Skip to main content
Erschienen in: Meccanica 1/2014

01.01.2014

Static and vibration analysis of functionally graded beams using refined shear deformation theory

verfasst von: Thuc P. Vo, Huu-Tai Thai, Trung-Kien Nguyen, Fawad Inam

Erschienen in: Meccanica | Ausgabe 1/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Static and vibration analysis of functionally graded beams using refined shear deformation theory is presented. The developed theory, which does not require shear correction factor, accounts for shear deformation effect and coupling coming from the material anisotropy. Governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled axial-flexural response. A two-noded Hermite-cubic element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for functionally graded beams with simply-supported, cantilever-free and clamped-clamped boundary conditions to investigate effects of the power-law exponent and modulus ratio on the displacements, natural frequencies and corresponding mode shapes.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

Literatur
1.
Zurück zum Zitat Ching HK, Yen SC (2005) Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites, Part B, Eng 36(3):223–240 ADSCrossRef Ching HK, Yen SC (2005) Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites, Part B, Eng 36(3):223–240 ADSCrossRef
2.
Zurück zum Zitat Zhong Z, Yu T (2007) Analytical solution of a cantilever functionally graded beam. Compos Sci Technol 67(3–4):481–488 CrossRef Zhong Z, Yu T (2007) Analytical solution of a cantilever functionally graded beam. Compos Sci Technol 67(3–4):481–488 CrossRef
3.
Zurück zum Zitat Birsan M, Altenbach H, Sadowski T, Eremeyev V, Pietras D (2012) Deformation analysis of functionally graded beams by the direct approach. Composites, Part B, Eng 43(3):1315–1328 CrossRef Birsan M, Altenbach H, Sadowski T, Eremeyev V, Pietras D (2012) Deformation analysis of functionally graded beams by the direct approach. Composites, Part B, Eng 43(3):1315–1328 CrossRef
4.
Zurück zum Zitat Sankar BV (2001) An elasticity solution for functionally graded beams. Compos Sci Technol 61(5):689–696 CrossRef Sankar BV (2001) An elasticity solution for functionally graded beams. Compos Sci Technol 61(5):689–696 CrossRef
5.
Zurück zum Zitat Zhu H, Sankar BV (2004) A combined Fourier series–Galerkin method for the analysis of functionally graded beams. J Appl Mech 71(3):421–424 CrossRefMATH Zhu H, Sankar BV (2004) A combined Fourier series–Galerkin method for the analysis of functionally graded beams. J Appl Mech 71(3):421–424 CrossRefMATH
6.
Zurück zum Zitat Simsek M, Kocaturk T (2009) Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Compos Struct 90(4):465–473 CrossRef Simsek M, Kocaturk T (2009) Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Compos Struct 90(4):465–473 CrossRef
7.
Zurück zum Zitat Khalili SMR, Jafari AA, Eftekhari SA (2010) A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads. Compos Struct 92(10):2497–2511 CrossRef Khalili SMR, Jafari AA, Eftekhari SA (2010) A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads. Compos Struct 92(10):2497–2511 CrossRef
8.
Zurück zum Zitat Alshorbagy AE, Eltaher M, Mahmoud F (2011) Free vibration characteristics of a functionally graded beam by finite element method. Appl Math Model 35(1):412–425 CrossRefMATHMathSciNet Alshorbagy AE, Eltaher M, Mahmoud F (2011) Free vibration characteristics of a functionally graded beam by finite element method. Appl Math Model 35(1):412–425 CrossRefMATHMathSciNet
9.
Zurück zum Zitat Chakraborty A, Gopalakrishnan S, Reddy JN (2003) A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 45(3):519–539 CrossRefMATH Chakraborty A, Gopalakrishnan S, Reddy JN (2003) A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 45(3):519–539 CrossRefMATH
10.
Zurück zum Zitat Li X-F (2008) A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams. J Sound Vib 318(4–5):1210–1229 ADSCrossRef Li X-F (2008) A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams. J Sound Vib 318(4–5):1210–1229 ADSCrossRef
11.
Zurück zum Zitat Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30(3):741–747 CrossRef Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30(3):741–747 CrossRef
12.
Zurück zum Zitat Kadoli R, Akhtar K, Ganesan N (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model 32(12):2509–2525 CrossRefMATH Kadoli R, Akhtar K, Ganesan N (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model 32(12):2509–2525 CrossRefMATH
