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Journal articles on the topic 'Generalized differential quadrature method'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Chen, Chang-New. "A generalized differential quadrature element method." Computer Methods in Applied Mechanics and Engineering 188, no. 1-3 (2000): 553–66. http://dx.doi.org/10.1016/s0045-7825(99)00283-2.

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2

Du, H., K. M. Liew, and M. K. Lim. "Generalized Differential Quadrature Method for Buckling Analysis." Journal of Engineering Mechanics 122, no. 2 (1996): 95–100. http://dx.doi.org/10.1061/(asce)0733-9399(1996)122:2(95).

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3

Loy, C. T., K. Y. Lam, and C. Shu. "Analysis of Cylindrical Shells Using Generalized Differential Quadrature." Shock and Vibration 4, no. 3 (1997): 193–98. http://dx.doi.org/10.1155/1997/538754.

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The analysis of cylindrical shells using an improved version of the differential quadrature method is presented. The generalized differential quadrature (GDQ) method has computational advantages over the existing differential quadrature method. The GDQ method has been applied in solutions to fluid dynamics and plate problems and has shown superb accuracy, efficiency, convenience, and great potential in solving differential equations. The present article attempts to apply the method to the solutions of cylindrical shell problems. To illustrate the implementation of the GDQ method, the frequenci

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4

Hajhosseini, Mohammad. "Analysis of complete vibration bandgaps in a new periodic lattice model using the differential quadrature method." Journal of Vibration and Control 26, no. 19-20 (2020): 1708–20. http://dx.doi.org/10.1177/1077546320902549.

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In this study, a new periodic lattice model with special vibration-absorbing properties is introduced. This periodic structure consists of the connected beam elements with circular cross-sections. Four models with different sets of cross-sectional radii are considered for this periodic lattice. The theoretical equations of longitudinal, torsional, and transverse vibrations of beams are solved using the combination of generalized differential quadrature and generalized differential quadrature rule methods to calculate the first three complete bandgaps. Investigating the effects of geometrical p

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5

Marzani, Alessandro, Francesco Tornabene, and Erasmo Viola. "Nonconservative stability problems via generalized differential quadrature method." Journal of Sound and Vibration 315, no. 1-2 (2008): 176–96. http://dx.doi.org/10.1016/j.jsv.2008.01.056.

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6

Bota, Constantin, Bogdan Căruntu, Mădălina Sofia Paşca, Dumitru Ţucu, and Marioara Lăpădat. "Least Squares Differential Quadrature Method for the Generalized Bagley–Torvik Fractional Differential Equation." Mathematical Problems in Engineering 2020 (July 16, 2020): 1–7. http://dx.doi.org/10.1155/2020/4806387.

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In this paper, the least squares differential quadrature method for computing approximate analytical solutions for the generalized Bagley–Torvik fractional differential equation is presented. This new method is introduced as a straightforward and accurate method, fact proved by the examples included, containing a comparison with previous results obtained by using other methods.

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7

Ferreira, A. J. M., E. Viola, F. Tornabene, N. Fantuzzi, and A. M. Zenkour. "Analysis of Sandwich Plates by Generalized Differential Quadrature Method." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/964367.

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We combine a layer-wise formulation and a generalized differential quadrature technique for predicting the static deformations and free vibration behaviour of sandwich plates. Through numerical experiments, the capability and efficiency of this strong-form technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.

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8

Du, H., M. K. Lim, and R. M. Lin. "Application of generalized differential quadrature method to structural problems." International Journal for Numerical Methods in Engineering 37, no. 11 (1994): 1881–96. http://dx.doi.org/10.1002/nme.1620371107.

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9

Yuan, Haiyan, and Cheng Song. "Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/679075.

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This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of(k,l)-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a(k,l)-algebraically stable two-step Runge-Kutta method with0<k<1is proved. For the convergence, the concepts ofD-convergence, diagonally stable, and generalized stage order are firstly introduced; then it is proved by some theorems that if a two-step Runge-Kutta method is algeb

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10

Sari, Murat, and Gürhan Gürarslan. "Numerical Solutions of the Generalized Burgers-Huxley Equation by a Differential Quadrature Method." Mathematical Problems in Engineering 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/370765.

