Letter to the editor

The flexural vibration of thin isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries

The present study deals with an exact analysis of free transverse vibrations of annular plates having small core and sliding inner edge and the outer edge being elastically restrained based on classical plate theory. This study focuses mainly on the influence of variations in the elastic restraint parameters on the fundamental frequencies of plate vibration. The natural frequencies for the first six modes of annular plate vibrations are computed for different materials and varying values of the radius parameter and these natural frequencies may correspond to either axisymmetric and/or non-axisymmetric modes of plate vibration. The extensive data of values of fundamental frequency parameter presented in this paper is believed to be of use in the design of acoustic underwater transducers, ocean and naval structures, compressor and pump elements, offshore platforms. These results may serve as bench mark values for researchers to validate their results obtained using approximate numerical methods.

The present paper deals with exact analysis of free lateral vibrations of annular plates with inner and outer edges elastically restrained and resting on Winkler type elastic foundation. Exact solution is obtained from the formulation based on the classical plate theory assumptions. The frequencies of the annular plate are computed for various values of elastic rotational and translational restraints, foundation restraint and radius of an annular plate and the results for the first three modes of the plate vibrations are presented in both graphical and tabular form suitable for use in design. The effect of varying values of rotational and translational restraints, foundation restraint and radius of the annular plate on the vibration behavior of annular plates is studied in detail. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers to validate their numerical methods when applied for such annular plate problems.

This paper presents a generalized formulation for the in-plane modal characteristics of circular annular disks under combinations of all possible classical boundary conditions. The in-plane free vibration of an elastic and isotropic disk is studied on the basis of the two-dimensional linear plane stress theory of elasticity. The boundary characteristic orthogonal polynomials are employed in the Rayleigh–Ritz method to obtain the natural frequencies and associated mode shapes. Two approaches have been used to represent a clamped boundary condition. The first approach assumes a polynomial expression that satisfies the clamped conditions, while the second approach uses a disk with free boundary supported on artificial springs with stiffness tending to infinity. The natural frequencies are tabulated and compared with data available in the literature. Mode shapes are presented to illustrate the free vibration behavior of the disk.

Buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory. The plate is resting on Winkler-type foundation. An approximate solution has been obtained by Ritz method, which employs basis functions based upon static deflection of polar orthotropic plates. The effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter, flexibility parameter, in-plane force and nodal diameter. The critical buckling load for clamped and simply supported plates have been obtained. A comparison of results with those available in literature has been presented.