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Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section

Year 2018, , 813 - 819, 01.12.2018
https://doi.org/10.2339/politeknik.426643

Abstract

Vibration behavior of a bar with
variable cross-section, which its material properties vary with temperature, is
investigated in this study. In the analysis, not only theoretical solution but
also numerical solution is performed for validation. The numerical analysis is
overcome by SolidWorks program based on finite element method. Four types of
effects on the bar are investigated. These are effects of temperature
variation, geometric ratio, slenderness ratio and mode numbers variation. The
temperature is increased from 22
°C
to 250
°C.
The geometric ratio is varied from 0 to -1/L at intervals of 0.25/L. The
slenderness ratio is varied from 1/10 to 1/20 by increasing the length of bar
from 200 mm to 400 mm. As for the mode numbers, the first three mode shapes are
examined in the analysis. The boundary condition of the bar is taken as
clamped-free. According to the results, the natural frequency decreases with
increasing the temperature. The natural frequency also decreases with
decreasing the slenderness ratio. But, it increases with decreasing the
geometric ratio and also increases with increasing the mode number. When the
theoretical and numerical results are examined, it is seen that the results are
in harmony.

References

  • [1] Demir E., Çallıoğlu H. and Sayer M., “Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation”, Science and Engineering of Composite Materials, 20(4): 359–370, (2013).
  • [2] Çallıoğlu H., Sayer M., Demir E., “Elastic-plastic stress analysis of rotating functionally graded discs”, Thin-Walled Structures, 94: 38–44, (2015).
  • [3] Li Q. S., “Free longitudinal vibration analysis of multi-step non-uniform bars based on piecewise analytical solutions”, Engineering Structures, 22(9): 1205–1215, (2000).
  • [4] Bert C. W. and Zeng H., “Analysis of axial vibration of compound bars by differential transformation method”, Journal of Sound and Vibration, 275(3-5): 641–647, (2004).
  • [5] Ma H., “Exact solutions of axial vibration problems of elastic bars”, International Journal for Numerical Methods in Engineering, 75(2): 241–252, (2008).
  • [6] Arndt M., Machado R. D. and Scremin A., “An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses”, Journal of Sound and Vibration, 329(6): 659–672, (2010).
  • [7] Velasco S., Roman F. L. and White J. A., “A simple experiment for measuring bar longitudinal and flexural vibration frequencies”, American Journal of Physics, 78(12): 1429–1432, (2010).
  • [8] Ranjbaran A., Shokrzadeh A. R. and Khosravi S., “A new finite element analysis of free axial vibration of cracked bars”, International Journal for Numerical Methods in Biomedical Engineering, 27(10): 1611–1621, (2011).
  • [9] Akgoz B., Civalek O., “Lomgitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)”, Composites Part B-Engineering, 55: 263-268, (2013).
  • [10] Bui H. L., Tran M. T., Le M. Q. and Tran D. T., “Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin’s maximum principle”, Meccanica, 51(6): 1491–1502, (2016).
  • [11] II’gamov M. A., “Longitudinal vibrations of a bar with incipient transverse cracks”, Mechanics of Solids, 52(1): 18-24, (2017).
  • [12] Lee M., Park I. and Lee U., “An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration”, Structural Engineering and Mechanics, 61(4): 551-561, (2017).
  • [13] https://en.wikipedia.org/wiki/Ti-6Al-4V, (2018).
  • [14] Shen H. S., “Functionally Graded Materials Nonlinear Analysis of Plates and Shells”, CRC Press Taylor & Francis Group, Boca Raton, Florida, Usa, (2009).
  • [15] Hagedorn P. and DasGupta A., “Vibrations and Waves in Continuous Mechanical Systems”, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, England, (2007).

Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section

Year 2018, , 813 - 819, 01.12.2018
https://doi.org/10.2339/politeknik.426643

Abstract

Vibration behavior of a bar with
variable cross-section, which its material properties vary with temperature, is
investigated in this study. In the analysis, not only theoretical solution but
also numerical solution is performed for validation. The numerical analysis is
overcome by SolidWorks program based on finite element method. Four types of
effects on the bar are investigated. These are effects of temperature
variation, geometric ratio, slenderness ratio and mode numbers variation. The
temperature is increased from 22
°C
to 250
°C.
The geometric ratio is varied from 0 to -1/L at intervals of 0.25/L. The
slenderness ratio is varied from 1/10 to 1/20 by increasing the length of bar
from 200 mm to 400 mm. As for the mode numbers, the first three mode shapes are
examined in the analysis. The boundary condition of the bar is taken as
clamped-free. According to the results, the natural frequency decreases with
increasing the temperature. The natural frequency also decreases with
decreasing the slenderness ratio. But, it increases with decreasing the
geometric ratio and also increases with increasing the mode number. When the
theoretical and numerical results are examined, it is seen that the results are
in harmony.

