Study on Natural Modes of Vibration For Clamped-Free Annular Plates
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Abstract
This work presents an analytical and numerical investigation of the natural frequencies and mode shapes of clamped-free annular plates, widely used in engineering applications. The characteristic equations are derived for several numbers of nodal diameters (n=0,1,2,3) based on an original and consistent formulation of the governing equations and boundary conditions. The obtained results are compared with classical references, revealing and correcting several discrepancies. Recurrence formulas for Bessel functions are used to obtain original, compact, and validated analytical expressions. A novel formulation for n=3, unavailable in existing literature, is developed with full detail. The results are evaluated numerically and validated through Finite Element Analysis (FEA), showing excellent agreement. Extensive non-dimensional frequency parameters are provided, offering a reliable reference that is easy to use in practical applications.
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