13.
Zurück zum Zitat Benatta M, Mechab I, Tounsi A, Bedia EA (2008) Static analysis of functionally graded short beams including warping and shear deformation effects. Comput Mater Sci 44(2):765–773 CrossRef Benatta M, Mechab I, Tounsi A, Bedia EA (2008) Static analysis of functionally graded short beams including warping and shear deformation effects. Comput Mater Sci 44(2):765–773 CrossRef
14.
Zurück zum Zitat Ben-Oumrane S, Abedlouahed T, Ismail M, Mohamed BB, Mustapha M, Abbas ABE (2009) A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput Mater Sci 44(4):1344–1350 CrossRef Ben-Oumrane S, Abedlouahed T, Ismail M, Mohamed BB, Mustapha M, Abbas ABE (2009) A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput Mater Sci 44(4):1344–1350 CrossRef
15.
Zurück zum Zitat Simsek M (2009) Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method. Int J Eng Appl Sci 1(3):1–11 Simsek M (2009) Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method. Int J Eng Appl Sci 1(3):1–11
16.
Zurück zum Zitat Giunta G, Belouettar S, Carrera E (2010) Analysis of FGM beams by means of classical and advanced theories. Mech Adv Mat Struct 17(8):622–635 CrossRef Giunta G, Belouettar S, Carrera E (2010) Analysis of FGM beams by means of classical and advanced theories. Mech Adv Mat Struct 17(8):622–635 CrossRef
17.
Zurück zum Zitat Li X-F, Wang B-L, Han J-C (2010) A higher-order theory for static and dynamic analyses of functionally graded beams. Arch Appl Mech 80:1197–1212 CrossRefMATH Li X-F, Wang B-L, Han J-C (2010) A higher-order theory for static and dynamic analyses of functionally graded beams. Arch Appl Mech 80:1197–1212 CrossRefMATH
18.
Zurück zum Zitat Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5):1651–1656 CrossRef Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5):1651–1656 CrossRef
19.
Zurück zum Zitat Simsek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705 CrossRef Simsek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705 CrossRef
20.
Zurück zum Zitat Simsek M (2010) Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos Struct 92(4):904–917 CrossRef Simsek M (2010) Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos Struct 92(4):904–917 CrossRef
21.
Zurück zum Zitat Giunta G, Crisafulli D, Belouettar S, Carrera E (2011) Hierarchical theories for the free vibration analysis of functionally graded beams. Compos Struct 94(1):68–74 CrossRef Giunta G, Crisafulli D, Belouettar S, Carrera E (2011) Hierarchical theories for the free vibration analysis of functionally graded beams. Compos Struct 94(1):68–74 CrossRef
22.
Zurück zum Zitat Salamat-talab M, Nateghi A, Torabi J (2012) Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. Int J Mech Sci 57(1):63–73 CrossRef Salamat-talab M, Nateghi A, Torabi J (2012) Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. Int J Mech Sci 57(1):63–73 CrossRef
23.
Zurück zum Zitat Nateghi A, Salamat-talab M, Rezapour J, Daneshian B (2012) Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory. Appl Math Model 36(10):4971–4987 CrossRefMATHMathSciNet Nateghi A, Salamat-talab M, Rezapour J, Daneshian B (2012) Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory. Appl Math Model 36(10):4971–4987 CrossRefMATHMathSciNet
24.
Zurück zum Zitat Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82(3):390–402 CrossRef Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82(3):390–402 CrossRef
25.
Zurück zum Zitat Thai H-T, Vo TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 62(1):57–66 CrossRef Thai H-T, Vo TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 62(1):57–66 CrossRef
26.
Zurück zum Zitat Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752 CrossRefMATH Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752 CrossRefMATH
27.
Zurück zum Zitat Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton
Metadaten
Titel
Static and vibration analysis of functionally graded beams using refined shear deformation theory
verfasst von
Thuc P. Vo
Huu-Tai Thai
Trung-Kien Nguyen
Fawad Inam
Publikationsdatum
01.01.2014
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 1/2014
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9780-1

Weitere Artikel der Ausgabe 1/2014

Meccanica 1/2014 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.