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.

Dynamic Analysis and Critical Speed of Pressurized Rotating Composite Laminated Conical Shells Using Generalized Differential Quadrature Method

2010 ◽  
Vol 26 (1) ◽  
pp. 61-70 ◽  
Author(s):  
M. Ghayour ◽  
S. Ziaei Rad ◽  
R. Talebitooti ◽  
M. Talebitooti
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Conical Shells ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential ◽  
Laminated Conical Shells

AbstractFree vibration analysis of rotating composite laminated conical shells with different boundary conditions using the generalized differential quadrature method (GDQM), is investigated. Equations of motion are derived based on Love's first approximation theory by taking the effects of initial hoop tension and the centrifugal and Coriolis acceleration due to rotation and initial uniform pressure load into account. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying the GDQM. The results are obtained for the frequency characteristics of different orthotropic parameters, rotating velocities, cone angles and boundary conditions. The presented results are compared with those available in the literature and good agreements are achieved.

A Study on the Buckling Characteristics of Conical Shell Using Differential Quadrature Method

2010 ◽  
Author(s):  
E. Jomehzadeh ◽  
S. H. Mirtalaie ◽  
H. Noori
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Conical Shell ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Vertex Angle ◽  
Accuracy Evaluation ◽  
Quadrature Method ◽  
Special Cases ◽  
The Stability

In this paper, the buckling analysis of conical shell under transverse pressure or axial compression is studied using the Differential Quadrature Method (DQM) for various boundary conditions. Based on the Donnell theory of shell, the equilibrium equations are obtained using Hamilton’s principle. The adjacent equilibrium criterion is employed to defining the stability equations of conical shell subjected to lateral pressure and axial compression. Then the stability equations are solved numerically using DQM and employing the concept of extra degrees of freedom. The acquired results in special cases are compared with the results in literature for the accuracy evaluation of the method and a good agreement can be seen. The non-dimensional critical buckling loads are tabulated for different vertex angles, some thickness-radius ratios and various combinations of boundary conditions. Also, the effects of the vertex angle, boundary conditions, length-radius ratio and thickness-length ratio on the buckling behavior of the conical shell are investigated in details.

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.

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

2019 ◽  
Vol 55 (1-2) ◽  
pp. 42-52
Author(s):  
Milad Ranjbaran ◽  
Rahman Seifi
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method

2016 ◽  
Vol 23 (19) ◽  
pp. 3247-3265 ◽  
Author(s):  
Majid Ghadiri ◽  
Navvab Shafiei
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Small Scale ◽  
Quadrature Method ◽  
Bending Vibrations ◽  
Classical Plate Theory ◽  
Axial Forces

This study investigates the small-scale effect on the flapwise bending vibrations of a rotating nanoplate that can be the basis of nano-turbine design. The nanoplate is modeled as classical plate theory (CPT) with boundary conditions as the cantilever and propped cantilever. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton’s principle is used to derive the governing equation and boundary conditions for the classic plate based on Eringen’s nonlocal elasticity theory and the differential quadrature method is employed to solve the governing equations. The effect of the small-scale parameter, nondimensional angular velocity, nondimensional hub radius, setting angle and different boundary conditions in the first four nondimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nanomachines such as nanomotors and nano-turbines and other nanostructures.

FREE VIBRATION ANALYSIS OF TRIPLY COUPLED PRE-TWISTED ROTOR BLADES BY THE DIFFERENTIAL QUADRATURE METHOD

2011 ◽  
Vol 11 (01) ◽  
pp. 127-147 ◽  
Author(s):  
O. SEPAHI ◽  
M. R. FOROUZAN ◽  
P. MALEKZADEH
Keyword(s):  
Rotor Blade ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Rotor Blades ◽  
Dynamic Responses ◽  
Quadrature Method ◽  
Method Of Solution ◽  
Combined Flap

Key parameters on the dynamic characteristics of triply coupled pretwisted rotor blades are investigated. The issues of concern include the combined flap-wise bending, chord-wise bending, and torsion vibrations of the pretwisted rotor blade, considering the centrifugal force and Coriolis effects. The governing differential equations of motion presented by Houbolt and Brooks for the rotor blade are used as the basis of study, which contain many factors previously ignored. The differential quadrature method is adopted as the method of solution for its ease in implementation, accuracy, and fast convergence. The dynamic responses of the rotor blade are obtained for different cases of coupling and geometries, which agree well with existing results. The dynamic responses of the rotor blades are plotted against parameters such as angular velocity, pretwisting angle, and hub radius in proper curves and discussed in details.

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.

scholarly journals Dynamic Analysis of a Tapered Composite Thin-Walled Rotating Shaft Using the Generalized Differential Quadrature Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren ◽  
Xiaoxiao Wu ◽  
Hongcan Ma
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Rotating Shaft ◽  
Generalized Differential Quadrature Method ◽  
Thin Walled ◽  
Generalized Differential

A dynamic model of a tapered composite thin-walled rotating shaft is presented. In this model, the transverse shear deformation, rotary inertia, and gyroscopic effects have been incorporated. The equations of motion are derived based on a refined variational asymptotic method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the generalized differential quadrature method (GDQM). The validity of the dynamic model is proved by comparing the numerical results with those obtained in the literature and by using ANSYS. The effects of taper ratio, boundary conditions, ply angle, length to mean radius ratios, and mean radius to thickness ratios on the natural frequencies and critical rotating speeds are investigated.

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