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Free Vibration of Functionally Graded Rayleigh Beam

Year 2017, , 127 - 137, 03.07.2017
https://doi.org/10.24107/ijeas.322884

Abstract

In the present study the free
vibration of Rayleigh beam composed of functionally graded materials (FGMs) is
investigated. For this purpose, the equation of the motion of functionally
graded (FG) beam derived according to Rayleigh beam theory. The material properties
are assumed to vary continuously through the thickness of the beam according to
the power-law form. Resulting equations are solved for simply supported
boundary conditions. In order to validate the results, a comparisons is carried
out with available results for homogeneous beam. The effects of varying
material properties on the dimensionless free vibration frequency parameters
are examined. 

References

  • [1] Wakashima K., Hirano T., Niino M.. Space applications of advanced structural materials. ESA SP303-97, 1990
  • [2] Koizumi, M., The concept of FGM. Ceramic Transactions, Functionally Gradient Materials, vol. 34, pp. 3–10, 1993.
  • [3] Suresh, S., Mortensen, A.,. Fundamentals of Functionally Graded Materials. IOM Communications, London, 1998.
  • [4] Chakraverty, S., Pradhan, KK., Vibration of Functionally Graded Beams and Plates. Academic Press, 2016.
  • [5] Carrera, E., Giunta, G. and Petrolo, M., Beam Structures: Classical and Advanced Theories. John Wiley and Sons Ltd, 2011.
  • [6] Han, M.S., Benaroya, H., Wei, T., Dynamics of transversely vibrating beams using four engineering theories. Journal Sound and Vibration, 225, 935-988. 1999.
  • [7] Civalek, O., Kiracioglu, O., Free vibration analysis of Timoshenko beams by DSC method. International Journal of Numerical Methods in Biomedical Engineering, 26, 1890-1898, 2010.
  • [8] Coşkun, S.B., Öztürk, B., Atay, M.T., Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques. INTECH Open Access Publisher, 2011.
  • [9] Li, X.F., Tang, A.Y., Xi, L.Y., Vibration of a Rayleigh cantilever beam with axial force and tip mass. Journal of Constructional Steel Research,80, 15-22, 2013.
  • [10] Avcar M., Free Vibration analysis of beams considering different geometric characteristics and boundary conditions. International Journal of Mechanics and Applications, 4, 94-100, 2014.
  • [11] Avcar, M., Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam. Structural Engineering and Mechanics,55, 871-884. 2015.
  • [12] Arıbaş, Ü.N., Eratlı, N., Omurtag, M.H., Free Vibration Analysis of Moderately Thick, Sandwich, Circular Beams. In Proceedings of the World Congress on Engineering (Vol. 2), 2016. .
  • [13] FF Calim Free Vibration Analysis of Timoshenko Beam with Variable Cross-Section. Omer Halisdemir University Journal of Engineering Sciences, 6, 76-82, 2017.
  • [14] Sankar B.V., An elasticity solution for functionally graded beams. Composites Science and Technology, 61 , 689–696. 2001.
  • [15] Aydogdu, M., Taskin, V., Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design, 28 , 1651–1656, 2007.
  • [16] Li X.F., A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and Vibration, 318, 1210–1229, 2008.
  • [17] Sina S.A., Navazi H.M., Haddadpour H., An analytical method for free vibration analysis of functionally graded beams. Materials and Design, 30, 741–747, 2009.
  • [18] Şimsek, M., Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240, 697-705, 2010.
  • [19] Nuttawit, W., Variddhi, U., Free vibration analysis of functionally graded beams with general elastically end constraints by DTM. World Journal of Mechanics, 2, 297–310, 2012.
  • [20] Al Rjoub, Y.S., Hamad, A.G., Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE. Journal of Civil Engineering, 21, 792-806, 2017.
  • [21] Rao, S.S., Vibration of continuous systems. John Wiley & Sons, 2007.
Year 2017, , 127 - 137, 03.07.2017
https://doi.org/10.24107/ijeas.322884

