Abstract
In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.
Highlights
Plates are the most widely used structural element in the field of engineering
Refined shear deformation theories presented by Reissner [5], Levy [6], Mindlin [7], Hencky [8] and Kromm [9] are the refinement of the classical plate theory (CPT) considering the effect of transverse shear deformation
Amale et al [23] provided a new hyperbolic shear deformation theory that considers parabolic transverse shear strains across the thickness direction for free vibration analysis of plates
Summary
Plates are the most widely used structural element in the field of engineering. Behaviour of the thick plates either, isotropic or anisotropic, subjected to static and dynamic loading requires the use of refined shear deformation theories, as the classical plate theory neglects the effect of transverse shear deformation generated in the thick plates. Amale et al [23] provided a new hyperbolic shear deformation theory that considers parabolic transverse shear strains across the thickness direction for free vibration analysis of plates. In the literature review presented above, it’s seen that the third order shear deformation theories have been widely used for the analysis of all types of plates to predict their true behaviour when subjected to various kinds of loads. Considering the above stated fact, a modified fifth order shear deformation theory [27] is presented for the free vibration analysis of thick isotropic square plates. The higher frequencies corresponding to the thickness stretch mode cannot be obtained using the classical plate and existing higher order shear deformation theories with zero transverse normal strain. The solution of the eigenvalue problem yields the frequencies corresponding to bending, thickness shear and thickness stretch modes
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