Abstract
This paper aims to study the influence of different geometric properties and support conditions on the vibration of layered plates of nonuniform thickness under shear deformation theory. The layered plates are supposed to have arbitrarily nonuniform thickness as linear, exponential, and sinusoidal. The spline approximation is used to approximate translational and angular displacement functions. Eigen frequency parameters are calculated by solving eigenvalue problem. The geometrical influences such as number of lay-ups, different ply orientations, each ply consisting of different material, side-to-thickness ratio, and aspect ratio are taken into consideration to examine the frequency variation of plates for two different support conditions.
Highlights
Plates with nonuniform thickness are extensively used as the aerospace and marine structural components attracting the attention of contemporary engineers. e plates with nonuniform thickness can help designer to modify resonant frequency, decrease the size and weight, increase the stiffness, and adjust flexural rigidity of the structure
Plates with nonuniform thickness are generally difficult to analyze and get the analytical solution. erefore, some researchers investigated such plates and obtained solution, as the investigations carried by Appl and Byers [1] on plates of linear thickness variation for supported plates
A four-unknown refined plate theory for dynamic analysis of functionally graded (FG)-sandwich plates under various boundary conditions were examined by Menasria et al [33]
Summary
Plates with nonuniform thickness are extensively used as the aerospace and marine structural components (e.g., turbine disks and aircraft wings) attracting the attention of contemporary engineers. e plates with nonuniform thickness can help designer to modify resonant frequency, decrease the size and weight, increase the stiffness, and adjust flexural rigidity of the structure. Sandwich functionally graded plates were examined using refined FSDT for their static analysis by Mantari and Granados [15]. Zippo et al [24] studied Sandwich plates for their active vibration under free-edge boundary condition using control method. A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions were examined by Menasria et al [33]. Allam et al [34] studied the bending and free vibration of composite plates using refined higher-order shear deformation theory with four unknown variables. Belbachir et al [31] studied thermal flexural analysis of composite plates based on higher-order shear deformation theory. Civalek et al [42] used the nonlocal finite element method to examine size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes.
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