Abstract

References

  • [1] Wakashima K., Hirano T., Niino M.. Space applications of advanced structural materials. ESA SP303-97, 1990
  • [2] Koizumi, M., The concept of FGM. Ceramic Transactions, Functionally Gradient Materials, vol. 34, pp. 3–10, 1993.
  • [3] Suresh, S., Mortensen, A.,. Fundamentals of Functionally Graded Materials. IOM Communications, London, 1998.
  • [4] Chakraverty, S., Pradhan, KK., Vibration of Functionally Graded Beams and Plates. Academic Press, 2016.
  • [5] Carrera, E., Giunta, G. and Petrolo, M., Beam Structures: Classical and Advanced Theories. John Wiley and Sons Ltd, 2011.
  • [6] Han, M.S., Benaroya, H., Wei, T., Dynamics of transversely vibrating beams using four engineering theories. Journal Sound and Vibration, 225, 935-988. 1999.
  • [7] Civalek, O., Kiracioglu, O., Free vibration analysis of Timoshenko beams by DSC method. International Journal of Numerical Methods in Biomedical Engineering, 26, 1890-1898, 2010.
  • [8] Coşkun, S.B., Öztürk, B., Atay, M.T., Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques. INTECH Open Access Publisher, 2011.
  • [9] Li, X.F., Tang, A.Y., Xi, L.Y., Vibration of a Rayleigh cantilever beam with axial force and tip mass. Journal of Constructional Steel Research,80, 15-22, 2013.
  • [10] Avcar M., Free Vibration analysis of beams considering different geometric characteristics and boundary conditions. International Journal of Mechanics and Applications, 4, 94-100, 2014.
  • [11] Avcar, M., Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam. Structural Engineering and Mechanics,55, 871-884. 2015.
  • [12] Arıbaş, Ü.N., Eratlı, N., Omurtag, M.H., Free Vibration Analysis of Moderately Thick, Sandwich, Circular Beams. In Proceedings of the World Congress on Engineering (Vol. 2), 2016. .
  • [13] FF Calim Free Vibration Analysis of Timoshenko Beam with Variable Cross-Section. Omer Halisdemir University Journal of Engineering Sciences, 6, 76-82, 2017.
  • [14] Sankar B.V., An elasticity solution for functionally graded beams. Composites Science and Technology, 61 , 689–696. 2001.
  • [15] Aydogdu, M., Taskin, V., Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design, 28 , 1651–1656, 2007.
  • [16] Li X.F., A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and Vibration, 318, 1210–1229, 2008.
  • [17] Sina S.A., Navazi H.M., Haddadpour H., An analytical method for free vibration analysis of functionally graded beams. Materials and Design, 30, 741–747, 2009.
  • [18] Şimsek, M., Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240, 697-705, 2010.
  • [19] Nuttawit, W., Variddhi, U., Free vibration analysis of functionally graded beams with general elastically end constraints by DTM. World Journal of Mechanics, 2, 297–310, 2012.
  • [20] Al Rjoub, Y.S., Hamad, A.G., Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE. Journal of Civil Engineering, 21, 792-806, 2017.
  • [21] Rao, S.S., Vibration of continuous systems. John Wiley & Sons, 2007.
There are 21 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Mehmet Avcar

Hyam Hazim Alsaid Alwan This is me

Publication Date July 3, 2017
Acceptance Date June 28, 2017
Published in Issue Year 2017

Cite

APA Avcar, M., & Hazim Alsaid Alwan, H. (2017). Free Vibration of Functionally Graded Rayleigh Beam. International Journal of Engineering and Applied Sciences, 9(2), 127-137. https://doi.org/10.24107/ijeas.322884
AMA Avcar M, Hazim Alsaid Alwan H. Free Vibration of Functionally Graded Rayleigh Beam. IJEAS. July 2017;9(2):127-137. doi:10.24107/ijeas.322884
Chicago Avcar, Mehmet, and Hyam Hazim Alsaid Alwan. “Free Vibration of Functionally Graded Rayleigh Beam”. International Journal of Engineering and Applied Sciences 9, no. 2 (July 2017): 127-37. https://doi.org/10.24107/ijeas.322884.
EndNote Avcar M, Hazim Alsaid Alwan H (July 1, 2017) Free Vibration of Functionally Graded Rayleigh Beam. International Journal of Engineering and Applied Sciences 9 2 127–137.
IEEE M. Avcar and H. Hazim Alsaid Alwan, “Free Vibration of Functionally Graded Rayleigh Beam”, IJEAS, vol. 9, no. 2, pp. 127–137, 2017, doi: 10.24107/ijeas.322884.
ISNAD Avcar, Mehmet - Hazim Alsaid Alwan, Hyam. “Free Vibration of Functionally Graded Rayleigh Beam”. International Journal of Engineering and Applied Sciences 9/2 (July 2017), 127-137. https://doi.org/10.24107/ijeas.322884.
JAMA Avcar M, Hazim Alsaid Alwan H. Free Vibration of Functionally Graded Rayleigh Beam. IJEAS. 2017;9:127–137.
MLA Avcar, Mehmet and Hyam Hazim Alsaid Alwan. “Free Vibration of Functionally Graded Rayleigh Beam”. International Journal of Engineering and Applied Sciences, vol. 9, no. 2, 2017, pp. 127-3, doi:10.24107/ijeas.322884.
Vancouver Avcar M, Hazim Alsaid Alwan H. Free Vibration of Functionally Graded Rayleigh Beam. IJEAS. 2017;9(2):127-3.

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