scholarly journals Differential Quadrature Analysis of Free Vibration of Symmetric Cross-Ply Laminates with Shear Deformation and Rotatory Inertia

1995 ◽  
Vol 2 (4) ◽  
pp. 321-338 ◽  
Author(s):  
Moinuddin Malik ◽  
Charles W. Bert
Keyword(s):  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Quadrature Method ◽  
Computationally Efficient ◽  
Rotatory Inertia ◽  
Solution Approach ◽  
Simply Supported ◽  
Plate Equations

In the present work, laminates having two opposite edges simply supported are considered. The boundary conditions at the other two opposite edges may be general, and between these two edges, the thickness of the plate may be nonuniform. The theory used for the vibration analysis of such laminates includes shear deformation and rotatory inertia. The solution approach of the problem is semianalytical. By using the trigonometric functions describing the mode shapes between the simply supported edges, the governing plate equations are reduced to ordinary differential equations. The solution of the reduced equations is then sought by the differential quadrature method. The results reported in this article serve two objectives of the present investigations. One, it is demonstrated that the proposed semianalytical quadrature method offers a numerically accurate and computationally efficient technique for the title problem. Two, the relative effects of shear deformation and rotatory inertia are analyzed in a quantitative manner.

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.

Diagnosis of Type, Location and Size of Cracks by Using Generalized Differential Quadrature and Rayleigh Quotient Methods

2013 ◽  
Vol 43 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Majid Akbarzadeh Khorshidi ◽  
Delara Soltani
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Rayleigh Quotient ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Quadrature Method ◽  
Torsion Spring ◽  
Free Boundary Conditions ◽  
Generalized Differential ◽  
The Relationship

Abstract In this paper, an appropriate and accurate algorithm is pro- posed to diagnosis of lateral or vertical cracks on beam, based on beam natural frequencies. Clamped-free boundary conditions are assumed for the beam. The crack in beam is modelled by without mass torsion spring. Then, the relationship between the beam natural frequencies, location and stiffness of the crack is presented by using the Rayleigh quotient and the governing equation is solved by using generalized differential quadrature method (GDQM). If there is only one crack in the beam, then three natural frequencies are used as inputs to the algorithm and mode shapes corresponding to each the natural frequencies are calculated. Finally, type, location and severity of cracks in beam, are diagnosed.

Analysis of the vibration of axially moving viscoelastic plate with free edges using differential quadrature method

2017 ◽  
Vol 24 (17) ◽  
pp. 3908-3919 ◽  
Author(s):  
Mouafo Teifouet Armand Robinson
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Viscoelastic Plate ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Simply Supported ◽  
System Parameters ◽  
Complex Eigenvalues ◽  
Axially Moving ◽  
Viscoelastic Rectangular Plate

The two-dimensional viscoelastic differential constitutive relation is employed in this paper, in order to establish the equation of motion of axially moving viscoelastic rectangular plate. Two boundary conditions are investigated, namely the clamped free and two opposite edges simply supported and two others free. The differential quadrature method is used to solve the resulting complex eigenvalues equation. The influence of boundary conditions on the instability of a moving viscoelastic plate is analyzed firstly, and secondly the effects of system parameters such as plate's viscosity and aspect ratio on the vibration frequencies are presented.

Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method

2015 ◽  
Vol 54 (6) ◽  
pp. 1061-1073 ◽  
Author(s):  
Hasan Rahimi Pour ◽  
Hossein Vossough ◽  
Mohammad Mehdi Heydari ◽  
Gholamhossein Beygipoor ◽  
Alireza Azimzadeh
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method

Differential Quadrature Solutions for Steady-State Incompressible and Compressible Lubrication Problems

1994 ◽  
Vol 116 (2) ◽  
pp. 296-302 ◽  
Author(s):  
M. Malik ◽  
C. W. Bert
Keyword(s):  
Steady State ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Efficient Technique ◽  
Quadrature Method ◽  
Computationally Efficient

This paper presents the very first application of the differential quadrature method to the solution of steady-state incompressible and compressible lubrication problems. It is shown that the differential quadrature method is a numerically accurate and computationally efficient technique which can compete against existing methods in use for the solution of lubrication problems.

