Modeling size-dependent thermoelastic energy dissipation of graphene nanoresonators using nonlocal elasticity theory

This paper deals with the size-dependent geometrically nonlinear free vibration of magneto-electro-thermo elastic (METE) nanoplates using the nonlocal elasticity theory. The mathematical formulation is developed based on the first-order shear deformation plate theory, von Kármán-type of kinematic nonlinearity and nonlocal elasticity theory. The influences of geometric nonlinearity, rotary inertia, transverse shear deformation, magneto-electro-thermal loading and nonlocal parameter are considered. First, the generalized differential quadrature (GDQ) method is utilized to reduce the nonlinear partial differential equations to a system of time-dependent nonlinear ordinary differential equations. Afterwards, the numerical Galerkin method, periodic time differential operators and pseudo-arc length continuation algorithm are employed to compute the nonlinear frequency versus the amplitude for the METE nanoplates. The presented methodology enables one to describe the large-amplitude vibration characteristics of METE nanoplates with various sets of boundary conditions. A detailed parametric study is carried out to analyze the important parameters such as the nondimensional nonlocal parameter, external electric potential, external magnetic potential, temperature change, length-to-thickness ratio, aspect ratio and various edge conditions on the nonlinear free vibration characteristics of METE nanoplates. The results demonstrate that considering the size effect on the vibration response of METE nanoplate results in decreasing the natural frequency, a remarkable increasing effect on the hardening behavior and subsequently increasing the nonlinear-to-linear frequency ratio.

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Size-Dependent Buckling and Postbuckling Analyses of First-Order Shear Deformable Magneto-Electro-Thermo Elastic Nanoplates Based on the Nonlocal Elasticity Theory

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455417500146 ◽

2017 ◽

Vol 17 (01) ◽

pp. 1750014 ◽

Cited By ~ 40

Author(s):

R. Ansari ◽

R. Gholami

Keyword(s):

Boundary Conditions ◽

Elasticity Theory ◽

Shear Deformation ◽

Nonlocal Elasticity ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Small Scale ◽

First Order ◽

Size Dependent ◽

Shear Deformable

This paper presents a nonlocal nonlinear first-order shear deformable plate model for investigating the buckling and postbuckling of magneto-electro-thermo elastic (METE) nanoplates under magneto-electro-thermo-mechanical loadings. The nonlocal elasticity theory within the framework of the first-order shear deformation plate theory along with the von Kármán-type geometrical nonlinearity is used to derive the size-dependent nonlinear governing partial differential equations and associated boundary conditions, in which the effects of shear deformation, small scale parameter and thermo-electro-magneto-mechanical loadings are incorporated. The generalized differential quadrature (GDQ) method and pseudo arc-length continuation algorithm are used to determine the critical buckling loads and postbuckling equilibrium paths of the METE nanoplates with various boundary conditions. Finally, the influences of the nonlocal parameter, boundary conditions, temperature rise, external electric voltage and external magnetic potential on the critical buckling load and postbuckling response are studied.

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