Transient dynamic analysis of functionally graded micro-beams considering small-scale effects


Eshraghi I., Dag S.

ARCHIVES OF MECHANICS, vol.73, no.4, pp.303-337, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.24423/aom.3786
  • Title of Journal : ARCHIVES OF MECHANICS
  • Page Numbers: pp.303-337
  • Keywords: boundary element method, functionally graded materials, Timoshenko micro-beam, vibrations, modified couple stress theory, BOUNDARY-ELEMENT METHOD, NONLINEAR FORCED VIBRATION, D-BEM APPROACH, WAVE-EQUATION, TIME-DOMAIN, STRESS, PLATES, FORMULATION, FREQUENCY

Abstract

A DOMAIN-BOUNDARY ELEMENT METHOD, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. In-corporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is ob-tained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro-and macro-scale beams. Numerical results illustrate elasto-dynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.