Dynamic Stability of Temperature-Dependent Graphene Sheet Embedded in an Elastomeric Medium

Abstract

This work applies the first-order shear deformation theory (FSDT) to study the dynamic stability of orthotropic temperature-dependent single-layered graphene sheet (SLGS) embedded in a temperature-dependent elastomeric medium and subjected to a biaxial oscillating loading in a thermal environment. Possible thermal effects are considered in the size-dependent governing equations of the problem. These last ones are derived by means of the Hamilton’s variational principle combined with the Eringen’s differential constitutive model. Navier’s solution as well as Bolotin’s approach are applied to obtain the dynamic instability region (DIR) of the graphene sheet. Thus, a parametric study is carried out to explore the sensitivity of the DIR of the graphene sheet to the temperature variation, the static load factor, the aspect ratio, the foundation type, and the nonlocal parameter (NP). Results indicate that the dimensionless pulsation frequency reduces for increasing values of temperature and NP, whereas the size effect becomes even more pronounced for increasing temperatures. In addition, the adoption of temperature-dependent mechanical properties, rather than independent ones, yields a global shift of the DIR to smaller pulsating frequencies. This proves the relevance of the temperature-dependent mechanical properties to obtain reliable results, in a physical sense.

Vibrations and buckling of triangular graphene sheet in polymer matrix

“…The considering problem was studied by many authors in the case when the nanoplate has a rectangular plate. Namely, the linear and nonlinear vibrations, buckling and stability of single-or double-layer nanoplates are considered in the works [17][18][19][20][21][22][23][24], where the studied plate is supposed to be embedded in the Winkler-Pasternak foundation. Nonlinear vibrations of bilayer graphene embedded in a nonlinear polymer matrix are investigated by Jomehzadeh et al [25] Nonlocal postbuckling analysis was performed by Naderi and Saidi [26], where the studied graphene sheet (GS) system is embedded in a polymer environment, while its influence is considered as a nonlinear function of deflection.…”

“…Thus, an increase in the linear coefficient of interaction force 𝛼 1 yields an increase in the critical buckling parameter 𝜆 𝑐𝑟 = 𝑝 𝑙𝑒 𝑎 2 𝐷 (𝑚 = 1, 𝑛 = 2), see Figure 6a. In the case of nonlinear interaction between the GS and polymer matrix, we obtain a nonlinear load-deflection relation (18). Figure 6b demonstrates the postbuckling path (𝑚 = 1, 𝑛 = 2) for leg length 𝑎 = 5 𝑛𝑚 and nonlocal parameter 𝜇 = 1 𝑛𝑚 2 .…”

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

“…Several experimental evidences in literature, have revealed that the behavior of micro-structures is size-dependent [2][3][4][5]. Thus, a large number of works has been recently published to conceive novel structural solutions, systems, and devices, while adopting different types of reinforcement phase, such as graphene nanoplatelets [6][7][8][9][10][11][12][13][14], or carbon nanotubes [15][16][17][18][19]. Among a large variety of numerical strategies, higher order theories represent the most useful tool for the investigation of the static and dynamic response of materials at different scales [20][21][22][23][24].…”

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

“…A large variety of size-dependent theories of elasticity have been applied recently in literature to study the mechanics of nanostructures, including Eringen's nonlocal models [28][29][30][31], modified couple stress theories [32][33][34][35][36], and nonlocal strain gradient laws [37,38]. Many further coupled nonlinear problems involving composite nanostructures can be found in previous studies [39][40][41][42][43][44][45][46][47][48][49].…”