Free Vibration Analysis of Functionally Graded Beams

  • Khalane Sanjay Anandrao Advanced Systems Laboratory, Hyderabad
  • R. K. Gupta Advanced Systems Laboratory, Hyderabad
  • P. Ramachandran Defence Research and Development Laboratory, Hyderabad
  • G. Venkateswara Rao Vardhaman College of Engineering, Hyderabad
Keywords: Functionally graded material, finite element method, free vibration, Euler-Bernoulli beam theory, Timoshenko beam theory

Abstract

Free vibration analysis of functionally graded beams is carried out for various classical boundary conditions. Two separate finite element formulations, one based on Euler-Bernoulli beam theory and other based on Timoshenko beam theory are developed. Principle of virtual work is used to obtain the finite element system of equations. Numerical results are provided to demonstrate the effect of transverse shear on the natural frequencies and mode shapes for different length-to-thickness ratios and volume fraction exponents of functionally graded material (FGM) beams for the boundary conditions considered. It was observed that transverse shear significantly affects the fundamental frequency and mode shape for lower length to thickness ratios of FGM beams. Further, the effect was observed to be more prominent at higher modes for all the volume fraction exponents of FGM beam.

Defence Science Journal, 2012, 62(3), pp.139-146, DOI:http://dx.doi.org/10.14429/dsj.62.1326

Author Biographies

Khalane Sanjay Anandrao, Advanced Systems Laboratory, Hyderabad
Mr K. Sanjay Anandrao received his BE (Mechanical Engg) from University of Pune in 1991 and ME (Aerospace Engg) from Indian Institute of Science, Bangalore in 1995. He is currently working as Scientist ‘F’ at Advanced Systems Laboratory (ASL), Hyderabad. His areas of interest include : Design of composite structures, FGM, stability of structures
R. K. Gupta, Advanced Systems Laboratory, Hyderabad
Dr Rajesh Kumar Gupta obtained his ME (Aerospace Engg) from IISc, Bangalore in 1984. He received his doctorate in Mechanical Engineering from JNTU. Hyderabad in 2011. Presently he is working as Technology Director at ASL, Hyderabad. His areas of interest are: Aerospace structures, vibration, composites, aerospace system configuration design.
P. Ramachandran, Defence Research and Development Laboratory, Hyderabad
Dr P. Ramachandran obtained his Masters degree (Aerospace Engg) and PhD (Mechanical Engg) from Indian Institute of Technology, Madras in 1991 and 2007, respectively. He is currently working as Scientist ‘F’ in Defence Research and Development Laboratory (DRDL), Hyderabad. His areas of interest include: Vibration and acoustic response of structures, aerospace design,
structural analysis and instrumentation.
G. Venkateswara Rao, Vardhaman College of Engineering, Hyderabad
Dr G.V. Rao is currently working as Research Professor in the Department of Mechanical Engineering, Vardhaman College of Engineering (VCE), Shamshabad, Hyderabad. He is Fellow of many institutions like, Indian National Academy of Engineering, Indian Academy of Sciences, Institution of Engineers (India) and Aeronautical Society of India. He is recipient of the Shanti Swarup Bhatnagar (SSB) prize in the area of engineering sciences in 1989. He has authored more than 565 technical papers.

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Published
2012-07-06
How to Cite
Anandrao, K., Gupta, R., Ramachandran, P., & Rao, G. (2012). Free Vibration Analysis of Functionally Graded Beams. Defence Science Journal, 62(3), 139-146. https://doi.org/10.14429/dsj.62.1326
Section
Applied Physics & Fluid Dynamics