Effects of residual surface stress and surface elasticity on the nonlinear free vibration of nanoscale plates

2012 ◽  
Vol 112 (1) ◽  
pp. 013520 ◽  
Author(s):  
K. F. Wang ◽  
B. L. Wang
Keyword(s):  
Free Vibration ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Nonlinear Free Vibration ◽  
Residual Surface Stress

Surface Effects on the Buckling of Piezoelectric Nanobeams

2012 ◽  
Vol 486 ◽  
pp. 519-523 ◽  
Author(s):  
Kai Fa Wang ◽  
Bao Lin Wang
Keyword(s):  
Shear Deformation ◽  
Electric Potential ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Stress Surface ◽  
Piezoelectric Nanobeam

In this paper, we analyze the influence of surface effects including residual surface stress, surface piezoelectric and surface elasticity on the buckling behavior of piezoelectric nanobeams by using the Timoshenko beam theory and surface piezoelectricity model. The critical electric potential for buckling of piezoelectric nanobeams with different boundary condition is obtained analytically. From the results, it is found that the surface piezoelectric reduces the critical electric potential. However, a positive residual surface stress increases the critical electric potential. In addition, the shear deformation reduces the critical electric potential, and the influence of shear deformation become more significant for a stubby piezoelectric nanobeam.

Surface Effects on Large Deflection of Nanobeams Subjected to a Follower Load

2020 ◽  
Vol 12 (06) ◽  
pp. 2050067
Author(s):  
Yun Xing ◽  
Yi Han ◽  
Hua Liu ◽  
Jialing Yang
Keyword(s):  
Large Deformation ◽  
Surface Stress ◽  
Large Deflection ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Residual Stress ◽  
Residual Surface Stress ◽  
Deformation Problem ◽  
Cross Sectional Dimension

As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

POSTBUCKLING OF PIEZOELECTRIC NANOBEAMS WITH SURFACE EFFECTS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250018 ◽  
Author(s):  
YUHANG LI ◽  
CHI CHEN ◽  
BO FANG ◽  
JIAZHONG ZHANG ◽  
JIZHOU SONG
Keyword(s):  
Electric Field ◽  
Significant Role ◽  
Energy Method ◽  
Material Properties ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Material ◽  
Residual Surface Stress ◽  
Piezoelectric Nanobeam

Surface effects, including surface elasticity, surface piezoelectricity and residual surface stress, on the postbuckling of piezoelectric nanobeams due to an electric field are investigated using an energy method in this paper. The critical buckling voltage and amplitude are obtained analytically in terms of the bulk and surface material properties and geometric parameters. The results show that surface effects play a significant role in the postbuckling of piezoelectric nanobeams. It is found that the influences of surface piezoelectricity and residual surface stress are more prominent than the surface elasticity. These results might be helpful for designing piezoelectric nanobeam-based devices.

Elastohydrodynamic Lubrication Line Contact Based on Surface Elasticity Theory

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Jie Su ◽  
Hong-Xia Song ◽  
Liao-Liang Ke
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elasticity Theory ◽  
Surface Stress ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Residual Surface Stress

Abstract Using surface elasticity theory, this article first analyzes the surface effect on the elastohydrodynamic lubrication (EHL) line contact between an elastic half-plane and a rigid cylindrical punch. In this theory, the surface effect is characterized with two parameters: surface elastic modulus and residual surface stress. The density and viscosity of the lubricant, considered as Newtonian fluid, vary with the fluid pressure. A numerical iterative method is proposed to simultaneously deal with the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Then, the fluid pressure and film thickness are numerically determined at the lubricant contact region. Influences of surface elastic modulus, residual surface stress, punch radius, resultant normal load, and entraining velocity on the lubricant film thickness and fluid pressure are discussed. It is found that the surface effect has remarkable influences on the micro-/nano-scale EHL contact of elastic materials.

