Three-dimensional free vibration analysis of annular sector plates with arbitrary boundary conditions

The objective of this investigation is to apply the spectro-geometric method to study the vibration behavior of the annular sector plates with arbitrary boundary restraints on the basis of the three-dimensional theory of elasticity. All the classical homogeneous boundary conditions can be universally considered as the special cases when the stiffness for each of restraining springs is set equal to either zero or infinity in this study. Under the current solution framework, each displacement of the annular sector plate is, regardless of boundary conditions, invariantly expanded as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series and all the series expanded coefficients are determined with the Rayleigh–Ritz procedure. The present solution method can be generally applied to a broad range of annular sector plates, regardless of their thicknesses and sector angles. The current results are compared with those previously published in literature and the finite element analysis data to validate the current formulation. More results for plates with different boundary restraints and geometrical parameters are presented, which may serve as benchmark solutions for others.