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The circular/annular plates are basic elements which are used in different structures. The vibrational properties of these structures are important for dynamic analysis. In this paper, an analytical solution based on the multiple scales in perturbation technique has been used for determining the natural frequencies of an axisymmetric annular plate with large deformation in the out-of-plane and in-plane modes. The governing equations are extracted by employing the first-order shear deformation theory which contains  four coupled nonlinear partial differential equations with variable coefficients . A sensitivity analysis has been performed and the effects of the geometrical parameters on the frequencies are studied. Also, the effects of radial and transverse amplitudes on the frequencies are discussed. The calculations show that the nonlinear frequencies depend on the transverse amplitude as well as the radial deformation.

Effect of transverse and radial deformations on nonlinear frequencies of annular plates: perturbation approach