prescribed Overall Motion

“…Even though a non-linear formulation for plates undergoing overall motion was suggested in reference [11], numerical results were not given in the work. Some numerical results for the vibration analysis of rotating plates are available in references [12,13].…”

Flapwise bending vibration of rotating plates

“…The results indicates that only 0.7% more convergence could be obtained by increasing the number of modes from 35 (5 × 7) to 63 (7 × 9). The results obtained by using the present modelling method are compared to those obtained by using the Southwell's method (see Reference [5]) to show the reliability of the modelling method presented in this paper. The parameters used to obtain the results are shown in Tables II and III.…”

“…In spite of the need, only a few research papers on the dynamics of rotating plates could be found in a literature survey conducted by the present authors. Dokainish and Rawtani [5] used a ÿnite-element technique to determine the modal characteristics of rotating cantilever plates. A similar approach was taken by Ramamurti and Kielb [6] to determine the modal characteristics of twisted rotating plates.…”

Formulation of numerical procedures for dynamic analysis of spinning structures

“…and the complete expression for the matrix is simply obtained as k = k(f2,) + k(Q,) + k(Q,), which when appropriately combined, yields the global centrifugal force matrix K' for the entire structure, as defined in equation (2).…”