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Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation i

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11

Shahverdi, H., V. Khalafi, and S. Noori. "Aerothermoelastic Analysis of Functionally Graded Plates Using Generalized Differential Quadrature Method." Latin American Journal of Solids and Structures 13, no. 4 (2016): 796–818. http://dx.doi.org/10.1590/1679-78252072.

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12

Mokhtari, R., A. Samadi Toodar, and N. G. Chegini. "Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations." Communications in Theoretical Physics 56, no. 6 (2011): 1009–15. http://dx.doi.org/10.1088/0253-6102/56/6/06.

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13

Ng, T. Y., Li Hua, K. Y. Lam, and C. T. Loy. "Parametric instability of conical shells by the Generalized Differential Quadrature method." International Journal for Numerical Methods in Engineering 44, no. 6 (1999): 819–37. http://dx.doi.org/10.1002/(sici)1097-0207(19990228)44:6<819::aid-nme528>3.0.co;2-0.

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14

Moslemi Petrudi, Amin, Masoud Rahmani, and Ionut Cristian Scurtu. "Analytical Study of Dynamic and Vibrational of Composite Shell with Piezoelectric Layer using GDQM Method." Technium: Romanian Journal of Applied Sciences and Technology 4, no. 7 (2022): 22–39. http://dx.doi.org/10.47577/technium.v4i7.7160.

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Piezoelectric materials, due to their electromechanical coupling properties, are widely used as actuators and sensors in intelligent structures to control vibrations and bends of multilayer sheets with piezoelectric layers. In this paper, the response of free vibrations of a multilayer composite shell with the new Generalized Differential Quadrature Method (GDQM) for different boundary conditions is investigated. The governing equations are obtained by assuming first-order shear theory and using Hamilton's principle. The generalized quadrature differential method is used to solve the obtained

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15

Moslemi Petrudi, Amin, Masoud Rahmani, and Ionut Cristian Scurtu. "Analytical Study of Dynamic and Vibrational of Composite Shell with Piezoelectric Layer using GDQM Method." Technium: Romanian Journal of Applied Sciences and Technology 4, no. 7 (2022): 22–39. http://dx.doi.org/10.47577/technium.v4i7.7160.

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Piezoelectric materials, due to their electromechanical coupling properties, are widely used as actuators and sensors in intelligent structures to control vibrations and bends of multilayer sheets with piezoelectric layers. In this paper, the response of free vibrations of a multilayer composite shell with the new Generalized Differential Quadrature Method (GDQM) for different boundary conditions is investigated. The governing equations are obtained by assuming first-order shear theory and using Hamilton's principle. The generalized quadrature differential method is used to solve the obtained

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16

Bhrawy, Ali H., Abdulrahim AlZahrani, Dumitru Baleanu, and Yahia Alhamed. "A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/692193.

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The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss coll

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17

El-Kady, M., S. M. El-Sayed, and H. E. Fathy. "Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/165492.

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Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.

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18

Kuang, J. H., and M. H. Hsu. "Eigensolutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method." Journal of Engineering for Gas Turbines and Power 124, no. 4 (2002): 1011–17. http://dx.doi.org/10.1115/1.1492833.

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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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19

Mustafa, Abdelfattah, Reda S. Salama, and Mokhtar Mohamed. "Analysis of Generalized Nonlinear Quadrature for Novel Fractional-Order Chaotic Systems Using Sinc Shape Function." Mathematics 11, no. 8 (2023): 1932. http://dx.doi.org/10.3390/math11081932.

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This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine shape function, which is used in combination with the fractional operator of the generalized Caputo kind to convert nonlinear fractional differential equations into a nonlinear algebraic system. The nonlinearity problem is then solved using an iterative approach. Numerical results for a variety of chaotic systems

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20

Golkaram, M., and MM Aghdam. "Free transverse vibration analysis of thin rectangular plates locally suspended on elastic beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 7 (2012): 1515–24. http://dx.doi.org/10.1177/0954406212462204.

