Abstract
In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular sector plates with elastic restraints along each of its edges. The in-plane displacement fields are universally expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. The expansion coefficients are considered as the generalized coordinates, and determined using the Rayleigh-Ritz technique. Several examples are presented to demonstrate the effectiveness and reliability of the current method for predicting the modal characteristics of annular sector plates with various cutout ratios and sector angles under different boundary conditions. It is also shown that annular and circle plates can be readily included as the special cases of the annular sector plates when the sector angle is set equal to 360°.
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