Full Content is available to subscribers

Subscribe/Learn More  >

Fractional Derivative Viscoelastic Model for the Analysis of Two Colliding Spherical Shells

[+] Author Affiliations
Yury A. Rossikhin, Marina V. Shitikova

Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia

Paper No. IMECE2012-87346, pp. 21-32; 12 pages
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 12: Vibration, Acoustics and Wave Propagation
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4528-8
  • Copyright © 2012 by ASME


The collision of two isotropic spherical shells is investigated for the case when the viscoelastic features of the shells represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of two shells, wherein the generalized fractional-derivative standard linear law instead of the Hertz contact law is employed as a low of interaction. The pans of the shells beyond the contact domain are assumed to be elastic, and their behavior is described by the equations of motion which take rotary inertia and shear deformations into account. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. Due to the short duration of contact interaction, the reflected waves are not taken into account. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. To determine the desired values behind the wave fronts, one-term ray expansions are used, as well as the equations of motion of the contact domains for the both spherical shells.

Copyright © 2012 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

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 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