Skip to main content
Top
Published in: Mechanics of Composite Materials 6/2022

25-01-2022

Coupled Flexural-Torsional Free Vibration of an Axially Functionally Graded Circular Curved Beam

Authors: Joon Kyu Lee, Byoung Koo Lee

Published in: Mechanics of Composite Materials | Issue 6/2022

Log in

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

search-config
loading …

Abstract

The coupled flexural-torsional free vibration of circular horizontally curved beams made of an axially functionally graded (AFG) material was investigated. Beams with rectangular and elliptical cross-sections were designed to obey quadratic functions of Young’s modulus and the mass density in the axial direction. Using the Timoshenko and St. Venant beam theories, the governing differential equations of motion were derived. Based on the trial eigenvalue method together with the numerical integration method, the differential equations were solved to obtain the natural frequencies. For validation purposes, the frequencies computed in this study and ADINA were compared. Parametric studies were also performed to clarify how the natural frequency of the flexural-torsion coupling depends on modular ratio, cross-sectional shape, aspect ratio, slenderness ratio, and opening angle of the beams.

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!

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!

Literature
1.
go back to reference C. H. Norris, J. B. Wilbur, and S. Utku, Elementary Structural Analysis, New York, NY, USA, McGraw-Hill Inc. (1976). C. H. Norris, J. B. Wilbur, and S. Utku, Elementary Structural Analysis, New York, NY, USA, McGraw-Hill Inc. (1976).
2.
go back to reference T. Horibe and K. Mori, “Large deflections of tapered cantilever beams made of axially functionally graded materials,” Mech. Eng. J., 5, 1-10 (2018).CrossRef T. Horibe and K. Mori, “Large deflections of tapered cantilever beams made of axially functionally graded materials,” Mech. Eng. J., 5, 1-10 (2018).CrossRef
3.
go back to reference S. S. Rao, Vibration of Continuous Systems, Hoboken, NJ, USA, John Wiley & Sons, Inc. (2007). S. S. Rao, Vibration of Continuous Systems, Hoboken, NJ, USA, John Wiley & Sons, Inc. (2007).
4.
go back to reference X. F. Li, “A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Bernoulli–Euler beam,” J. Sound. Vibr., 318, 1210-1229 (2008).CrossRef X. F. Li, “A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Bernoulli–Euler beam,” J. Sound. Vibr., 318, 1210-1229 (2008).CrossRef
5.
go back to reference S. Kukla and J. Rychlewska, “Free vibration analysis of functionally graded beam,” J. Appl. Math. Comput. Mech., 12, 39-44 (2013).CrossRef S. Kukla and J. Rychlewska, “Free vibration analysis of functionally graded beam,” J. Appl. Math. Comput. Mech., 12, 39-44 (2013).CrossRef
6.
go back to reference G. Chandran and M. G. Rajendran, “Study on buckling of column made of functionally graded material,” Int. J. Mech. Prod. Eng., 2, 52-54 (2014). G. Chandran and M. G. Rajendran, “Study on buckling of column made of functionally graded material,” Int. J. Mech. Prod. Eng., 2, 52-54 (2014).
7.
go back to reference S. Ranganathan, F. Abed, and M. G. Aldadah, “Buckling of slender columns with functionally graded micro-structures,” Mech. Adv. Mater. Struct., 23, 1360-1367 (2016).CrossRef S. Ranganathan, F. Abed, and M. G. Aldadah, “Buckling of slender columns with functionally graded micro-structures,” Mech. Adv. Mater. Struct., 23, 1360-1367 (2016).CrossRef
8.
go back to reference I. Elishakoff, M. Eisenberger, and A. Delmas, “Buckling and vibration of functionally graded material columns sharing Duncan’s mode shape, and new cases,” Structures, 5, 170-174 (2016).CrossRef I. Elishakoff, M. Eisenberger, and A. Delmas, “Buckling and vibration of functionally graded material columns sharing Duncan’s mode shape, and new cases,” Structures, 5, 170-174 (2016).CrossRef
9.
