Analytical responses of functionally graded beam under moving mass using Caputo and Caputo–Fabrizio fractional derivative models

Abu-Alshaikh, Ibrahim; Almbaidin, Amro A.

doi:10.1177/1077546320908103

Cited by 4 publications

(2 citation statements)

References 35 publications

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“…The dynamic response of single-beam, double-beam, and multi-layer beam systems under the action of a moving mass, a moving load, or successive moving loads has been relatively well studied (Abu-Alshaikh and Almbaidin, 2020;Feng et al, 2020;Ghannadiasl and Khodapanah Ajirlou, 2020;Jiang et al, 2019aJiang et al, , 2019bJiang et al, , 2020Yau and Frýba, 2007). In contrast, further studies on the dynamic response of beam systems with uneven interlayer parameters are required.…”

Section: Introductionmentioning

confidence: 99%

Research on dynamic response of multi-layer beam system considering random interlayer parameters

Zhou

Jiang

et al. 2022

Journal of Vibration and Control

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To study the influence of interlayer stiffness and interlayer damping on the dynamic response of multi-layer beams under moving loads, a method for calculating the dynamic response of a multi-layer beam system considering random interlayer stiffness or random interlayer damping under successive moving loads based on the Karhunen–Loéve expansion and point estimation method is proposed. The accuracy of the proposed method was verified by using several numerical examples. The influence of interlayer stiffness, interlayer damping, standard deviation of interlayer stiffness, and standard deviation of interlayer damping on the dynamic response of a girder-rail system was analyzed by using the proposed calculation method. The results show that when the moving load velocity is high, the number of critical velocity of the rail significantly increases with decreasing interlayer stiffness. In addition, dynamic responses of the rail and girder increase with decreasing interlayer damping and the dynamic response of rail at the midspan significantly increases as the standard deviation of interlayer stiffness increases. Neglecting interlayer damping can lead to significant fluctuation in the dynamic response of rail, a significant increase in the number of critical velocity of rail, and increases in the dynamic responses of rail and girder. Changing interlayer stiffness, interlayer damping, standard deviation of interlayer stiffness, or standard deviation of interlayer damping will have no obvious influence on the dynamic response of girder.

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Section: Introductionmentioning

confidence: 99%

Research on dynamic response of multi-layer beam system considering random interlayer parameters

Zhou

Jiang

et al. 2022

Journal of Vibration and Control

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“…Faroughi et al (2020) studied wave propagation in 2D FG porous rotating nanobeams using a general nonlocal higher-order beam model. Abu-Alshaikh and Almbaidin (2020) used the Caputo and Caputo–Fabrizio fractional derivative models to investigate the response of the FG Euler beam under moving mass. Abida et al (2020) investigated a viscoelastic–viscoplastic model with hygromechanical coupling for flax fiber–reinforced polymer composites.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

Akbaş

Bashiri

Assie

et al. 2020

Journal of Vibration and Control

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This study presents dynamic responses of a composite thick beam with a functionally graded porous layer under dynamic sine pulse load. The boundary conditions of the composite beam are considered as viscoelastic supports. Three layers are considered, and face sheet layers have porous functionally graded materials in which the distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric distribution, X distribution, and ◊ distribution). The layered composite thick beam is modeled as a two-dimensional plane stress problem. The equation of motion is obtained by Lagrange’s equations. In formation of the problem, the finite element method is used with a 12-node 2D plane element. In the solution process of the dynamic problem, a numerical time integration method of the Newmark method is used. In numerical analyses, influences of stiffness and damping coefficients of viscoelastic supports, material gradation index, porosity parameter, and porosity models on the dynamic response of thick functionally graded porous beam are investigated under the pulse load.

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Analytical and FE modeling of a bi-directional functionally graded Timoshenko beam under thermomechanical loading

Omar,

Al-Huniti,

Al-Jeradat

2024

Eng. Res. Express

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Functionally graded materials (FGMs) have variable volume fractions in different directions, making structural analysis challenging due to shear deformation. This study investigates the behavior of a two-directional functionally graded material (TDFGM) Timoshenko beam under thermomechanical loads. Varied material properties in both axial and transverse directions are analyzed using a mathematical approach and a finite element model. The mathematical approach involves transforming the system of two ordinary differential equations to a single fourth-order differential equation to determine deflection and rotation. Additionally, a bilinear quadrilateral element is used to validate the mathematical solution. The results show that increasing grading parameters reduced transverse deflection, with a maximum reduction of 38.97% for CF beams and 39.26% for SS beams when the gradation index a z increased from 0 to 1 under mechanical loading. Under combined mechanical and thermal loading, higher temperatures on the beam’s hot side lead to increased deflection, with notable increases at higher gradation indices. Moreover, increased maximum deflection by 6.29% for CF beams and 4.05% for SS beams when considering temperature-dependent properties. It was observed that when TDFGM Timoshenko beams were heated for thermal loading, the SS beam deflected in the opposite direction of the applied mechanical load. The results agree with previous research and indicate alignment between mathematical and finite element solutions. The impact of boundary conditions on the deflection of Timoshenko beams made of TDFGM is discussed. The introduced methodology enhances TDFGM beam bending analysis, allowing control over behavior through grading parameters and boundary conditions selection.

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Analytical responses of functionally graded beam under moving mass using Caputo and Caputo–Fabrizio fractional derivative models

Cited by 4 publications

References 35 publications

Research on dynamic response of multi-layer beam system considering random interlayer parameters

Research on dynamic response of multi-layer beam system considering random interlayer parameters

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

Analytical and FE modeling of a bi-directional functionally graded Timoshenko beam under thermomechanical loading

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