Vibration and buckling analysis of laminated sandwich conical shells using higher order shear deformation theory and differential quadrature method

2017 ◽  
Vol 21 (4) ◽  
pp. 1445-1480 ◽  
Author(s):  
M Nasihatgozar ◽  
SMR Khalili
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Stiffness Ratio ◽  
Conical Shells ◽  
The Core ◽  
The Face

Vibration and buckling analysis of laminated sandwich truncated conical shells with compressible or incompressible core are presented in this work considering curvature effects. The formulation uses the quadratic and cubic functions for transverse and in-plane displacements of the core and the first-order shear deformation theory for the face sheets. The motion equations of each individual layer are derived according to the principle of minimum total potential energy considering the continuity of the displacements and the internal stress fields at the interfaces. Differential quadrature method is applied in order to obtain the frequency and buckling load of the sandwich structure. The effects of different parameters such as core to face sheet stiffness ratio, number of layers of the face sheets, boundary condition, geometrical parameters of the core and the face sheets, semi vertex angle of the cone, trapezoidal shape, and in-plane stresses of the core are examined on the vibration and buckling response of sandwich truncated conical shells. Comparison of the present results with those reported in the literature confirms the accuracy of the proposed theory. Numerical results indicate that the effects of in-plane stresses of the core significantly affect the frequency with increasing the core to face sheet stiffness ratio.

Free vibration of functionally graded sandwich plates based on nth-order shear deformation theory via differential quadrature method

2018 ◽  
Vol 22 (5) ◽  
pp. 1660-1680 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Zhonglong Wang ◽  
Xiaoxiang Liu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Sandwich Plates ◽  
Numerical Comparison ◽  
Quadrature Method

The present study is concerned with free vibration of functionally graded sandwich plates on elastic foundation based on nth-order shear deformation theory. The material properties of functionally graded plate are assumed to vary according to power law distribution of the volume fraction of the constituents, and two common types of FG sandwich plates are considered. Governing differential equations are derived by means of Hamilton’s principle. The differential quadrature method is developed to formulate the problem, and rapid convergence is observed in this study. A numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. Furthermore, effects of gradient indexes, thickness side ratio, aspect ratio, foundation parameters, boundary condition and different sandwich types on the natural frequency of plates are also studied.

Axisymmetric free vibration and stress analyses of saturated porous annular plates using generalized differential quadrature method

2019 ◽  
Vol 25 (21-22) ◽  
pp. 2799-2818 ◽  
Author(s):  
Leila Bemani Khouzestani ◽  
Ahmad Reza Khorshidvand
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Various Boundary Conditions ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential ◽  
Stress Analyses

The current study presents free vibration and stress analyses of an annular plate which is made of saturated porous materials based on the first order shear deformation plate theory which accounts for the shear deformation effects. The pores are distributed in the thickness direction according to three different types, namely, porosity nonlinear nonsymmetric distribution, porosity nonlinear symmetric distribution, and porosity monotonous distribution. Employing Hamilton’s principle and variational formulation, the motion equations are derived and solved via the generalized differential quadrature method as a highly accurate and rapid convergence numerical method for various boundary conditions. The results are validated with simpler cases in the literature and different parameters of the structures such as pores distribution, porosity, pressure of fluids within the pores, and also the aspect ratio of the plate is considered and discussed regarding their effects on the results. It is seen that enhancing the porosity coefficient which means increasing the void volume, reduces the structure’s stiffness more than its density and so the frequency and stresses decrease. The findings of this work may be useful to design structures with desired mechanical properties.

scholarly journals Analysis of Cylindrical Shells Using Generalized Differential Quadrature

1997 ◽  
Vol 4 (3) ◽  
pp. 193-198 ◽  
Author(s):  
C.T. Loy ◽  
K.Y. Lam ◽  
C. Shu
Keyword(s):  
Fluid Dynamics ◽  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Generalized Differential

The analysis of cylindrical shells using an improved version of the differential quadrature method is presented. The generalized differential quadrature (GDQ) method has computational advantages over the existing differential quadrature method. The GDQ method has been applied in solutions to fluid dynamics and plate problems and has shown superb accuracy, efficiency, convenience, and great potential in solving differential equations. The present article attempts to apply the method to the solutions of cylindrical shell problems. To illustrate the implementation of the GDQ method, the frequencies and fundamental frequencies for simply supported-simply supported, clamped-clamped, and clamped-simply supported boundary conditions are determined. Results obtained are validated by comparing them with those in the literature.

Free vibration and buckling analysis of functionally graded deep beam-columns on two-parameter elastic foundations using the differential quadrature method

2009 ◽  
Vol 223 (6) ◽  
pp. 1273-1284 ◽  
Author(s):  
S Sahraee ◽  
A R Saidi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Deep Beam ◽  
Quadrature Method ◽  
Beam Columns ◽  
Two Parameter

In this research, a differential quadrature method is applied for free vibration and buckling analysis of deep beam-columns composed of functionally graded materials on two-parameter elastic foundations. Derivation of equations is based on the unconstrained higher-order shear deformation theory taking into account the complete effects of shear deformation, depth change, and rotary inertia. It is assumed that the effective mechanical properties of functionally graded (FG) beam-columns are temperature dependent and vary continuously throughout the thickness direction according to volume fraction of the constituents defined by power-law function. The accuracy, convergence, and flexibility of the differential quadrature technique for simply supported FG deep beam-columns with complicated governing differential equations and boundary conditions are examined and verified with the known data in the literature.

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