Open Access

ARTICLE

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

Xiaojun Huang¹, Liaojun Zhang^2,*, 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:

(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

Received 28 December 2023; Accepted 06 March 2024; Issue published 20 May 2024

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.

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Keywords

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