Vibration analysis of graphene sheets resting on the orthotropic elastic medium subjected to hygro-thermal and in-plane magnetic fields based on the nonlocal strain gradient theory

Abstract

This paper develops a nonlocal strain gradient plate model for vibration analysis of the graphene sheets under in-plane magnetic field and hygro-thermal environments. For more accurate analysis of the graphene sheets, the proposed theory contains two-scale parameters related to the nonlocal and strain gradient effects. The graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, elastic foundation, and magnetic field on vibration characteristics of the graphene sheets are examined.

Mono-scale and multi-scale formulations of gradient-enriched dynamic piezomagnetics

“…In dynamic magneto-mechanical coupling, Mindlin's gradient theory [24] has been used in the vibration analysis of micro-bar and nano-plates [25]. Similarly, Eringen's gradient theory [26] has been employed to analyse the effects of magnetic field on the vibration of [27,28,29], and wave propagation in [30,31], carbon nanotubes and nano-beams. A Kelvin-Voigt model [32] has been used to explore the effect of magnetic field on the vibration of graphene sheet with different Winkler coefficients [33].…”

Buckling of bimorph functionally graded piezoelectric cylindrical nanoshell

“…Therefore, by substituting equation (30) into equation (21), the incremental values of stress resultants are obtained. Upon substitution of equation (21) in equation (25), the terms in resulting equations with subscript 0 drop out due to satisfying equilibrium conditions and nonlinear terms of incremental values are ignored, because they are small compared to linear terms.…”

“…26 The nonlocal strain gradient theory, another nonclassical continuum theory, proposed by Lim et al, considers higher order stress gradients and strain gradient nonlocality simultaneously. [27][28][29][30] Also this theory consists of both nonlocal effects of the strain field and first gradient strain field. Buckling and postbuckling were studied by Li et al based on the nonlocal stain gradient theory and the influence of size effect was presented significant.…”

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

“…Kiasat et al [32], Pouresmaeeli et al [33], Liu et al [34] and Hosseini et al [35] studied the free vibrations of thin plates made of functionally graded materials and composite materials, using the Love-Kirchhoff theory, also known as the classical plate theory (CPT), resting on visco-Winkler and visco-Winkler-Pasternak foundations, using the Kelvin-Voigt viscoelastic model. As for Ebrahimi and Barati [36] and Arefi and Zenkour [37], they used a refined higher-order plate theory with a trigonometric shear stress function for the purpose of exploring the influence of viscoelastic parameters, due to hygrothermal and piezoelectric charges, on the vibration frequency of FGM nanoplates and viscoelastic sandwich nanoplates with nonlocal effect.…”