Abstract
This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.
Highlights
There are different kinds of plates like rectangular, circular, and annular circular have been used as structural elements of numerous engineering fields such as nuclear, civil, mechanical, aerospace, and marine
Yang et al [3] proposed the first order shear deformation theory (FSDT); according to them, there is a state of constant shear strain through the thickness of the plate
The annular circular plates for supported boundary condition based on the higher order shear deformation theory are investigated
Summary
There are different kinds of plates like rectangular, circular, and annular circular have been used as structural elements of numerous engineering fields such as nuclear, civil, mechanical, aerospace, and marine. Love-Kirchhoff proposed the classical theory which was based on the assumption that the straight lines normal to the undeformed and deformed midplane remain straight and normal and do not undergo stretching in the thickness direction This theory accurately measures the stress analysis of thin composites plates but suitable for thick laminated plates since it overpredicts the natural frequencies [1, 2]. In third-order plate theory, the displacement is expanded up to the cubic term in thickness coordinates to have quadratic variation of transverse shear strains and transverse shear stresses through the plate thickness. The inclusion of TSDT to equilibrium equations makes the solution more complex These theories the classical plate theory (CPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theories (HSDT) are shown
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