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Free transverse vibration of thin rectangular plates locally suspended on deformable beam is presented using generalized differential quadrature method. The plate is completely free at all edges except a local region which is attached to a thin beam with rectangular cross section. The other side of the beam is fixed and the whole system is subjected to free transverse vibrations. According to classical plate theory and Euler–Bernoulli beam assumption, two coupled partial differential equations of the system are obtained. The governing equations and solution domain are discretized based on the

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21

Demir, Ozgur, Demet Balkan, Rahim Can Peker, Muzaffer Metin, and Aytac Arikoglu. "Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method." Journal of Sandwich Structures & Materials 22, no. 3 (2018): 743–70. http://dx.doi.org/10.1177/1099636218767491.

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This paper focuses on the vibration analysis of three-layered curved sandwich beams with elastic face layers and viscoelastic core. First, the equations of motion that govern the free vibrations of the curved beams together with the boundary conditions are derived by using the principle of virtual work, in the most general form. Then, these equations are solved by using the generalized differential quadrature method in the frequency domain, for the first time to the best of the authors’ knowledge. Verification of the proposed beam model and the generalized differential quadrature solution is c

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22

Hsu, Ming-Hung. "Vibration Analysis of Annular Plates Using the Modified Generalized Differential Quadrature Method." Journal of Applied Sciences 6, no. 7 (2006): 1591–95. http://dx.doi.org/10.3923/jas.2006.1591.1595.

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23

Barulina, M. A. "Application of Generalized Differential Quadrature Method to Two-dimensional Problems of Mechanics." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 18, no. 2 (2018): 206–16. http://dx.doi.org/10.18500/1816-9791-2018-18-2-206-216.

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24

Arikoglu, A., and I. Ozkol. "Vibration Analysis of Composite Sandwich Plates by the Generalized Differential Quadrature Method." AIAA Journal 50, no. 3 (2012): 620–30. http://dx.doi.org/10.2514/1.j051287.

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25

Panmei, Meirikim, and Roshan Thoudam. "A local differential quadrature method for the generalized nonlinear Schrödinger (GNLS) equation." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 14, no. 4 (2024): 394–403. http://dx.doi.org/10.11121/ijocta.1546.

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A local differential quadrature method based on Fourier series expansion numerically solves the generalized nonlinear Schrodinger equation. For time integration, a Runge-Kutta fourth-order method is used. Matrix stability analysis is used to examine the method's stability. Three test problems involving the motion of a single solitary wave, the interaction of two solitary waves, and a solution that blows up in finite time, respectively, demonstrate the accuracy and efficiency of the provided method. Finally, the numerical results obtained from the presented method are compared with the exact so

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26

Akbaş, Şeref. "Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method." International Journal Of Engineering & Applied Sciences 8, no. 2 (2016): 30. http://dx.doi.org/10.24107/ijeas.252143.

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27

Fereidoon, A., M. Asghardokht seyedmahalle, and A. Mohyeddin. "Bending analysis of thin functionally graded plates using generalized differential quadrature method." Archive of Applied Mechanics 81, no. 11 (2011): 1523–39. http://dx.doi.org/10.1007/s00419-010-0499-3.

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28

LAM, K. Y., H. LI, T. Y. NG, and C. F. CHUA. "GENERALIZED DIFFERENTIAL QUADRATURE METHOD FOR THE FREE VIBRATION OF TRUNCATED CONICAL PANELS." Journal of Sound and Vibration 251, no. 2 (2002): 329–48. http://dx.doi.org/10.1006/jsvi.2001.3993.

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29

Ahmad, Imtiaz, Sayed Abdel-Khalek, Ahmed Alghamdi, and Mustafa Inc. "Numerical simulation of the generalized Burger’s-Huxley equation via two meshless methods." Thermal Science 26, Spec. issue 1 (2022): 463–68. http://dx.doi.org/10.2298/tsci22s1463a.

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Numerical solution of the generalized Burger?s-Huxley equation is established utilizing two effective meshless methods namely: local differential quadrature method and global method of line. Both the proposed meshless methods used radial basis functions to discretize space derivatives which convert the given model equation system of ODE and then we have utilized the Euler method to get the required numerical solution. Numerical experiments are carried out to check the efficiency and accuracy of the suggested meshless methods.

