A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates (original) (raw)
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Electronic Journal of Vocational Colleges, 2018
In this research, an efficient shear deformation plate theory for a functionally graded plate has been investigated by the use of the new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory account for higher-order variation of transverse shear strain through the depth of the plate and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Based on the present higher-order shear deformation plate theory, the equations of the motion are derived from Hamilton's principal. The plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. The influences played by the transverse shear deformation, aspect ratio, side-to-thickness ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded plate are investigated.
Effect Of Shear Theories On Free Vibration Of Functionally Graded Plates
2008
Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.
Vietnam Journal of Mechanics, 2014
In the present investigation, free vibration analysis of functionally graded material (FGM) plate is performed incorporating higher order shear deformation theory in conjunction with C0 based finite element formulation. The cubic component of thickness term is incorporated in in-plane fields and constant variation of thickness is assumed for transverse component. The theory incorporates the realistic parabolic variation of transverse shear stresses thus eliminates the use of shear correction factor. Aluminium/Zirconia plate is considered for the analysis and the effective properties are assumed to have smooth and gradual variation in the thickness direction and remain constant in in-plane direction. The spatial variation of properties pertaining to homogeneous and FGM plate is estimated by means of power law, which is described by the four parameters. With respect to dynamic analysis, it is vital for an analyst to know whether the top of the plate is ceramic or metal rich, and inver...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015
In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite-element method. The theory based on full 12-unknown higher order shear deformation theory simultaneously satisfies zeros transverse stresses at top and bottom surfaces of FG plates. A four-node rectangular element with 16 degrees of freedom per node is used. Poisson's ratios, Young's moduli, and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power-law functions. Results are verified with available results in the literature. Parametric studies are performed for different power-law indices, side-to-thickness ratios.
Free Vibration of Functionally Graded Plates with a Higher-Order Shear and Normal Deformation Theory
International Journal of Structural Stability and Dynamics, 2013
Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the us...
A new hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The energy functional of the system is obtained using Hamilton's principle. Analytical solutions of deflection and stresses are obtained using Navier-type procedure. Free vibration frequencies are then accurately calculated using a set of boundary characteristic orthogonal polynomials associated with Ritz method. Numerical comparisons are conducted to verify and to demonstrate the accuracy and efficiency of the present theory. Excellent agreement with the known results in the literature has been obtained.
Materials, 2019
A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of differe...
Composites Part B: Engineering, 2019
The aim of this work is to establish a two dimensional (2D) and quasi three dimensional (quasi-3D) shear deformation theories, which can model the free vibration of FG plates resting on elastic foundations using a new shear strain shape function. The proposed theories have a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. The mechanical properties of the plates are assumed to vary through the thickness according to a power law distribution in terms of the volume fractions of the constituents. The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Hamilton's principle is employed to determine the equations of motion. The closed form solutions are derived by using Navier's method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. The efficiency of the proposed theory is ascertained by comparing the results of numerical examples with the different 2D, 3D and quasi-3D solutions found in literature.
Journal of Composites Science
This study presents a hyperbolic shear deformation theory for free vibration of functionally graded plates on elastic foundations. The field of displacements is chosen based on the assumptions that axial and transverse displacements consist of components due to bending and shear. The components of the axial shear displacements give rise to the parabolic variation in the shear strain through the thickness, such that the shear stresses vanish on the plate boundaries. Therefore, the shear correction factor is not necessary. The material properties of the functionally graded plate are assumed to vary through the thickness according to the power law of the volume fraction of the constituents. The elastic foundation is modeled as a Pasternak foundation. The equations of motion are derived using Hamilton’s principle. The analytical solutions were established from Navier’s approach, and the results obtained are found to be in good agreement with the solutions of three-dimensional elasticity...
2010
A general approach for free vibration of functionally graded materials (FGMs) plates based on second-order shear deformation theory (SSDT) is presented. Material properties are assumed to be graded in the thickness direction by power law distribution in term of the volume fractions of the constituents. The equilibrium equations are derived by energy method and then solved analytically by applying Navier's method for a plate with simply supported boundary conditions. It is found that the fundamental frequencies versus side-to-side ratio for FG quadrangular plates are between full-ceramic plate and full-metal plate. It is shown that for the grading index smaller than two (p<2) the decreasing slope of the frequency is greater than that in other parts for all values of side-to-thickness ratio in square FG plate. Natural frequencies for different mode shape are compared and verified with the known results in the literature. It is seen that the results of the second-order theory ar...