MCST-based finite element solution for short-fiber-reinforced microbeam vibration with the effects of rotary inertia and Pasternak medium

A survey of the literature shows the absence of a microstructure-dependent finite element model that accounts for the vibration of short-fiber-reinforced microbeams with modified couple stress theory, rotary inertia, and Pasternak elastic medium. The present work is directed toward filling this gap in the literature. In the present study, the longitudinal and transverse Young’s moduli of the short-fiber-reinforced material are modeled using the Halpin-Tsai equations. Additionally, the rule of mixture is considered for the calculation of the short-fiber-reinforced material mass density. Using Rayleigh beam theory, modified couple stress theory and finite element methodology, the research investigates the various effects such as the fiber Young's modulus, fiber mass density, fiber volume fraction, material length scale parameter and elastic medium stiffnesses. In this study, fibers are assumed to be randomly distributed in the matrix since fiber orientation in small-scale composite structures is difficult and even impossible in some cases. The results of the analysis presented in this study are expected to be helpful in the design of nano-electro-mechanical systems and micro-electro-mechanical systems.