Magnetic field and non-local effects on axial vibration of embedded nanorods reinforced with short fibers

Abstract

In this work, an attempt is made for the first time to present the axial vibration of non-local rods made of a polymer matrix reinforced with short fibers under the influence of a magnetic field and an elastic medium. This paper examines the influences of small-scale based on the non-local theory and a transverse magnetic field on free axial vibration of short-fiber-reinforced nanorods embedded in an elastic medium for the first time in the literature and prefers the finite element method. Using the Lorentz magnetic force derived from Maxwell’s relation, the equation of motion for the non-local axial vibration of the short-fiber-reinforced nanorods subjected to the transverse magnetic field and embedded in an elastic medium is constituted. Then, a size-dependent finite element formulation of embedded and magnetically affected short-fiber-reinforced nanorods is posed based on the weighted residual method. The dimensionless frequencies of clamped–clamped and clamped-free embedded short-fiber-reinforced nanorods are calculated by using the finite element method based on various arguments such as mode number, fiber properties, non-local parameter, magnetic parameter, magnetic field strengths’ ratio and elastic medium. The changes in frequencies due to the effects of these arguments are presented with a number of figures and tables and a detailed discussion is carried out.