Vibration analysis of thick annular sandwich plates based on Reddy’s theory

Abstract

Free axisymmetric vibrations of uniform annular sandwich plates with relatively stiff core and membrane facings have been studied on the basis of Reddy’s higher-order shear deformation theory. The core and facings are considered to be made up of isotropic materials. The governing equations of motion and natural boundary conditions are developed using Hamilton’s principle. Chebyshev collocation technique is employed to obtain the frequency equations for clamped-clamped, clamped-simply supported and clamped-free edge conditions. The lowest three roots of these equations have been computed and reported as the values of frequency parameters for the first three modes of vibration. After validating the results of the proposed approach, detailed numerical results are given to analyze the effects of thickness of the core, face thickness and radii ratio on the natural frequencies. The results obtained for various plate parameters are compared numerically and graphically with those available in the literature. It also shows that the application of first-order theory is inappropriate for analyzing the vibration of annular sandwich plates with thick core. Three-dimensional mode shapes for a specified plate for all the three boundary conditions have been plotted.