Eigen Solutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

Differential Quadrature ◽

Quadrature Method ◽

Discrete Eigenvalue ◽

Generalized Differential ◽

Eigen Solutions

The eigenvalue problems of grouped turbo blades were numerically formulated by using the generalized differential quadrature method (GDQM). Different boundary approaches accompanying the GDQM to transform the partial differential equations of grouped turbo blades into a discrete eigenvalue problem are discussed. Effects of the number of sample points and the different boundary approaches on the accuracy of the calculated natural frequencies are also studied. Numerical results demonstrated the validity and the efficiency of the GDQM in treating this type of problem.

Eigensolutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.1492833 ◽

2002 ◽

Vol 124 (4) ◽

pp. 1011-1017 ◽

Cited By ~ 4

Author(s):

J. H. Kuang ◽

M. H. Hsu

Keyword(s):

Partial Differential Equations ◽

Eigenvalue Problem ◽

Natural Frequencies ◽

Eigenvalue Problems ◽

Differential Quadrature ◽

Quadrature Method ◽

Discrete Eigenvalue ◽

Generalized Differential

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

The Journal of Strain Analysis for Engineering Design ◽

10.1177/0309324719886976 ◽

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 ◽

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.

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

Applied Sciences ◽

10.3390/app7020131 ◽

2017 ◽

Vol 7 (2) ◽

pp. 131 ◽

Cited By ~ 55

Author(s):

Francesco Tornabene ◽

Nicholas Fantuzzi ◽

Michele Bacciocchi ◽

Erasmo Viola ◽

Junuthula Reddy

Keyword(s):

Numerical Investigation ◽

Variable Thickness ◽

Natural Frequencies ◽

Differential Quadrature ◽

Quadrature Method ◽

Sandwich Shells ◽

Generalized Differential

Eigen Solutions of an Orthotropy Composite Blade Solved by the Differential Quadrature Method

Volume 4: Turbo Expo 2002, Parts A and B ◽

10.1115/gt2002-30423 ◽

2002 ◽

Cited By ~ 1

Author(s):

J. H. Kuang ◽

M. H. Hsu

Keyword(s):

Eigenvalue Problem ◽

Differential Quadrature ◽

Beam Model ◽

Quadrature Method ◽

Discrete Eigenvalue ◽

Composite Blade ◽

Sample Points ◽

Eigen Solutions ◽

Inclined Angle

The eigenvalue problem of an orthotropy composite blade is formulated by employing the differential quadrature method (DQM). The Euler-Bernoulli beam model is used to characterize the orthotropy composite blade. The differential quadrature method is used to transform the partial differential equations of an orthotropy composite blade into a discrete eigenvalue problem. The Chebyshev-Gauss-Lobatto sample point equation is used to select the sample points. In this study, the effects of the fiber orientation, internal damping, external damping, inclined angle and the rotation speed on the eigen solutions for an orthotropy composite blade are investigated. The effect of the number of sample points on the accuracy of the calculated natural frequencies is also discussed. The integrity and computational efficiency of the DQM in this problem will be demonstrated through a number of case studies. Numerical results indicated that the differential quadrature method is valid and efficient for an orthotropy composite blade formulation.