Frequency analysis of a FGM micro-beam subjected to subtangential forces

This paper is prepared to explore the frequency analysis of afunctionally graded material (FGM) micro-beam subjectedto a subtangential force. The Euler-Bernoulli beam modeland the modified strain gradient theory (MSGT) is used totake size effects into account in terms of three length scaleparameters. However, the MSGT includes modified couplestress theory (MCST) and classical theory (CT) as specialcases. Applying Hamilton’s principle and Galerkin method,the governing equation and corresponding boundaryconditions are obtained and then solved numerically,respectively. The results illustrated effects of nonconservativeparameter and different material gradient indexon the natural frequencies of the system.

Keywords:

frequency analysis , Modified straingradient theory , Functionally graded materials , Subtangential force