Abstract
The vibrational characteristics of multilayer magnetic nanocomposite beams reinforced by graphene nanoplatelets (GPLs) are analytically investigated in this paper. The effects of an elastic foundation are also studied. The material properties of piece-wise GPL-reinforced nanocomposites (GPLRCs) are assumed to be graded in the thickness direction of the beams and can be estimated by using the modified Halpin–Tsai model and rules of mixtures. The two-dimensional elasticity theory is adopted to derive the governing equation combined with the state space method, and the analytical frequency equations for simply supported beams are obtained. In addition, the effects of a magnetic field are involved via Maxwell’s equation, and the corresponding Lorentz forces are considered in this work. Numerical examples are carried out to examine the effects of magnetic fields in various directions, the GPL distribution pattern, the scale parameter and weight function of GPLs, as well as an elastic foundation, on the vibration behaviors of functionally graded (FG)-GPLRC beams.
Highlights
Graphene-based nanocomposites, a novel kind of promising functionalized nanomaterials, show a wide range of applications in engineering, such as sensors, fuel cells, supercapacitors, and batteries, due to the excellent mechanical, chemical, and physical properties [1,2,3,4]
The recent trend is the addition of graphene nanoplatelets (GPLs) as nano-reinforcements dispersed into a polymer matrix to yield polymer nanocomposites
The state space equations for the j-th layer of the functionally graded (FG)-GPL-reinforced nanocomposites (GPLRCs) beam in the magnetic fields along the x, y, and z directions are established as given in a unified matrix form of Equation (19), and the corresponding coefficient matrices An are defined in Equations (20), (22) and (24), respectively
Summary
Graphene-based nanocomposites, a novel kind of promising functionalized nanomaterials, show a wide range of applications in engineering, such as sensors, fuel cells, supercapacitors, and batteries, due to the excellent mechanical, chemical, and physical properties [1,2,3,4]. The volume/weight fraction of GPLs varies linearly or nonlinearly through the thickness of the structures, and the mechanical behaviors of the nanocomposites emerge as functional gradations Yang and his coauthors proposed the piece-wise FG-GPL reinforced models for beams [18,19,20], plates [21,22,23,24,25], and shells [26,27,28], where the isotropic Halpin–Tsai equation was adopted to predict the effective Young’s modulus of the nanocomposites. The main aim of the present paper is to examine the free vibration of functionally graded GPL reinforced multilayer nanocomposite beams resting on an elastic foundation within in-plane and out-of-plane magnetic fields.
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