Free vibration of circular annular plate with different boundary conditions

Abstract

This paper deals with the numerical simulation of free vibration analysis of a thin circular annular plate for various boundary conditions at the outer edge and inner edge. Classical plate theory is used to derive the governing differential equation for the transverse deflection of the thin isotropic plate. The finite element method is used to evaluate the first six natural frequencies and mode shapes of the thin uniform circular annular plate with radius ratios / for different boundary conditions. These natural frequencies results are compared with those available in the literature. The results are verified with classical plate theory with our Abaqus results and checked with the previous research literature on the topic.

Free Vibration of Annular Plates Constrained by Translational and/or Rotational Springs on Outer and Inner Edges

“…In the 2010's, new analysis techniques are introduced, for example, by Hamiltonian approach [9] and convolution and differential quadrature methods [10]. Other techniques are also used in references [11,12]. More recently, the author presented numerical results in five significant figures for the nine combinations [13].…”

Accurate Results by the Ritz Method for Free Vibration of Uniform Annular Plates

“…Since then, several authors studied vibration of annular plates [6][7][8][9][10][11] mostly considering polar orthotropy in the material. Recently, Zhou and others [12] presented in 2011 Hamiltonian approach in the problem, Mercan and others [13] used the differential quadrature method in 2016, and Jaiman and Singh [14] presented results from the finite element method in 2019. In these recent works, however, much of their effort is devoted to methodology, and numerical results are limited to some of possible boundary conditions.…”

Analysis of the dynamical behaviour of spinning annular disks with various boundary conditions

“…Yıldırım (Yıldırım 2020) describe the best material distribution for pressurised annular disks. Some studies investigate free vibration analysis of annular plates by using the finite element method (FEM) (Mattikalli and Kurahatti 2018, Qin et al 2018, Jaiman and Singh 2019.…”