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30

Chang-New Chen. "Differential Quadrature, Generalized Methods, Related Discrete Element Analysis Methods And EDQ Based Time Integration Method." Recent Patents on Engineering 1, no. 2 (2007): 163–76. http://dx.doi.org/10.2174/187221207780832147.

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31

Geeta Arora and Varun Joshi. "Simulation of Generalized Nonlinear Fourth Order Partial Differential Equation with Quintic Trigonometric Differential Quadrature Method." Mathematical Models and Computer Simulations 11, no. 6 (2019): 1059–83. http://dx.doi.org/10.1134/s207004821906005x.

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32

Ng, T. Y., H. Li, K. Y. Lam, and C. F. Chua. "Frequency Analysis of Rotating Conical Panels: A Generalized Differential Quadrature Approach." Journal of Applied Mechanics 70, no. 4 (2003): 601–5. http://dx.doi.org/10.1115/1.1577600.

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Based on the generalized differential quadrature (GDQ) method, this paper presents, for the first instance, the free-vibration behavior of a rotating thin truncated open conical shell panel. The present governing equations of free vibration include the effects of initial hoop tension and the centrifugal and Coriolis accelerations due to rotation. Frequency characteristics are obtained to study in detail the influence of panel parameters and boundary conditions on the frequency characteristics. Further, qualitative differences between the vibration characteristics of rotating conical panels and

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33

Abdelfattah, Waleed Mohammed, Ola Ragb, Mokhtar Mohamed, Mohamed Salah, and Abdelfattah Mustafa. "Quadrature Solution for Fractional Benjamin–Bona–Mahony–Burger Equations." Fractal and Fractional 8, no. 12 (2024): 685. http://dx.doi.org/10.3390/fractalfract8120685.

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In this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo sense, classical differential quadrature method, and discrete singular convolution methods based on two different kernels. Also, the solution strategy is to apply perturbation analysis or an iterative method to reduce the problem to a series of linear initial boundary value problems. Consequently, w

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34

Fazilati, Jamshid, Vahid Khalafi, and Hossein Shahverdi. "Three-dimensional aero-thermo-elasticity analysis of functionally graded cylindrical shell panels." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 5 (2018): 1715–27. http://dx.doi.org/10.1177/0954410018763861.

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In the present paper, the aero-thermo-elastic behavior of a finite (three-dimensional) cylindrical curved panel geometry made from functionally graded material under high supersonic airflow is investigated. A generalized differential quadrature formulation is adopted while a steady-state through-the-thickness thermal field is also assumed. The geometry curvature and structural nonlinearity effects are included based on von Karman–Donnell strain–displacement relations. The nonlinear piston theory of third order is utilized in order to predict the unsteady aerodynamics loads induced from surroun

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35

sarvari, ‎Zahra‎‎ ‎., Mojtaba Ranjbar, and Shahram Rezapour. "Polynomial differential quadrature method for numerical solution of the generalized Black-Scholes ‎equation." Mathematical Analysis and Convex Optimization 2, no. 1 (2021): 119–30. http://dx.doi.org/10.52547/maco.2.1.12.

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36

Keleshteri, M. M., and J. Jelovica. "Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method." Engineering Structures 252 (February 2022): 113666. http://dx.doi.org/10.1016/j.engstruct.2021.113666.

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37

Khaniki, H. Bakhshi, Sh Hosseini-Hashemi, and A. Nezamabadi. "Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method." Alexandria Engineering Journal 57, no. 3 (2018): 1361–68. http://dx.doi.org/10.1016/j.aej.2017.06.001.

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38

Ebrahimi, Farzad, Navvab Shafiei, Mohammad Kazemi, and Seyed Mostafa Mousavi Abdollahi. "Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method." Mechanics of Advanced Materials and Structures 24, no. 15 (2016): 1257–73. http://dx.doi.org/10.1080/15376494.2016.1227499.

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39

Mokhtari, R., A. Samadi Toodar, and N. G. Chegini. "Numerical Simulation of Coupled Nonlinear Schrödinger Equations Using the Generalized Differential Quadrature Method." Chinese Physics Letters 28, no. 2 (2011): 020202. http://dx.doi.org/10.1088/0256-307x/28/2/020202.