Elastic Energy of Surfaces and Residually Stressed Solids: An Energy Approach for the Mechanics of Nanostructures

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Xiang Gao ◽  
Daining Fang
Keyword(s):  
Surface Energy ◽  
Elastic Energy ◽  
Surface Stress ◽  
Strain Energy ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Small Deformation ◽  
Energy Approach ◽  
Residual Surface Stress ◽  
The Impact

The surface energy plays a significant role in solids and structures at the small scales, and an explicit expression for surface energy is prerequisite for studying the nanostructures via energy methods. In this study, a general formula for surface energy at finite deformation is constructed, which has simple forms and clearly physical meanings. Next, the strain energy formulas both for isotropic and anisotropic surfaces under small deformation are derived. It is demonstrated that the surface elastic energy is also dependent on the nonlinear Green strain due to the impact of residual surface stress. Then, the strain energy formula for residually stressed elastic solids is given. These results are instrumental to the energy approach for nanomechanics. Finally, the proposed results are applied to investigate the elastic stability and natural frequency of nanowires. A deep analysis of these two examples reveals two length scales characterizing the significance of surface energy. One is the critical length of nanostructures for self-buckling; the other reflects the competition between residual surface stress and surface elasticity, indicating that the surface effect does not always strengthen the stiffness of nanostructures. These results are conducive to shed light on the importance of the residual surface stress and the initial stress in the bulk solids.

Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

2019 ◽  
Vol 19 (11) ◽  
pp. 1950127 ◽  
Author(s):  
Mohamed A. Attia ◽  
Rabab A. Shanab ◽  
Salwa A. Mohamed ◽  
Norhan A. Mohamed
Keyword(s):  
Surface Energy ◽  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Surface Stress ◽  
Couple Stress ◽  
Surface Elasticity ◽  
Functionally Graded ◽  
Residual Surface Stress ◽  
Stress Surface ◽  
Modified Couple Stress

An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time. The nanobeam theory is formulated based on the Timoshenko kinematics, augmented by von Kármán’s geometric nonlinearity. The modified couple stress and Gurtin–Murdoch surface elasticity theories are incorporated to capture the long-range interaction and surface energy, respectively. Unlike existing Timoshenko nanobeam models, the effects of surface elasticity, residual surface stress, surface mass density and Poisson’s ratio, in addition to bending and axial deformations, are incorporated in the newly developed model. A power law function is used to model the material distribution through the thickness of the beam, considering the gradation of bulk and surface material parameters. A variational formulation of the nonlinear nonclassical governing equations and associated nonclassical boundary conditions is established by employing Hamilton’s principle. The generalized differential quadrature method is exploited in conjunction with either the Pseudo-arclength continuation or Runge–Kutta method to solve the problem with an exact implementation of the nonclassical boundary conditions. The formulation and solution procedure presented are verified by comparing the obtained results with available ones. Based on the parametric study, it is concluded that the nonclassical boundary conditions, material length scale parameter, residual surface stress, surface elasticity, bulk elasticity modulus, gradient index, nonlinear amplitude and thickness have important influences on the linear and nonlinear vibration responses of functionally graded Timoshenko nanobeams.

Surface Effects on the Buckling of Nanowires Based on Modified Core-Shell Model

2014 ◽  
Vol 901 ◽  
pp. 3-9
Author(s):  
Hai Yan Yao ◽  
Guo Hong Yun
Keyword(s):  
Critical Load ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Core Shell ◽  
Nanowire Diameter ◽  
Residual Surface Stress ◽  
Work Surface ◽  
Effective Elasticity ◽  
S Model

In this work, surface effects including surface elasticity and residual surface stress on the buckling of nanowires are theoretically investigated. Based on modified core-shell (MC-S) model, the effective elasticity incorporating surface elasticity effect of the nanowire is derived, and by using the generalized Young-Laplace equation the residual surface stress is accounted for. The ratio of critical load with and without surface effects are obtained for a nanowire loaded in uniaxial compression. Taking silver (Ag) nanowires as an example, the analyzed results demonstrate that the influence of surface effects on the critical load of buckling becomes more and more significant as the nanowire diameter decreases. Moreover, it is shown that the influence of residual surface stress on the critical load is more prominent than that of surface elasticity.

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