Asymmetric compressive stability of rotating annular plates

In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotatingwith a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium quations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium riterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.

Vibration and Buckling Analysis of a Rotating Annular Plate Subjected to a Compressive Centrifugal Body Force

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

Axisymmetric Vibration of Rotating Annular Plate with Variable Thickness Subjected to Tensile Centrifugal Body Force

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

Effects of Shear Deformation and Rotary Inertia on the Free Vibration of a Rotating Annular Plate

This Tech Brief addresses the effects of shear deformation and rotary inertia on the free vibration of a rotating annular plate. Several studies have been done to understand these effects (Irie et al, 1982; Sinha, 1987). In particular, the importance of these terms is well known for disks with a thickness ratio h/a > 0.05 where h is the thickness of the disk and a is its outer radius. However, there is a need to show how they affect the disk vibration as the thickness ratio increases. It is well accepted that shear deformation and rotary inertia should be included in the analysis when h/a > 0.05 (Batoz and Dhatt, 1990). However, this Tech Brief will show that this criterion is not valid for all the modes. It will present the evolution of the number of modes correctly evaluated versus the thickness ratio, and, finally, will give a heuristic criterion to predict when it is necessary to consider shear deformation and rotary inertia.