Indian Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access

Application of Differential Quadrature Method to Investigate Dynamics of a Curved Beam Structure Acted upon by a Moving Concentrated Load


Affiliations
1 Department of Civil Engineering, University of Science and Culture, Tehran, Iran, Islamic Republic of
2 Departments of Civil Engineering, Sharif University of Technology, Tehran, Iran, Islamic Republic of
 

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM) in the associated problem is explored. In the structural problems with specific geometry, use of DQM which is independent of domain discretization, is proved to be efficient.

Keywords

Differential Quadrature Method (dqm), Semicircular Curved Beam, Moving Load,Galerkin Method, FiniteElement Method
User

  • Bellman R and Casti J (1971) Differential quadrature and long-term integration. J. Maths. Analysis &Appli . 34, 235-238.

  • Bellman R, Kashef BG and Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Computational Phys. 10, 40-52.

  • Bert CW, Jang SK and Striz AG (1988) Two new approximate methods for analyzing free vibration of structural components. AIAA J. 26, 612-618.

  • Fryba L (1999) Vibration of solids and structures under moving loads. Thomas Telford, London.

  • Jang SK, Bert CW and Striz AG (1989) Application of differential quadrature to deflection and buckling of structural components. Intl. J. Numerical Methods Engg. 28, 561-577.

  • Laura P.A.A and Gutierrez R.H (1993) Analysis of vibrating Timoshenko beams using the method of differential quadrature. Shock & Vibration. 1, 89-93.

  • Liu G.R and Wu T.Y (2001) Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition. J. Sound & Vibration. 246, 461-481.

  • Shu C (2000) Differential Quadrature and its application in engineering. Springer. London.

  • Shu C (1991) Generalized differential–integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD thesis. Univ. Glasgow, Scotland.

  • Tsumura T (1956) Strength Design Data Book. Shokabo Publ. Co. Ltd. Tokyo.

  • Wang X, Liu F, Wang X and Gan L (2005) New approaches in application of differential quadrature method to fourth-order differential equations. Commun. Numerical Methods in Engg. 21, 61-71.


Abstract Views: 532

PDF Views: 573




  • Application of Differential Quadrature Method to Investigate Dynamics of a Curved Beam Structure Acted upon by a Moving Concentrated Load

Abstract Views: 532  |  PDF Views: 573

Authors

Ali Nikkhoo
Department of Civil Engineering, University of Science and Culture, Tehran, Iran, Islamic Republic of
Hassan Kananipour
Department of Civil Engineering, University of Science and Culture, Tehran, Iran, Islamic Republic of
Hossein Chavoshi
Department of Civil Engineering, University of Science and Culture, Tehran, Iran, Islamic Republic of
Raham Zarfam
Departments of Civil Engineering, Sharif University of Technology, Tehran, Iran, Islamic Republic of

Abstract


Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM) in the associated problem is explored. In the structural problems with specific geometry, use of DQM which is independent of domain discretization, is proved to be efficient.

Keywords


Differential Quadrature Method (dqm), Semicircular Curved Beam, Moving Load,Galerkin Method, FiniteElement Method

References





DOI: https://doi.org/10.17485/ijst%2F2012%2Fv5i8%2F30519