Free vibration of short-fiber-reinforced tapered micro column via the modified couple stress theory

This study aims to shed light on a current topic that has not been previously addressed in the literature. This study presents the free vibration of short-fiber-reinforced composite micro columns with variable cross-section, considering the size effect. The composite micro columns are formed by a polymer matrix reinforced with short-fibers. Short-fibers are randomly dispersed throughout the polymer matrix of composite micro columns. The Halpin-Tsai model is used to compute the effective elasticity modulus, and the rule of mixture is used to get the effective mass density. The micro columns’ cross-section shows a linear variation in both the width and height axes. Furthermore, the modified couple stress theory is adopted to study the size effect, a crucial parameter at small scales. The assumptions of Bernoulli-Euler beam theory are considered because micro columns are treated as thin structures. The fundamental vibration frequencies of short-fiber-reinforced tapered micro columns are determined using the Rayleigh-Ritz method. The effects of the following factors on the variation of composite micro columns’ fundamental vibration frequencies with clamped-free and clamped-clamped boundary conditions are examined in detail: the height variation ratio, the material length scale parameter, the width variation ratio, the double taper ratio, the fiber-to-matrix elasticity modulus ratio, the fiber-to-matrix mass density ratio, the fiber volume fraction, and the fiber length-to-diameter ratio.