Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Mechanics of Composite Materials
Published in: Mechanics of Composite Materials 1/2024

26-02-2024

One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections

Authors: V. N. Burlayenko, R. Kouhia, S. D. Dimitrova

Published in: Mechanics of Composite Materials | Issue 1/2024

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A comparison of one-dimensional (1D) and three-dimensional (3D) models for simulating free vibrations of axially functionally graded material (AFGM) beams with non-uniform cross-sections was carried out. Both models were constructed using ABAQUS and the eigenvalue problem was solved to determine the natural frequencies and their corresponding mode shapes. User-defined material model subroutines (UMAT) were developed using 1D beam or 3D hexagonal graded finite elements to implement material gradients into appropriate finite element models. The performance of both models was evaluated using data for beams with non-uniform cross-sections and material gradation profiles for which natural frequencies were available in the literature. The accuracy and effectiveness of each modeling approach proposed were estimated by comparing the results obtained. Generally, distinctions between the 1D and 3D models become more pronounced as the geometric complexity and material inhomogeneity of AFGM beams increases, especially for high-frequency modes.
previous article Loading Capacities of Bonded Composite Pipe Joints of Different Structures
next article Investigation of the Effect of Adding Waste Eggshell Particles to a Resin Used for SLA Printing Applications

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
E. H. Atkin, “Tapered beams: suggested solutions for some typical aircraft cases,” Aircr. Eng. Aerosp. Technol., 10, No. 11, 347-351 (1938).CrossRef
2.
J. R. Banerjee and A. Ananthapuvirajah, “Free flexural vibration of tapered beams,” Comput. Struct., 224, 1-6 (2019).CrossRef
3.
R. Attarnejad, A. Shahba, and M. Eslaminia, “Dynamic basic displacement functions for free vibration analysis of tapered beams,” J. Vib. Control., 17, No. 14, 2222-2238 (2011).MathSciNetCrossRef
4.
G. Jaiani, “On cusped shell-like structures”, In: H. Altenbach, V. Eremeyev, (eds), Shell-Like Structures. Adv. Struct. Mater., Vol. 15, Springer, Berlin - Heidelberg (2011), pp. 63-74.
5.
G. Jaiani, Cusped Shell-like Structures, Springer Briefs in Applied Science and Technology, Springer-Heidelberg-Dordrecht-London-New York (2011).
6.
M. Koizumi, “FGM activities in Japan”, Compos. Part B, 28, Nos. 1-2, 1-4 (1997).CrossRef
7.
V. N. Burlayenko, H. Altenbach, and T. Sadowski, “Dynamic fracture analysis of sandwich composites with face sheet/core debond by the finite element method”, in: H. Altenbach, V. Belyaev, V. Eremeyev, V. Krivtsov, A. Porubov(eds.), Dynamical Processes in Generalized Continua and Structures. Adv. Struct. Mater., 103, Springer, Cham (2019), pp. 163-194.
8.
Z. Z. Wang, J. Zhao, X. Ma et al., “Numerical simulation of progressive delamination in composite laminates under mode I and mode II loadings”, Mech. Compos. Mater., 56, 735-746 (2021).ADSCrossRef
9.
C. Frey, J. Hahn, N. Schneider, et al., “A layerwise higher-order approach for the free-edge effect in angle-ply laminates,” Mech. Compos. Mater., 59, 299-318 (2023).ADSCrossRef
10.
I. M. El-Galy, B. I. Saleh, and M. H. Ahmed, “Functionally graded materials classifications and development trends from industrial point of view,” SN Appl. Sci., 1, 1-23 (2019).CrossRef
11.
I. Elishakoff and Z. Guédé, “Analytical polynomial solutions for vibrating axially graded beams,” Mech. Adv. Mater. Struct., 11, 517-533 (2004).CrossRef
12.
Q. S. Li, “A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness,” Int. J. Solids Struct., 37, 5123-5141 (2000).CrossRef
13.
W. R. Chen and H. Chang, “Closed-form solutions for free vibration frequencies of functionally graded Euler-Bernoulli beams,” Mech. Compos. Mater., 53, 79-98 (2017).ADSCrossRef
14.
A. Y. Tang, J. X. Wu, X. F. Li, and K. Y. Lee, “Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams,” Int. J. Mech. Sci., 89, 1-11 (2014).CrossRef
15.
Y. Huang and X.-F. Li, “A new approach for free vibration of axially functionally graded beams with non-uniform cross-section,” J. Sound Vib., 329, 2291-2303 (2010).ADSCrossRef
16.
H. Hein and L. Feklistova, “Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets,” Eng. Struct., 33, 3696-3701 (2011).CrossRef
17.
J. K. Lee and B. K. Lee, “Coupled flexural-torsional free vibration of an axially functionally graded circular curved beam,” Mech. Compos. Mater., 57, 833-846 (2022).ADSCrossRef
