0
Research Papers

Some Intriguing Results Pertaining to Functionally Graded Columns

[+] Author and Article Information
Isaac Elishakoff

Fellow ASME
e-mail: elishako@fau.edu

Yohann Miglis

Department of Ocean and Mechanical Engineering,
Florida Atlantic University,
Boca Raton, FL 33431-0991

1Corresponding author.

Manuscript received October 24, 2011; final manuscript received October 19, 2012; accepted manuscript posted October 30, 2012; published online May 23, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 80(4), 041021 (May 23, 2013) (9 pages) Paper No: JAM-11-1395; doi: 10.1115/1.4007983 History: Received October 24, 2011; Revised October 19, 2012; Accepted October 30, 2012

Some intriguing results are reported in conjunction with closed form solutions obtained for a clamped-free vibrating inhomogeneous column under an axial concentrated load using the semi-inverse method. Fourth order polynomial is postulated for both the vibration mode shape and buckling displacement. Solution is provided for the flexural rigidity and the natural frequency. It is shown that, for each level of axial loading, there may exist up to five flexural rigidities satisfying the governing differential equation and boundary conditions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 2

Flexural rigidities and associated mode shapes corresponding to the roots (a) k4 = −0.041411, (b) k1 = −0.01573492764, (c) k2 = −0.006766827430, (d) k3 = 0.001291278483, (e) k5 = 0.01033391077

Grahic Jump Location
Fig. 3

Dependence of the squared natural frequency versus load (a) k = k4, (b) k = k1, (c) k = k2, (d) k = k3, (e) k = k5

Grahic Jump Location
Fig. 4

Vibrating clamped-free beam loaded at its tip

Grahic Jump Location
Fig. 5

Five possible flexural rigidities and displacements for (a) k1, (b) k2, (c) k3, (d) k4, (e) k5

Grahic Jump Location
Fig. 1

Variation of the roots of Eq. (38) with axial load P; (a) roots k1, k3, k4, k5 and (b) rook k2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In