Surface Stress Effect on the Pull-In Instability of Hydrostatically and Electrostatically Actuated Rectangular Nanoplates With Various Edge Supports

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
M. Faghih Shojaei ◽  
V. Mohammadi ◽  
M. A. Darabi
Keyword(s):  
Boundary Conditions ◽  
Governing Equation ◽  
Surface Stress ◽  
Plate Thickness ◽  
Stress Effect ◽  
Residual Surface Stress ◽  
Electrostatically Actuated ◽  
Stress Effects ◽  
Size Dependent ◽  
Surface Stress Effect

This paper is aimed to investigate the size-dependent pull-in behavior of hydrostatically and electrostatically actuated rectangular nanoplates including surface stress effects based on a modified continuum model. To this end, based on the Gurtin–Murdoch theory and Hamilton's principle, the governing equation and corresponding boundary conditions of an actuated nanoplate are derived; the step-by-step linearization scheme and the differential quadrature (GDQ) method are used to discretize the governing equation and associated boundary conditions. The effects of the thickness of the nanoplate, surface elastic modulus and residual surface stress on the pull-in instability of the nanoplate are investigated. Plates made of two different materials including aluminum (Al) and silicon (Si) are selected to explain the variation of the pull-in voltage and pressure with respect to plate thickness.

Surface Stress Effect on the Vibrational Response of Circular Nanoplates With Various Edge Supports

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
M. Faghih Shojaei ◽  
V. Mohammadi ◽  
S. Sahmani
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Surface Stress ◽  
High Surface ◽  
Continuum Theory ◽  
Volume Ratio ◽  
Stress Effect ◽  
Size Dependent ◽  
Surface Stress Effect ◽  
Generalized Differential

The classical continuum theory cannot be directly used to describe the behavior of nanostructures because of their size-dependent attribute. Surface stress effect is one of the most important size dependencies of structures at this submicron size, which is due to the high surface to volume ratio of nanoscale domain. In the present study, the nonclassical governing differential equation together with corresponding boundary conditions are derived using Hamilton's principle, into which the surface energies are incorporated through the Gurtin-Murdoch elasticity theory. The model developed herein contains intrinsic length scales to take the size effect into account and is used to analyze the free vibration response of circular nanoplates including surface stress effect. The generalized differential quadrature (GDQ) method is employed to discretize the governing size-dependent differential equation along with simply supported and clamped boundary conditions. The classical and nonclassical frequencies of circular nanoplates with various edge supports and thicknesses are calculated and are compared to each other. It is found that the influence of surface stress can be different for various circumferential mode numbers, boundary conditions, plate thicknesses, and surface elastic constants.

scholarly journals Nonlinear Vibrational Analysis of Nanobeams Embedded in an Elastic Medium including Surface Stress Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
S. Azizi ◽  
B. Safaei ◽  
A. M. Fattahi ◽  
M. Tekere
Keyword(s):  
Surface Stress ◽  
High Surface ◽  
Surface Elasticity ◽  
Vibrational Analysis ◽  
Harmonic Balance Method ◽  
Volume Ratio ◽  
Stress Effect ◽  
Nanoscale Structures ◽  
Stress Effects ◽  
Surface Stress Effect

Due to size-dependent behavior of nanostructures, the classical continuum models are not applicable for the analyses at this submicron size. Surface stress effect is one of the most important matters which make the nanoscale structures have different properties compared to the conventional structures due to high surface to volume ratio. In the present study, nonlinear free vibrational characteristics of embedded nanobeams are investigated including surface stress effects. To this end, a thin surface layer is assumed on the upper and lower surfaces of the cross section to separate the surface and bulk of nanobeams with their own different material properties. Based on harmonic balance method, closed-form analytical solution is conducted for nonlinear vibrations to obtain natural frequencies of embedded nanobeams with and without considerations of surface elasticity and residual surface tension effects corresponding to the various values of nondimensional amplitude, elastic foundation modulus, and geometrical variables of the system. Selected numerical results are given to indicate the influence of each one in detail.

A Nonlinear Shear Deformable Nanoplate Model Including Surface Effects for Large Amplitude Vibrations of Rectangular Nanoplates with Various Boundary Conditions

2015 ◽  
Vol 07 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Reza Ansari ◽  
Mostafa Faghih Shojaei ◽  
Vahid Mohammadi ◽  
Raheb Gholami ◽  
Mohammad Ali Darabi
Keyword(s):  
Boundary Conditions ◽  
Surface Stress ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Free Vibrations ◽  
Model Parameters ◽  
Geometrically Nonlinear ◽  
Residual Surface Stress ◽  
Various Boundary Conditions ◽  
Shear Deformable

In this paper, a geometrically nonlinear first-order shear deformable nanoplate model is developed to investigate the size-dependent geometrically nonlinear free vibrations of rectangular nanoplates considering surface stress effects. For this purpose, according to the Gurtin–Murdoch elasticity theory and Hamilton's principle, the governing equations of motion and associated boundary conditions of nanoplates are derived first. Afterwards, the set of obtained nonlinear equations is discretized using the generalized differential quadrature (GDQ) method and then solved by a numerical Galerkin scheme and pseudo arc-length continuation method. Finally, the effects of important model parameters including surface elastic modulus, residual surface stress, surface density, thickness and boundary conditions on the vibration characteristics of rectangular nanoplates are thoroughly investigated. It is found that with the increase of the thickness, nanoplates can experience different vibrational behavior depending on the type of boundary conditions.

Surface stress effect in mechanics of nanostructured materials

2011 ◽  
Vol 24 (1) ◽  
pp. 52-82 ◽  
Author(s):  
Jianxiang Wang ◽  
Zhuping Huang ◽  
Huiling Duan ◽  
Shouwen Yu ◽  
Xiqiao Feng ◽  
...  
Keyword(s):  
Nanostructured Materials ◽  
Surface Stress ◽  
Stress Effect ◽  
Surface Stress Effect
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