18.
S. Rajasekaran, “Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams,” Int. J. Mech. Sci., 74, No. 3, 15-31 (2013).CrossRef
19.
D. Ghazaryan, V. N. Burlayenko, A. Avetisyan, and A. Bhaskar, “Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method,” J. Eng. Math., 110, No.1, 97-121 (2018).MathSciNetCrossRef
20.
P. Liu, K. Lin, H. Liu, and R. Qin, “Free transverse vibration analysis of axially functionally graded tapered Euler-Bernoulli beams through spline finite point method,” Shock Vib., 2016, 1-23 (2016).CrossRef
21.
Y. Chen, S. Dong, Z. Zang, et al. “Free transverse vibrational analysis of axially functionally graded tapered beams via the variational iteration approach,” J. Vib. Control., 27, No. 11-12, 1265-1280 (2021).MathSciNetCrossRef
22.
M. S. Sari and S. Al-Dahidi, “Vibration characteristics of multiple functionally graded nonuniform beams,” J. Vib. Control., 27, No. 19-20, 2205-2218 (2021).MathSciNetCrossRef
23.
J. Fang, D. Zhou, and Y. Dong, “Three-dimensional vibration of rotating functionally graded beams,” J. Vib. Control, 24, No. 15, 3292-3306 (2018).MathSciNetCrossRef
24.
M. Chen, G. Jin, Y. Zhang, F. Niu, and Z. Liu, “Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thickness,” Compos. Struct., 207, 304-322 (2019).CrossRef
25.
M. Soltani and B. Asgarian, “Lateral-torsional stability analysis of a simply supported axially functionally graded beam with a tapered I-section,” Mech. Compos. Mater., 56, 39-54 (2020).ADSCrossRef
26.
J.-H. Kim and G. H. Paulino, “Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials,” J. Appl. Mech., 69, No. 4, 502-514 (2002).ADSCrossRef
27.
M. H. Santare and J. Lambros, “Use of graded finite elements to model the behavior of nonhomogeneous materials”, J. Appl. Mech., 67, No. 4, 819-822 (2000).ADSCrossRef
28.
C.-E. Rousseau and H. V. Tippur, “Compositionally graded materials with cracks normal to the elastic gradient,” Acta Mater., 48, 4021-4033 (2000).ADSCrossRef
29.
A. Hajlaoui, E. Chebbi, M. Wali, and F. Dammak, “Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain,” Eng. Comput., 37, No. 3, 823-849 (2020).CrossRef
30.
A. Chaker, S. Koubaa, J. Mars et al. “An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates,” Eng. Comput., 37, 2145-2157 (2021).CrossRef
31.
V. N. Burlayenko, H. Altenbach, and S. D. Dimitrova, “A material model-based finite element free vibration analysis of one-, two- and three-dimensional axially FGM beams,” Proc. IEEE 2nd KhPI Week on Advanced Technology (KhPIWeek), Kharkiv, Ukraine (2021), pp. 628-633.
32.
V. N. Burlayenko, “Modelling thermal shock in functionally graded plates with finite element method,” Adv. Mater. Sci. Eng., 2016, 1-16 (2016).CrossRef
33.
V. N. Burlayenko, T. Sadowski, H. Altenbach, and S. Dimitrova, “Three-dimensional finite element modelling of free vibrations of functionally graded sandwich panels”, In: H. Altenbach, J. Chróścielewski, V. Eremeyev, K. Wiśniewski (eds.), Recent Developments in the Theory of Shells. Adv. Struct. Mater., 110, Springer, Cham (2019), pp. 157-177.
34.
V.N. Burlayenko, “A continuum shell element in layerwise models for free vibration analysis of FGM sandwich panels”, Continuum Mech. Thermodyn., 33, 1385-1407 (2021).ADSMathSciNetCrossRef
35.
E. J. Barbero, Finite Element Analysis of Composite Materials using Abaqus, (1st ed.), CRC Press, Boca Raton-London-New York (2013).CrossRef
36.
ABAQUS User’s Manual, Version 2016. Dassault Systèmes Simulia Corp., Providence, RI, USA (2016).
Metadata
Title
One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections
Authors
V. N. Burlayenko
R. Kouhia
S. D. Dimitrova
Publication date
26-02-2024
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 1/2024
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-024-10176-4

Other articles of this Issue 1/2024

Mechanics of Composite Materials 1/2024 Go to the issue

OriginalPaper

Effect of Mechanical Vibration and Impact Loading on the Performance of Poly (Vinylidene Fluoride) Composite

OriginalPaper

Mechanical Properties of Alfa, Sisal, and Hybrid Alfa/Sisal Fiber Satin Cloth Reinforced Epoxy

OriginalPaper

Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass

OriginalPaper

Investigation of Reinforcement Around the Lightening Hole in Composite Plates Under Tension and Shear Loads

OriginalPaper

Investigation of the Effect of Adding Waste Eggshell Particles to a Resin Used for SLA Printing Applications

OriginalPaper

Vibration Analysis of Shearable Composite Annular Plates Reinforced by Graphene Nanoplatelets Using the Differential Quadrature Method

Premium Partners

    Image Credits