Abstract
Abstract This paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.
Highlights
Today, composite materials have improved the performance in various mechanisms
In order to study the vibrational behavior of current composite model, natural frequencies are presented for the various geometrical parameters, α parameter represents ratio of length to lamina thickness (a/h). β parameter signifies width to lamina thickness (b/h)
A new model was presented for nanoscale composites
Summary
Composite materials have improved the performance in various mechanisms. by exploiting the low volume fraction of the reinforcement, the mechanical properties of structures have been greatly improved and lead to the ideal efficiency of consumables [1,2,3,4]. Barretta and Sciarra [36] investigated constitutive boundary conditions of nano- beams according to nonlocal strain gradient theory. Tadi et al [46, 47] studied free vibration and buckling of CNT based on anisotropic size dependent shell model. Yunlong et al [58] studied the mechanical properties of polymer composite reinforced by CNT and graphene sheet. New size dependent formulation is presented for the vibrational behavior of nano-composite. For sake of this aim, the anisotropic motion equations are extracted using Hamilton’s principle. The size effect is involved according to the couple stress theory It is noted the present vibrational equations are reduced to different states in certain conditions:. Different vibrational mode shapes of lamina have been shown
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