Free vibration analysis of functionally graded beams using an exact plane elasticity approach


Celebi K. , TÜTÜNCÜ N.

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE, vol.228, no.14, pp.2488-2494, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 228 Issue: 14
  • Publication Date: 2014
  • Doi Number: 10.1177/0954406213519974
  • Title of Journal : PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE
  • Page Numbers: pp.2488-2494
  • Keywords: Functionally graded beams, elasticity, free vibrations, natural frequencies, mode shapes, FREQUENCY, TIMOSHENKO, EQUATIONS

Abstract

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.