Free Vibration Frequencies of a Variable Cross-Section Timoshenko-Ehrenfest Beam using Fourier-p Element

Bazoune, Abdelaziz

doi:10.1007/s13369-023-08289-4

Arab J Sci Eng

2024

DOI: 10.1007/s13369-023-08289-4

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Free Vibration Frequencies of a Variable Cross-Section Timoshenko-Ehrenfest Beam using Fourier-p Element

Abdelaziz Bazoune

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Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

Burlayenko,

Kouhia,

Dimitrova

2024

Applied Sciences

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The study focuses on the free vibration analysis of beams made of axially functionally graded materials (AFGM) with curvilinear variable cross-sections along their length. The beams encompass various shapes, including concave and convex conic sections, with axial material properties varying according to polynomial and exponential laws. The equations of motion are derived using Hamilton’s principle within the framework of Timoshenko beam theory. These governing equations, subjected to various boundary conditions, are solved using the differential transform method (DTM). The proposed solution technique is validated by comparing computed natural frequencies with the existing literature and results obtained using three-dimensional finite element analysis in ABAQUS. The incorporation of material gradients into the beam finite element models was achieved using the user-defined material subroutine (UMAT). Additionally, a comprehensive study is conducted to examine the influence of various factors on the natural frequencies of functionally graded beams. These factors include parameters of material laws, types of variable beam shapes, slenderness ratio, and specific boundary conditions. This study provides a thorough understanding of the modal dynamics of the considered beams, offering valuable insights into the behavior of FGM structures.

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Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

Burlayenko,

Kouhia,

Dimitrova

2024

Applied Sciences

View full text Add to dashboard Cite

show abstract

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Free Vibration Frequencies of a Variable Cross-Section Timoshenko-Ehrenfest Beam using Fourier-p Element

Cited by 1 publication

References 49 publications

Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

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