Loading...

Propagation of SH Wave in Elastic Media with Cylindrical Inhomogeneity at Micro and Nano Scales by Couple Stress Theory

Goodarzi, Azadeh | 2009

673 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39924 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. It is well known that the classical continuum theory does not consider size effect in predicting material’s behavior, however at the micro and nano scales, this effect is not negligible and the classical theory has deficiencies at these scales. To take into account the size effect, higher order continuum theories introduce new material constants into the formulation. One famous version of these theories is couple stress which is applied in this research. This theory considers size effect of inhomogeneity by employing Characteristic length of materials. Quasi-static couple stress and classical dynamic approaches do not include explicitly the size of the material unit cell in the formulation of the problem. Contrary to these theories, the present approach fully takes into account this intrinsic material length by appropriately considering a micro-inertia term in the balance of angular momentum. In this investigation, the elasto-dynamic field of propagation of SH-wave in media with cylindrical inhomogeneity on the micro and nano scales has been obtained by considering couple stress and effect of micro inertia term. Subsequently, the problem has been solved for two limiting cases, cavity and rigid, and the results have been compared with classical theory. The wave considered here is a plane wave that causes transverse displacements in the direction of longitudinal axis of cylinder and the inhomogeneity has circular cross section. The formulation used here is in polar coordinates which lead to exact series solution involving Bessel’s and Modified Bessel’s functions. Comparison of the results reveals that the couple stress theory properly considers size effects in displacement and stress fields in matrix and inhomogeneity. The outcomes also demonstrate that increasing the size of inhomogeneity and distance from inhomogeneity leads to reducing the effect of couple stress, and the results approach to classical theory.

  9. Keywords:
  10. Conjugate Stresses ; Size Effect ; Microstructure ; Nanostructure ; Cylindrical Inhomogeneity ; SH Wave

 Digital Object List

 Bookmark

No TOC