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40

Shahverdi, Hossein, and Mohammad M. Navardi. "Free vibration analysis of cracked thin plates using generalized differential quadrature element method." Structural Engineering and Mechanics 62, no. 3 (2017): 345–55. http://dx.doi.org/10.12989/sem.2017.62.3.345.

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41

Jane, K. C., and C. C. Hong. "Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method." Mechanics Research Communications 27, no. 2 (2000): 157–64. http://dx.doi.org/10.1016/s0093-6413(00)00076-8.

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42

Fantuzzi, Nicholas, Francesco Tornabene, and Erasmo Viola. "Generalized Differential Quadrature Finite Element Method for vibration analysis of arbitrarily shaped membranes." International Journal of Mechanical Sciences 79 (February 2014): 216–51. http://dx.doi.org/10.1016/j.ijmecsci.2013.12.008.

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43

Girgin, Zekeriya. "Solution of the Blasius and Sakiadis equation by generalized iterative differential quadrature method." International Journal for Numerical Methods in Biomedical Engineering 27, no. 8 (2009): 1225–34. http://dx.doi.org/10.1002/cnm.1354.

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44

Esmaiili, M., G. Rezazadeh, R. Sotudeh-Gharebagh, and A. Tahmasebi. "Modeling of the Seedless Grape Drying Process using the Generalized Differential Quadrature Method." Chemical Engineering & Technology 30, no. 2 (2007): 168–75. http://dx.doi.org/10.1002/ceat.200600151.

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45

Fung, T. C. "Generalized Lagrange functions and weighting coefficient formulae for the harmonic differential quadrature method." International Journal for Numerical Methods in Engineering 57, no. 3 (2003): 415–40. http://dx.doi.org/10.1002/nme.692.

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46

Viola, Erasmo, Francesco Tornabene, and Nicholas Fantuzzi. "Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape." Composite Structures 106 (December 2013): 815–34. http://dx.doi.org/10.1016/j.compstruct.2013.07.034.

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47

Chen, Lidao, and Yong Liu. "Differential Quadrature Method for Fully Intrinsic Equations of Geometrically Exact Beams." Aerospace 9, no. 10 (2022): 596. http://dx.doi.org/10.3390/aerospace9100596.

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In this paper, a differential quadrature method of high-order precision (DQ−Pade), which is equivalent to the generalized Pade approximation for approximating the end of a time or spatial interval, is used to solve nonlinear fully intrinsic equations of beams. The equations are a set of first-order differential equations with respect to time and space, and the explicit unknowns of the equations involve only forces, moments, velocity and angular velocity, without displacements and rotations. Based on the DQ−Pade method, the spatial and temporal discrete forms of fully intrinsic equations were d

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48

Ansari, R., J. Torabi, and M. Faghih Shojaei. "Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach." Journal of Vibration and Control 24, no. 6 (2016): 1123–44. http://dx.doi.org/10.1177/1077546316659172.

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Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature met

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49

Maarefdoust, Mahdi, and Mehran Kadkhodayan. "Nonlinear elastic/plastic buckling analysis of thick/thin skew plates under uniaxial and biaxial loading." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 16 (2014): 2854–67. http://dx.doi.org/10.1177/0954406214564411.

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In this study, elastic/plastic buckling analysis of thick skew plates subjected to uniaxial compression or biaxial compression/tension loading using the generalized differential quadrature method is presented for the first time. The governing differential equations are derived based on the incremental and deformation theories of plasticity and first-order shear deformation theory. The elastic/plastic behavior of the plates is described by the Ramberg–Osgood model. Generalized differential quadrature discretization rules in association with an exact coordinate transformation are simultaneously

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50

Zhong, Weiyan, Feng Gao, and Yongsheng Ren. "Generalized Differential Quadrature Method for Free Vibration Analysis of a Rotating Composite Thin-Walled Shaft." Mathematical Problems in Engineering 2019 (March 20, 2019): 1–16. http://dx.doi.org/10.1155/2019/1538329.

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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

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