go back to reference M. Rezaiee-Pajand and A. R. Masoodi, “Exact natural frequencies and buckling loads of functionally graded material tapered beam-columns considering semi-rigid connections,” J. Vibr. Control, 24, 1787-1808 (2018).CrossRef M. Rezaiee-Pajand and A. R. Masoodi, “Exact natural frequencies and buckling loads of functionally graded material tapered beam-columns considering semi-rigid connections,” J. Vibr. Control, 24, 1787-1808 (2018).CrossRef
10.
go back to reference Y. Huang and X. F. Li, “A new approach for free vibration of axially functionally graded beams with non-uniform cross section,” J. Sound Vibr., 329, 2291-2303 (2010).CrossRef Y. Huang and X. F. Li, “A new approach for free vibration of axially functionally graded beams with non-uniform cross section,” J. Sound Vibr., 329, 2291-2303 (2010).CrossRef
11.
go back to reference A. Shahba and S. Rajasekaran, “Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials,” Appl. Math. Model., 36, 3094-3111 (2012).CrossRef A. Shahba and S. Rajasekaran, “Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials,” Appl. Math. Model., 36, 3094-3111 (2012).CrossRef
12.
go back to reference 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, 39-53 (2020).CrossRef 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, 39-53 (2020).CrossRef
13.
go back to reference B. Akgoz and O. Civalek, “Free vibration analysis of axially functionally graded Bernoulli-Euler microbeams based on the modified couple stress theory,” Compos. Struct., 98, 314-322 (2013).CrossRef B. Akgoz and O. Civalek, “Free vibration analysis of axially functionally graded Bernoulli-Euler microbeams based on the modified couple stress theory,” Compos. Struct., 98, 314-322 (2013).CrossRef
14.
go back to reference P. Malekzadeh, M. M. Atashi, and G. Karami, “In-plane free vibration of functionally graded circular arches with temperature-dependent properties under thermal environment,” J. Sound Vibr., 326, 837-851 (2009).CrossRef P. Malekzadeh, M. M. Atashi, and G. Karami, “In-plane free vibration of functionally graded circular arches with temperature-dependent properties under thermal environment,” J. Sound Vibr., 326, 837-851 (2009).CrossRef
15.
go back to reference P. Malekzadeh, “Two-dimensional in-plane free vibrations of functionally graded circular arches with temperaturedependent properties,” Compos. Struct., 91, 38-47 (2009).CrossRef P. Malekzadeh, “Two-dimensional in-plane free vibrations of functionally graded circular arches with temperaturedependent properties,” Compos. Struct., 91, 38-47 (2009).CrossRef
16.
go back to reference A. R. Noori, T. A. Aslan, and B. Temel, “An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with non-uniform cross section,” Compos. Struct., 200, 701-710 (2018).CrossRef A. R. Noori, T. A. Aslan, and B. Temel, “An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with non-uniform cross section,” Compos. Struct., 200, 701-710 (2018).CrossRef
17.
go back to reference S. Rajasekaran, “Free vibration of tapered arches made of axially functionally graded materials,” Struct. Eng. Mech., 45, 569-594 (2013).CrossRef S. Rajasekaran, “Free vibration of tapered arches made of axially functionally graded materials,” Struct. Eng. Mech., 45, 569-594 (2013).CrossRef
18.
go back to reference Z. Zhou, M. Chen, and K. Xie, “NURBS-based free vibration analysis of axially functionally graded tapered Timoshenko curved beams,” Appl. Math. Mech., 41, 567-586 (2020).CrossRef Z. Zhou, M. Chen, and K. Xie, “NURBS-based free vibration analysis of axially functionally graded tapered Timoshenko curved beams,” Appl. Math. Mech., 41, 567-586 (2020).CrossRef
19.
go back to reference G. C. Tsiatas and A. E. Charalampakis, “Optimizing the natural frequencies of axially functionally graded beams and arches,” Compos. Struct., 160, 256-266 (2017).CrossRef G. C. Tsiatas and A. E. Charalampakis, “Optimizing the natural frequencies of axially functionally graded beams and arches,” Compos. Struct., 160, 256-266 (2017).CrossRef
20.
