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 (r1/r2) 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.
Highlights
Plates are widely used as a structural element and have vast practical applications in many engineering fields such as aerospace, mechanical, civil, nuclear, electronic, automotive, marine and heavy machinery, etc
The first six non-dimensional natural frequencies and mode shapes of the circular annular plate are estimated by using the finite element method
Numerical analysis for free vibration analysis of a thin annular solid plate is carried out using the finite element method for different boundary conditions at the inner and outer radius
Summary
Plates are widely used as a structural element and have vast practical applications in many engineering fields such as aerospace, mechanical, civil, nuclear, electronic, automotive, marine and heavy machinery, etc. Various researchers have analyzed the free vibration behavior of circular annular plates of different shapes, sizes, thickness for different boundary conditions. Leissa [1] used the Ritz method to estimate the natural frequencies of the isotropic plate for different boundary conditions. Kim and Dickinson [2] used the Rayleigh-Ritz approximation method for free vibration of a thin plate to extract natural frequencies. Liew et al [4] used the polynomials-Ritz method for the vibration of circular plates by using three-dimensional elasticity solutions. Zhou et al [5] used the Chebyshev-Ritz method for three-dimensional vibration and mode shapes of the circular plate. Kumar et al [8] use a dynamic stiffness method to extract the natural frequency and mode shapes of a thin plate. Piyush et al [9] used the Rayleigh-Ritz method to compute the natural frequencies of the thin plate
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