Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams

Abstract

In this paper, forced vibration investigation of a nanocomposite beam reinforced with different distributions of graphene platelets (GPLs) in thermal environments is performed by the development of a higher-order refined beam element. The developed beam element contains ten degrees of freedom related to axial, bending and transverse shear displacements. A uniformly distributed dynamic load with harmonic oscillations is exerted to the nanocomposite beam. Different GPL distributions such as uniform, linear and nonlinear are considered. Convergence studies of the obtained results from the finite element method are also provided. Also, the obtained results based on the presented solution are verified with a previously published paper on vibration of GPL-reinforced beams. This research shows that the resonance behavior of a nanocomposite beam can be controlled by the GPL content and dispersions. Therefore, it is showed that the dynamical deflection is significantly affected by GPL weight fraction, type of GPL distribution, temperature change, elastic substrate and excitation frequency of applied dynamic load.

On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

“…e nondimensional fundamental frequencies ω � ωL 2 �������� ρ m A/E m I are compared, where A � b.h, I � b.h 3 /12. Table 2 shows the calculation and comparison results, which demonstrate that as the mesh size increases, the results converge to a frequency value that is near to the frequency calculated using the finite element approach [3] (based on a refined beam theory which is different from the beam theory used in this work). is shows that the approach employed in this study ensures the requisite level of dependability.…”

“…e natural frequency of the FG-GPLRC beam generated from this case is then compared to the finite element method (FEM) [3], which utilized a refined beam theory.…”

“…e geometry and material specifications are described in [3], with L/h � 10 and W GPL � 1% for a uniformly GPL-reinforced beam.…”

“…Also, based on the first-order shear deformation beam theory combined with the differential quadrature method, Song et al [2] investigated the nonlinear free vibration of edge-cracked graphene nanoplatelet-(GPL-) reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments. Barati and Shahverdi [3] studied the forced vibration problem of a nanocomposite beam reinforced with different distributions of graphene platelets in thermal environments using the development of a higherorder refined beam element. Wang and his co-workers [4] used a new Ritz-solution shape function and an improved third-order shear deformation theory to capture the solution for free and forced vibrations of a functionally graded polymer nanocomposite beam reinforced with a low content of graphene oxide and excited by a moving load with a constant velocity.…”

Nonlocal strain gradient shell theory for bending analysis of FG spherical nanoshells in thermal environment

“…Nonlocal elasticity is one of the size-dependent continuum theories which reflects the interaction between atoms (Eringen [20]). Many types of research have been applied to Eringen's nonlocal elasticity theory to analyze the nanosize structures [21][22][23][24][25][26][27]. Although Eringen's nonlocal elasticity theory has been applied for analyzing the nanosize structures, it distinguishes only the softening effect.…”