go back to reference J. K. Lee and B. K. Lee, “In-plane free vibration of circular arches made of axially functionally graded materials,” Int. J. Struct. Stab. Dy., 19, 1950084 (2019).CrossRef J. K. Lee and B. K. Lee, “In-plane free vibration of circular arches made of axially functionally graded materials,” Int. J. Struct. Stab. Dy., 19, 1950084 (2019).CrossRef
21.
go back to reference P. Malekzadeh, M. R. G. Haghighi, and M. M. Atashi, “Out-of-plane free vibration of functionally graded circular curved beams in thermal environment,” Compos. Struct., 92, 541-552 (2010).CrossRef P. Malekzadeh, M. R. G. Haghighi, and M. M. Atashi, “Out-of-plane free vibration of functionally graded circular curved beams in thermal environment,” Compos. Struct., 92, 541-552 (2010).CrossRef
22.
go back to reference P. Malekzadeh, M. R. G. Haghighi, and M. M. Atashi, “Out-of-plane free vibration analysis of functionally graded circular curved beams supported on elastic foundation,” Int. J. Struct. Stab. Dy., 2, 635-652 (2010). P. Malekzadeh, M. R. G. Haghighi, and M. M. Atashi, “Out-of-plane free vibration analysis of functionally graded circular curved beams supported on elastic foundation,” Int. J. Struct. Stab. Dy., 2, 635-652 (2010).
23.
go back to reference S. Y. Lee and J. C. Chao, “Exact solutions of out-of-plane vibration of curved non-uniform beam,” J. Appl. Mech., 68, 186-191 (2000).CrossRef S. Y. Lee and J. C. Chao, “Exact solutions of out-of-plane vibration of curved non-uniform beam,” J. Appl. Mech., 68, 186-191 (2000).CrossRef
24.
go back to reference B. K. Lee, S. J. Oh, J. M. Mo, and T. E. Lee “Out-of-plane free vibrations of curved beams with variable curvature,” J. Sound Vibr., 318, 227-246 (2008).CrossRef B. K. Lee, S. J. Oh, J. M. Mo, and T. E. Lee “Out-of-plane free vibrations of curved beams with variable curvature,” J. Sound Vibr., 318, 227-246 (2008).CrossRef
25.
go back to reference S. F. Borg and J. J. Gennaro, Advanced Structural Analysis, New York, NY, USA, D. Van Nostrand Reinhold, (1959). S. F. Borg and J. J. Gennaro, Advanced Structural Analysis, New York, NY, USA, D. Van Nostrand Reinhold, (1959).
26.
go back to reference S. P. Timoshenko, “On the correction for shear of the differential equation for transverse vibrations of prismatic bars,” Philos. Mag., 41, 744-746 (1921).CrossRef S. P. Timoshenko, “On the correction for shear of the differential equation for transverse vibrations of prismatic bars,” Philos. Mag., 41, 744-746 (1921).CrossRef
27.
go back to reference J. K. Lee and S. Jeong, “Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundation,” Appl. Math. Model., 40, 2242-2256 (2016).CrossRef J. K. Lee and S. Jeong, “Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundation,” Appl. Math. Model., 40, 2242-2256 (2016).CrossRef
28.
go back to reference A. K. Chopra, Dynamics of Structures, Upper Saddle River, NJ, USA, Prentice Hall Inc. (2001). A. K. Chopra, Dynamics of Structures, Upper Saddle River, NJ, USA, Prentice Hall Inc. (2001).
29.
go back to reference G. R. Cowper, “The shear coefficient in Timoshenko beam theory,” J. Appl. Mech., 33, 335-340 (1966).CrossRef G. R. Cowper, “The shear coefficient in Timoshenko beam theory,” J. Appl. Mech., 33, 335-340 (1966).CrossRef
30.
go back to reference W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, New York, NY, USA, McGraw-Hill Inc. (2001). W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, New York, NY, USA, McGraw-Hill Inc. (2001).
31.
go back to reference R. L. Burden, D. J. Faires, and A. M. Burden, Numerical Analysis, Boston, MT, USA, Cengage Learning (2016). R. L. Burden, D. J. Faires, and A. M. Burden, Numerical Analysis, Boston, MT, USA, Cengage Learning (2016).
Metadata
Title
Coupled Flexural-Torsional Free Vibration of an Axially Functionally Graded Circular Curved Beam
Authors
Joon Kyu Lee
Byoung Koo Lee
Publication date
25-01-2022
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 6/2022
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-022-10003-8

Other articles of this Issue 6/2022

Mechanics of Composite Materials 6/2022 Go to the issue

Premium Partners