0
Research Papers

Exact Analysis of Axisymmetric Dynamic Response of Functionally Graded Cylinders (or Disks) and Spheres

[+] Author and Article Information
I. Keles, N. Tutuncu

Department of Mechanical Engineering,  Ondokuz Mayis University, 55139, Samsun, Turkey e-mail: kelesibrahim@gmail.comDepartment of Mechanical Engineering,  Cukurova University, 01330, Adana, Turkey e-mail: ntutuncu@cu.edu.tr

J. Appl. Mech 78(6), 061014 (Aug 25, 2011) (7 pages) doi:10.1115/1.4003914 History: Received February 16, 2010; Revised March 21, 2011; Posted April 04, 2011; Published August 25, 2011; Online August 25, 2011

Free and forced vibration analyses of functionally graded hollow cylinders and spheres are performed and analytical benchmark solutions are presented. The material is assumed to be graded in the radial direction according to a simple power law. The Laplace transform method is used, and the inversion into the time domain is performed exactly using calculus of residues. The Complex Laplace parameter in the free vibration equation has directly given natural frequencies, and the results are given in tabular form. On the inner surface, various axisymmetric dynamic pressures are applied, and radial displacement and hoop stress are presented in the form of graphs. The exponent in the power law, called the inhomogeneity parameter, essentially refers to the degree of inhomogeneity. Increasing the inhomogeneity parameter provides a stress-shielding effect. Closed-form solutions obtained in the present paper are tractable, and they allow for further parametric studies. The inhomogeneity constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Association of Physics Teachers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Radial displacement on inside surface of cylinder due to P1(τ)

Grahic Jump Location
Figure 2

Radial displacement on inside surface of cylinder due to P2(τ)

Grahic Jump Location
Figure 3

Radial displacement on inside surface of cylinder due to P3(τ)

Grahic Jump Location
Figure 4

Hoop stress on inside surface of cylinder due to P1(τ)

Grahic Jump Location
Figure 5

Hoop stress on inside surface of cylinder due to P2(τ)

Grahic Jump Location
Figure 6

Hoop stress on inside surface of cylinder due to P3(τ)

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