Application of the generalized differential quadrature rule to eighth-order differential equations

2001 ◽  
Vol 17 (5) ◽  
pp. 355-364 ◽  
Author(s):  
T. Y. Wu ◽  
G. R. Liu
Keyword(s):  
Differential Equations ◽  
Quadrature Rule ◽  
Differential Quadrature ◽  
Eighth Order ◽  
Generalized Differential

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.

Investigation of MHD Natural Convection Flow Exposed to Constant Magnetic Field via Generalized Differential Quadrature Method

2014 ◽  
Author(s):  
Elgiz Baskaya ◽  
Melih Fidanoglu ◽  
Guven Komurgoz ◽  
Ibrahim Ozkol
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Constant Magnetic Field ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Convection Flow ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

In this work, nanofluid flow characteristics of an inclined channel flow exposed to constant magnetic field and pressure gradient is investigated. The nanofluid considered is water based Cu nanoparticles with a volume fraction of 0.06. The viscous dissipation is taken into account in the energy equation and the governing differential equations are nondimensionalized. The coupled one dimensional differential equations are solved via Generalized Differential Quadrature Method (GDQM) discretization followed by Newton Raphson method. Furthermore, the effect of magnetic field, inclination angle of the channel and volume fraction on nanoparticles in the nanofluid on velocity and temperature profiles are examined and represented by figures to give a thorough understanding of the system behavior. Designing systems utilizing nanofluids optimally, is highly dependent to achieving accurate model definitions figuring their inherent performance.

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