Three-Dimensional Static and Free Vibrational Analysis of Graphene Reinforced Composite Circular/Annular Plate Using Differential Quadrature Method

2019 ◽  
Vol 11 (08) ◽  
pp. 1950073 ◽  
Author(s):  
H. Bisheh ◽  
A. Alibeigloo ◽  
M. Safarpour ◽  
A. R. Rahimi
Keyword(s):  
Boundary Conditions ◽  
State Space ◽  
Annular Plate ◽  
Differential Quadrature Method ◽  
Weight Fraction ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Thickness Direction ◽  
Annular Plates ◽  
Reinforced Composite

Free vibrational and bending behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular and annular plate with various boundary conditions is studied using the differential quadrature method (DQM). The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin–Tsai model. Using equations of motion in the framework of the elasticity theory and constitutive relation, the state-space first-order differential equation along the thickness direction is derived. A semi-analytical solution is carried out based on the application of DQM along the radial direction and the state-space technique across the thickness of the plate. The present approach is validated by comparing the numerical results with those reported in the literature. Effect of graphene platelets (GPLs) weight fraction, different GPL distribution patterns, thickness-to-radius and outer-to-inner radius ratios and edge boundary conditions on the static and vibrational behavior of GPLs reinforced composite circular/annular plates are examined. The results implied that GPLs can improve the composite strength against different loading and GPLs could have an extraordinary reinforcing influence on the static and vibrational behavior of the circular/annular plates.

Elasticity Solution of Free Vibration and Bending Behavior of Functionally Graded Carbon Nanotube-Reinforced Composite Beam with Thin Piezoelectric Layers Using Differential Quadrature Method

2015 ◽  
Vol 07 (01) ◽  
pp. 1550002 ◽  
Author(s):  
A. Alibeigloo ◽  
K. M. Liew
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
State Space ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Reinforced Composite ◽  
Piezoelectric Layers

Based on the theory of elasticity, bending and free vibrational analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam embedded in piezoelectric layers are carried out, using the state-space differential quadrature method (DQM). Applying the DQM to the governing differential equations and boundary conditions along the longitudinal directions, new state equations about state variables at discrete points are derived. By using the state-space technique across the thickness direction, semi- analytical closed form solutions are derived. The method is validated by comparing numerical results for beams without piezoelectric layers. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of beam is studied. Furthermore, the effects of CNT volume fraction, kind of CNT distribution, length to thickness ratio and edge boundary conditions on the mechanical behavior of the beams are examined.

Free Vibration of Two-Directional Functionally Graded Annular Plates Using Chebyshev Collocation Technique and Differential Quadrature Method

2015 ◽  
Vol 15 (06) ◽  
pp. 1450086 ◽  
Author(s):  
Yajuvindra Kumar
Keyword(s):  
Annular Plate ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Axisymmetric Vibration ◽  
Quadrature Method ◽  
Chebyshev Collocation ◽  
Annular Plates ◽  
Collocation Technique

This article deals with the free axisymmetric vibration of two-directional functionally graded annular plates. Ceramic and metal are considered two constituents of the functionally graded material (FGM), which are graded through thickness and radial directions of the plate. The Chebyshev collocation technique and differential quadrature method are employed to derive the frequency equations for an annular plate with both edges clamped and another one with both edges simply supported. The results for nonhomogeneous isotropic annular plates are also presented. The accuracy and efficiency of the present approach are confirmed through comparison of the frequencies obtained for homogeneous isotropic annular plates. Identical results are obtained for the two methods used. The effects of volume fraction index, coefficient of radial variation, exponent of power law, inner to outer radii ratio, and boundary conditions are discussed on the first three natural frequencies. It is found that the frequency of a functionally graded annular plate is greater than that of a homogeneous annular plate.

A modified state space differential quadrature method for free vibration analysis of soft-core sandwich panels

2017 ◽  
Vol 21 (6) ◽  
pp. 1843-1879 ◽  
Author(s):  
Balavishnu Udayakumar ◽  
KV Nagendra Gopal
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Sandwich Panels ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Soft Core ◽  
Quadrature Method

Modifications and improvements to conventional state space differential quadrature method are proposed for free vibration analysis of thick, soft-core sandwich panels with arbitrary edge boundary conditions, using an exact two-dimensional elasticity model. The modifications are based on a systematic procedure to implement all possible combinations of edge boundary conditions including simply supported, clamped, free and guided edges. Natural frequencies and mode shapes are obtained and compared with exact elasticity solutions from state space method and approximate solution from finite element simulations; demonstrating the high numerical accuracy and rapid convergence of the modified method. Further, the proposed framework is compared to the conventional implementation of the state space differential quadrature method for thick cantilever sandwich panels and is shown to give results with better accuracy and faster convergence.

scholarly journals Free Vibration Analysis of Fiber Metal Laminate Annular Plate by State-Space Based Differential Quadrature Method

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
G. H. Rahimi ◽  
M. S. Gazor ◽  
M. Hemmatnezhad ◽  
H. Toorani
Keyword(s):  
State Space ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fiber Metal Laminate ◽  
Fiber Metal

A three-dimensional elasticity theory by means of a state-space based differential quadrature method is presented for free vibration analysis of fiber metal laminate annular plate. The kinds of composite material and metal layers are considered to be S2-glass and aluminum, respectively. A semianalytical approach which uses state-space in the thickness and differential quadrature in the radial direction is implemented for evaluating the nondimensional natural frequencies of the annular plates. The influences of changes in boundary condition, plate thickness, and lay-up direction on the natural frequencies are studied. A comparison is also made with the numerical results reported by ABAQUS software which shows an excellent agreement.

Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates on Elastic Foundations via State-Space Based Differential Quadrature Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
A. Jodaei ◽  
M. H. Yas
Keyword(s):  
Free Vibration ◽  
State Space ◽  
Present Method ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Elastic Foundations ◽  
Annular Plates

In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

Structural Analysis by the Differential Quadrature Method Using Modified Weighting Matrices

1998 ◽  
Author(s):  
Siu-Tong Choi ◽  
Yu-Tuan Chou
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Sampling Point ◽  
Order Partial Differential Equation ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Computationally Efficient ◽  
Base Points ◽  
Sampling Points

Abstract The differential quadrature method has lately been more and more often used for analysis of engineering problems as an alternative for the finite element method or finite difference method. In this paper, static, dynamic and buckling analyses of structural components are performed by the differential quadrature method. To improve the accuracy of this method, an approach is proposed for selecting the sampling points which include base points and conditional points. The base points are taken as the roots of the Legendre polynomials. Accuracy of the problems analyzed will be increased by using the base points. The conditional points are determined according to boundary conditions and specified conditions of external load. A modified algorithm is proposed for applying two or more boundary conditions in a sampling point at boundary of domain, such that the higher-order partial differential equation can be solved without adding new sampling points. By applying this approach to variety problems, such as deflections of beam under nonuniformly distributed loading, vibration and buckling analyses of beam and plate, it is found that numerical results of the present approach are more accurate than those obtained by the equally-spaced differential quadrature method and is computationally efficient.

scholarly journals A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

2019 ◽  
Vol 24 (2) ◽  
pp. 217-227
Author(s):  
Mostafa Talebitooti
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Algebraic Equations ◽  
Discrete Elements ◽  
Arbitrary Boundary ◽  
Stiffened Shells

A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

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