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

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.

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Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method

Composite Structures ◽

10.1016/j.compstruct.2015.12.004 ◽

2016 ◽

Vol 156 ◽

pp. 218-237 ◽

Cited By ~ 70

Author(s):

Michele Bacciocchi ◽

Moshe Eisenberger ◽

Nicholas Fantuzzi ◽

Francesco Tornabene ◽

Erasmo Viola

Keyword(s):

Variable Thickness ◽

Vibration Analysis ◽

Differential Quadrature Method ◽

Differential Quadrature ◽

Quadrature Method ◽

Generalized Differential Quadrature Method ◽

Plates And Shells ◽

Generalized Differential

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

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/2001-gt-0273 ◽

2001 ◽

Author(s):

J. H. Kuang ◽

M. H. Hsu

Keyword(s):

Eigenvalue Problem ◽

Natural Frequencies ◽

Eigenvalue Problems ◽

Differential Quadrature Method ◽

Differential Quadrature ◽

Quadrature Method ◽

Discrete Eigenvalue ◽

Generalized Differential Quadrature Method ◽

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.

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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 Method ◽

Differential Quadrature ◽

Quadrature Method ◽

Discrete Eigenvalue ◽

Generalized Differential Quadrature Method ◽

Generalized Differential

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.

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Vibration analysis of a rotating variable thickness bladed disk for aircraft gas turbine engine using generalized differential quadrature method

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410016684360 ◽

2017 ◽

Vol 231 (14) ◽

pp. 2739-2749 ◽

Cited By ~ 4

Author(s):

B Shahriari ◽

Mohammadhadi Jalali ◽

MR Karamooz Ravari

Keyword(s):

Gas Turbine ◽

Variable Thickness ◽

Vibration Analysis ◽

Differential Quadrature Method ◽

Differential Quadrature ◽

Quadrature Method ◽

Turbine Engine ◽

Bladed Disk ◽

Generalized Differential Quadrature Method ◽

Generalized Differential

In this paper, free vibration analysis of rotating variable thickness annular bladed disk suitable to be used in aircraft gas turbine engine is investigated. The numerical generalized differential quadrature method is introduced in this paper as a fast and efficient numerical method to be used for vibration analysis of bladed disks of real gas turbine engines. The boundary conditions are supposed to be similar to those of the real bladed disk used in the aircraft engines i.e. clamped for the inner edge and free for the outer edge. Considering the thickness of the disk to vary as a power function and the blades of the bladed disk to be rigid, the numerical solution is performed and the effects of thickness variation, geometric parameters, angular velocity, and number of blades on the natural frequencies and critical speeds are investigated. The obtained numerical results are compared with those reported in the literature indicating a good agreement.

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