Open Access iconOpen Access

ARTICLE

crossmark

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

Xiaojun Huang1, Liaojun Zhang2,*, Hanbo Cui1, Gaoxing Hu1

1 School of Architecture and Civil Engineering, Anhui Polytechnic University, Wuhu, 241000, China
2 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China

* Corresponding Author: Liaojun Zhang. Email: email

(This article belongs to the Special Issue: Recent Advances in Computational Methods for Performance Assessment of Engineering Structures and Materials against Dynamic Loadings)

Computer Modeling in Engineering & Sciences 2024, 140(2), 1647-1668. https://doi.org/10.32604/cmes.2024.049124

Abstract

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method (DQM) for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution. Firstly, based on the first-order shear deformation theory, the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement, transverse displacement, and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section. Then, ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section, the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement. Based on the differential quadrature method theory, the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations. Finally, the first several natural frequencies of the beam can be calculated. The feasibility and accuracy of the improved DQM are verified using the finite element method (FEM) and combined with the results of relevant literature.

Keywords


Cite This Article

APA Style
Huang, X., Zhang, L., Cui, H., Hu, G. (2024). Dynamic characteristics of functionally graded timoshenko beams by improved differential quadrature method. Computer Modeling in Engineering & Sciences, 140(2), 1647-1668. https://doi.org/10.32604/cmes.2024.049124
Vancouver Style
Huang X, Zhang L, Cui H, Hu G. Dynamic characteristics of functionally graded timoshenko beams by improved differential quadrature method. Comput Model Eng Sci. 2024;140(2):1647-1668 https://doi.org/10.32604/cmes.2024.049124
IEEE Style
X. Huang, L. Zhang, H. Cui, and G. Hu "Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method," Comput. Model. Eng. Sci., vol. 140, no. 2, pp. 1647-1668. 2024. https://doi.org/10.32604/cmes.2024.049124



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 295

    View

  • 140

    Download

  • 0

    Like

Share Link