Title: Analysing the dynamic behaviour of a functionally graded beam subjected to a moving force under varied boundary conditions

Authors: Mohamed Bouamama; Abbes Elmeiche; Azzeddine Belaziz; Abdelhak El Hannani; Hammoudi Abderazek

Addresses: Center of Research in Mechanics (CRM), BP N73B, Frres Ferrad, Ain El Bey, 25021 Constantine, Algeria ' Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Djillali Liabes of Sidi Bel Abbes, B.P. 89 Cité Ben M'Hidi, Sidi Bel, Abbes 22000, Algeria ' Center of Research in Mechanics (CRM), BP N73B, Frres Ferrad, Ain El Bey, 25021 Constantine, Algeria ' Ahmed Ben Yahia El Wancharissi University-Tissemsilt, BP 182, Road Bougara, Tissemsilt, Algeria ' Center of Research in Mechanics (CRM), BP N73B, Frres Ferrad, Ain El Bey, 25021 Constantine, Algeria

Abstract: In this article, the dynamics of both free and forced vibrations in functionally graded materials (FGM) beams are explored by examining various physical and geometrical parameters under different boundary conditions. The beam's material properties feature an upper ceramic facet and a lower metal facet, which vary continuously through the thickness direction following a power law function for the functionally graded materials (P-FGM). The external force is determined by a moving concentrated force, with or without considering the inertial effects of the transient load. The governing differential equations are derived through a theoretical formulation using the logarithmic shear function of the beam (LSDBT). For the study of free vibrations, an analytical method is employed, which involves separating variables and applying the modal approximation method of Rayleigh-Ritz. Numerical calculations are used to analyse forced vibrations, utilising Newmark's temporal method. A parametric investigation is conducted on different beam configurations to assess the impact of various parameters on the dynamic responses of the beam. The results from our proposed model demonstrate a strong agreement with the findings in the literature, validating the effectiveness and accuracy of our approach.

Keywords: FGM beams; free vibration; forced vibrations; moving force; eigenfrequencies; LSDBT.

DOI: 10.1504/IJSTRUCTE.2024.139781

International Journal of Structural Engineering, 2024 Vol.14 No.3, pp.271 - 290

Received: 19 Dec 2023
Accepted: 14 Feb 2024
Published online: 05 Jul 2024 *

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