References

  • [1] Demir E., Çallıoğlu H. and Sayer M., “Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation”, Science and Engineering of Composite Materials, 20(4): 359–370, (2013).
  • [2] Çallıoğlu H., Sayer M., Demir E., “Elastic-plastic stress analysis of rotating functionally graded discs”, Thin-Walled Structures, 94: 38–44, (2015).
  • [3] Li Q. S., “Free longitudinal vibration analysis of multi-step non-uniform bars based on piecewise analytical solutions”, Engineering Structures, 22(9): 1205–1215, (2000).
  • [4] Bert C. W. and Zeng H., “Analysis of axial vibration of compound bars by differential transformation method”, Journal of Sound and Vibration, 275(3-5): 641–647, (2004).
  • [5] Ma H., “Exact solutions of axial vibration problems of elastic bars”, International Journal for Numerical Methods in Engineering, 75(2): 241–252, (2008).
  • [6] Arndt M., Machado R. D. and Scremin A., “An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses”, Journal of Sound and Vibration, 329(6): 659–672, (2010).
  • [7] Velasco S., Roman F. L. and White J. A., “A simple experiment for measuring bar longitudinal and flexural vibration frequencies”, American Journal of Physics, 78(12): 1429–1432, (2010).
  • [8] Ranjbaran A., Shokrzadeh A. R. and Khosravi S., “A new finite element analysis of free axial vibration of cracked bars”, International Journal for Numerical Methods in Biomedical Engineering, 27(10): 1611–1621, (2011).
  • [9] Akgoz B., Civalek O., “Lomgitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)”, Composites Part B-Engineering, 55: 263-268, (2013).
  • [10] Bui H. L., Tran M. T., Le M. Q. and Tran D. T., “Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin’s maximum principle”, Meccanica, 51(6): 1491–1502, (2016).
  • [11] II’gamov M. A., “Longitudinal vibrations of a bar with incipient transverse cracks”, Mechanics of Solids, 52(1): 18-24, (2017).
  • [12] Lee M., Park I. and Lee U., “An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration”, Structural Engineering and Mechanics, 61(4): 551-561, (2017).
  • [13] https://en.wikipedia.org/wiki/Ti-6Al-4V, (2018).
  • [14] Shen H. S., “Functionally Graded Materials Nonlinear Analysis of Plates and Shells”, CRC Press Taylor & Francis Group, Boca Raton, Florida, Usa, (2009).
  • [15] Hagedorn P. and DasGupta A., “Vibrations and Waves in Continuous Mechanical Systems”, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, England, (2007).
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Ersin Demir

Publication Date December 1, 2018
Submission Date January 26, 2018
Published in Issue Year 2018

Cite

APA Demir, E. (2018). Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section. Politeknik Dergisi, 21(4), 813-819. https://doi.org/10.2339/politeknik.426643
AMA Demir E. Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section. Politeknik Dergisi. December 2018;21(4):813-819. doi:10.2339/politeknik.426643
Chicago Demir, Ersin. “Longitudinal Vibration of Temperature Dependent Bar With Variable Cross-Section”. Politeknik Dergisi 21, no. 4 (December 2018): 813-19. https://doi.org/10.2339/politeknik.426643.
EndNote Demir E (December 1, 2018) Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section. Politeknik Dergisi 21 4 813–819.
IEEE E. Demir, “Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section”, Politeknik Dergisi, vol. 21, no. 4, pp. 813–819, 2018, doi: 10.2339/politeknik.426643.
ISNAD Demir, Ersin. “Longitudinal Vibration of Temperature Dependent Bar With Variable Cross-Section”. Politeknik Dergisi 21/4 (December 2018), 813-819. https://doi.org/10.2339/politeknik.426643.
JAMA Demir E. Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section. Politeknik Dergisi. 2018;21:813–819.
MLA Demir, Ersin. “Longitudinal Vibration of Temperature Dependent Bar With Variable Cross-Section”. Politeknik Dergisi, vol. 21, no. 4, 2018, pp. 813-9, doi:10.2339/politeknik.426643.
Vancouver Demir E. Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section. Politeknik Dergisi. 2018;21(4):813-9.
 
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