Nonlinear free vibration of laminated composite Euler-Bernoulli beams based on finite strain using generalized differential quadrature method

2016 ◽  
Vol 24 (11) ◽  
pp. 917-923 ◽  
Author(s):  
A. R. Ghasemi ◽  
M. Mohandes
Keyword(s):  
Free Vibration ◽  
Finite Strain ◽  
Differential Quadrature Method ◽  
Laminated Composite ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Nonlinear Free Vibration ◽  
Generalized Differential Quadrature Method ◽  
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.

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 Generalized Differential Quadrature Method for Free Vibration Analysis of a Rotating Composite Thin-Walled Shaft

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Rotating Speed ◽  
Generalized Differential Quadrature Method ◽  
Variational Asymptotic ◽  
Thin Walled ◽  
Generalized Differential

A refined variational asymptotic method (VAM) and Hamilton’s principle were used to establish the free vibration differential equations of a rotating composite thin-walled shaft with circumferential uniform stiffness (CUS) configuration. The generalized differential quadrature method (GDQM) was adopted to discretize and solve the governing equations. The accuracy and efficiency of the GDQM were validated in analyzing the frequency of a rotating composite shaft. Compared to the available results in literature, the computational results by the GDQM are accurate. In addition, effects of boundary conditions, rotating speed, ply angle, ratio of radius over thickness, and ratio of length over radius on the frequency characteristics were also investigated.

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