Dynamic analysis of microbeams based on modified strain gradient theory using differential quadrature method

Abstract

Dynamic analysis of microbeams based on the modified strain gradient elasticity theory (MSGT) is carried out in this study. MSGT theory comprises additional material length scale parameters to effectively capture the size effect. Beams with fixedfixed, simply supported and fixed-free boundary conditions are analysed. Additionally, frequency analysis for beams based on modified coupled stress and continuum theory is also presented by neglecting one or more length scale parameters. Results obtained for various theories in the present analysis are compared with those available in literature. Differential quadrature method (DQM) is employed to perform the analysis. Two different techniques are presented for implementing different boundary conditions of beam. It is shown that frequencies obtained from the strain gradient theory are higher when compared to the frequencies predicted by modified coupled stress theory and classical theory, when beam thickness becomes comparable to the length scale parameter. Besides, we also show that implementation of DQM is simple, accurate and robust in solving vibrational problems of different nature.