Free axisymmetric vibrations of composite annular sandwich plates by higher-order theory using Chebyshev collocation technique

Abstract

Abstract Free axisymmetric vibrations of composite annular sandwich plates with thick isotropic core and orthotropic facings have been studied using Reddy's higher-order shear deformation theory. Core is assumed to be of uniform thickness while the face sheets are treated as membranes. Equations of motion and natural boundary conditions are developed using Hamilton's principle. Chebyshev collocation technique has been applied to get the frequency equations for clamped-clamped, clamped-simply supported and clamped-free edge conditions. Obtained equations are solved numerically for the lowest three roots and reported as the frequency parameters for the first three modes of vibration. Results obtained from the proposed approach are validated by comparing them numerically and graphically with their counterparts available in the literature. Detailed numerical results are given to analyze the effects of core thickness, thickness of faces and radii ratios on the frequency parameter. It is also shown that the published analysis based on first-order theory is not suitable for estimation of natural frequency of annular sandwich plate with thick core. Three dimensional mode shapes have been plotted for a specified plate for all the three boundary conditions.