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.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren ◽  
Xiaoxiao Wu ◽  
Hongcan Ma
Keyword(s):  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Governing Equations ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Generalized Differential Quadrature Method ◽  
Thin Walled ◽  
Generalized Differential

A dynamical model is developed for the tapered composite thin-walled rotating shaft with shape memory alloy (SMA) wires embedded in. The SMA wires are embedded at an interlayer of the shaft and arranged along the conical surface of the tapered composite shaft. Recovery stresses generated during the phase transformation are calculated based on one-dimensional Brinson’s model. The governing equations are obtained based on a refined variational asymptotic method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential governing equations by using the generalized differential quadrature method (GDQM). Numerical results of natural frequencies and critical speeds are obtained. The effects of the fraction of SMA wires, the initial strain of SMA wires, temperature, ply angle, taper ratio, boundary conditions, and rotating speed on the frequency characteristics are investigated.

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.

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.

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.

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.

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