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

Abstract

A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. Incorporating 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 obtained 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.