An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft

Authors

DOI:

https://doi.org/10.13052/ejcm1779-7179.29461

Keywords:

Rotor Dynamics;, differential quadrature finite elements method;, differential quadrature hierarchical finite elements method;, hp-version of FEM;, on-board shaft

Abstract

In this paper the dynamic analysis of a shaft rotor whose support is mobile is studied. For the calculation of kinetic energy and stiffness energy, the beam theory of Euler Bernoulli was used, and the matrices of elements and systems are developed using two methods derived from the differential quadrature method (DQM). The first method is the Differential Quadrature Finite Element Method (DQFEM) systematically, as a combination of the Differential Quadrature Method (DQM) and the Standard Finite Element Method (FEM), which has a reduced computational cost for problems in dynamics. The second method is the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) which is used by expressing the matrices of the hierarchical finite element method in a similar form to that of the Differential Quadrature Finite Element Method and introducing an interpolation basis on the element boundary of the hierarchical finite element method. The discretization element used for both methods is a three-dimensional beam element. In the differential quadrature finite element method (DQFEM), the mass, gyroscopic and stiffness matrices are simply calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The sampling points are determined by the Gauss-Lobatto node method. In the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) the same approaches were used, and the cubic Hermite shape functions and the special Legendre polynomial Rodrigues shape polynomial were added. The assembly of the matrices for both methods (DQFEM and DQHFEM) is similar to that of the classical finite element method. The results of the calculation are validated with the h- and hp finite element methods and also with the literature.

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Author Biographies

Saimi Ahmed, Mechanical Systems & Materials Engineering Laboratory, University Abou Bekr Belkaid Tlemcen, Algeria

Saimi Ahmed obtained his Ph.D in Mechanics of Materials and Structures from the University of Tlemcen, Algeria, in 2017. He is currently a Senior Lecturer at the National High School of Hydraulics Blida, Algeria. A researcher member of Mechanical Systems and Structural Engineering Laboratory, IS2M/UABT. His research interests are: Finite element methods, Structural vibration, Structural dynamics, Dynamics of rotors, Dynamics of rotating machines, computational mechanics, FG materials, Composite materials.

Hadjoui Abdelhamid, Mechanical Systems & Materials Engineering Laboratory, University Abou Bekr Belkaid Tlemcen, Algeria

Hadjoui Abdelhamid obtained his Ph.D in mechanical engineering from the University of Tlemcen, Algeria. He is currently a professor at the University of Tlemcen, Algeria (UABT). Research Director in Mechanical Systems and Structural Engineering Laboratory, IS2M/UABT. His research interests are: Materials Engineering, Structural Engineering, Mechanical Engineering, Structural Analysis, Finite elements Modeling, Structural Dynamics, Simulation, Dynamic Analysis, Modal Analysis, Structural Vibration, Vibration Analysis.

Bensaid Ismail, Mechanical Systems & Materials Engineering Laboratory, University Abou Bekr Belkaid Tlemcen, Algeria

Bensaid Ismail received his B.Sc, M.Sc and Ph.D degrees in Mechanical Engineering from Abou Beckr Belkaid University Tlemcen, Algeria. He is currently working in the level of the Mechanical engineering department at the same University. Dr. Bensaid does research in Mechanical and structural Engineering, Materials, Composite, Maintenance, Nanostructures and Dynamical Systems. He, as an author/co-author, has published more than 18 articles in various journals.

Fellah Ahmed, Mechanical Systems & Materials Engineering Laboratory, University Abou Bekr Belkaid Tlemcen, Algeria

Fellah Ahmed obtained a Ph. D in rehabilitation and reliability of structures and mechanical equipment from the University of Tlemcen, Algeria, in 2019. He is currently a research associate in the laboratory of engineering of mechanical systems and structures, IS2M/UABT. His research interests are: Finite element methods, Structural vibration, Structural dynamics, Dynamics of rotors, Dynamics of rotating machines, computational mechanics, FG materials, Composite materials.

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Published

2021-05-13

How to Cite

Ahmed, S. ., Abdelhamid, H., Ismail, B., & Ahmed, F. (2021). An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft. European Journal of Computational Mechanics, 29(4-6), 303–344. https://doi.org/10.13052/ejcm1779-7179.29461

Issue

2020: Vol 29 Iss 4-6

Section

Original Article