Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

Vyacheslav N. Burlayenko, Reijo Kouhia, Svetlana D. Dimitrova

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Abstract

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.

Original languageEnglish
Article number6446
JournalApplied Sciences
Volume14
Issue number15
DOIs
Publication statusPublished - Aug 2024
Publication typeA1 Journal article-refereed

Keywords

  • ABAQUS
  • axially functionally graded material
  • curvilinear tapered beam
  • differential transform method
  • free vibrations

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • General Materials Science
  • Instrumentation
  • General Engineering
  • Process Chemistry and Technology
  • Computer Science Applications
  • Fluid Flow and Transfer Processes

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