Geometrically Nonlinear Electromechanical Instability of FG Nanobeams by Nonlocal Strain Gradient Theory

2021 ◽  
pp. 2150051
Author(s):  
S. M. J. Hosseini ◽  
J. Torabi ◽  
R. Ansari ◽  
A. Zabihi
Keyword(s):  
Differential Equation ◽  
Strain Gradient ◽  
Electrostatic Force ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Electromechanical Instability ◽  
Nonlocal Strain Gradient

This paper is concerned with studying the size-dependent nonlinear dynamic pull-in instability and vibration of functionally graded Euler–Bernoulli nanobeams (FG-EBNs) with the von Kármán hypothesis based on the nonlocal strain gradient theory (NLSGT). To this end, the partial differential equation (PDE) is developed by Hamilton’s principle considering the intermolecular, fringing field and electrostatic nonlinear forces. Then, the Galerkin method (GM) is utilized to acquire the ordinary differential equation (ODE) and the results are obtained with the help of an analytical approach called the homotopy analysis method (HAM). To verify the outcome of this study, the nonlinear and linear frequencies obtained are compared with those of the literature. Consequently, the pull-in voltage of the FG nanobeam is obtained and the variations of nonlinear and linear frequencies are discussed in detail. Also, the effects of initial amplitude, electrostatic force, length scale, nonlocal parameter, material gradient index and boundary condition (BC) on the electromechanical behavior of FG-EBNs are analyzed with the results commented.

A nonlocal strain gradient theory for rotating thermo-mechanical characteristics on magnetically actuated viscoelastic functionally graded nanoshell

2020 ◽  
Vol 31 (12) ◽  
pp. 1511-1523
Author(s):  
Mohammad Mahinzare ◽  
Hossein Akhavan ◽  
Majid Ghadiri
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Smart Structure ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Nonlocal Strain Gradient

In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

scholarly journals An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

2019 ◽  
Vol 40 (12) ◽  
pp. 1723-1740 ◽  
Author(s):  
Z. Sharifi ◽  
R. Khordad ◽  
A. Gharaati ◽  
G. Forozani
Keyword(s):  
Strain Gradient ◽  
Analytical Study ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Functionally Graded Piezoelectric ◽  
Nonlocal Strain Gradient

AbstractIn this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton’s principle and derive the governing differential equations. Then, we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the side-tothickness ratio, and the nanoplate shape on natural frequencies are investigated.

Nonlinear Instability Modeling of a Nonlocal Strain Gradient Functionally Graded Capacitive Nano-Bridge in Thermal Environment

2018 ◽  
Vol 10 (08) ◽  
pp. 1850083 ◽  
Author(s):  
Ilgar Jafarsadeghi-Pournaki ◽  
Ghader Rezazadeh ◽  
Rasool Shabani
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Electrostatic Force ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Weighted Residual Method ◽  
Energy Principle ◽  
Nonlocal Strain Gradient

This paper develops a theoretical model directed towards investigation of the static pull-in instability of a functionally graded (FG) electrostatically actuated nano-bridge via nonlocal strain gradient theory (NLSGT) of elasticity and Euler–Bernoulli beam theory in thermal environment. The nano-beam is under the influence of electrostatic and van der Waals (vdW) forces. In addition to the nonlinear nature of the electrostatic force, the other type of nonlinearity namely geometric nonlinearity resulting from the mid-plane stretching is considered. Material properties of FG nano-beam are assumed to vary gradually along the thickness direction according to simple power-law form. With the purpose of eliminating the coupling between the stretching and bending due to the asymmetrical material variation along the thickness, a new surface reference is introduced. The nonlinear integro-differential governing equation is derived utilizing minimum total potential energy principle, linearized by means of the step-by-step linearization method (SSLM) and solved by Galerkin-based weighted residual method. The numerical investigations are performed while the emphasis is placed on studying the effect of various parameters including: nonlocal parameter, material characteristic length scale, material gradient index, thermal effect and intermolecular force on the static pull-in instability of FG nano-beam. To establish the validity of the present formulation, a comparison is conducted with experimental and numerical results reported in previous studies.

The Nonlocal Strain Gradient Theory for Hygrothermo-Electromagnetic Effects on Buckling, Vibration and Wave Propagation in Piezoelectromagnetic Nanoplates

2019 ◽  
Vol 11 (07) ◽  
pp. 1950067 ◽  
Author(s):  
Mohammad Alakel Abazid
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Nonlocal Parameter ◽  
Thermal Buckling ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Elastic Substrate ◽  
Nonlocal Strain Gradient Theory ◽  
Electromagnetic Effects ◽  
Nonlocal Strain Gradient

A nonlocal strain gradient theory (NSGT) is utilized to investigate the thermal buckling, free vibration and wave propagation in smart piezoelectromagnetic nanoplates in hygrothermal environments embedded in an elastic substrate. The main advantage of the NSGT over other continuum theories is that it contains both nonlocal parameter and material length scale parameter. The elastic substrate is modeled as Pasternak foundation model. According to the NSGT and the sinusoidal two-variable shear deformation plate theory, the governing equations of motion are derived involving the material parameters and hygrothermo-electromagnetic effects. The present solutions are checked through comparisons with those presented in the literature. Numerical results show the impacts of the nonlocal and gradient parameters, side-to-thickness ratio, hygrothermo-electromagnetic loads and substrate stiffness on the thermal buckling, frequencies and wave propagation in the smart nanoplates.

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