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Influences of surface effects and large deformation on the resonant properties of ultrathin silicon nanocantilevers

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Chinese Physics B 2012年第1期21卷 363-373页

作者： Zhang Jia-Hong Li Min Gu Fang Liu Qing-Quan Jiangsu Key Laboratory of Meteorological Observation and Information Processing Nanjing University of Information Science&TechnologyNanjing 210044China College of Math&Physics Nanjing University of Information Science&TechnologyNanjing 210044China

The purpose of the present work is to quantify the influences of the discrete nature, the surface effects, and the large deformation on the bending resonant properties of long and ultrathin （100） silicon nanocantilevers. We accomplish this by using an analytical semi-continuum Keating model within the framework of nonlinear, finite deformation kinematics. The semi-continuum model shows that the elastic behaviors of the silicon nanocantilevers are size-dependent and surface- dependent, which agrees well with the molecular dynamics results. It also indicates that the dominant effect on the fundamental resonant frequency shift of the silicon nanocantilever is adsorption-induced surface stress, followed by the discrete nature and surface reconstruction, whereas surface relaxation has the least effect. In particular, it is found that a large deformation tends to increase the nonlinear fundamental frequency of the silicon nanocantilever, depending not only on its size but also on the surface effects. Finally, the resonant frequency shifts due to the adsorption-induced surface stress predicted by the current model are quantitatively compared with those obtained from the experimental measurement and the other existing approach. It is noticed that the length-to-thickness ratio is the key parameter that correlates the deviations in the resonant frequencies predicted from the current model and the empirical formula.

关键词： resonant properties elastic properties surface effects silicon nanocantilevers

Nonlinear Vibration of FGM Sandwich Nanoplates with surface effects

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Acta Mechanica Solida Sinica 2023年第2期36卷 274-281页

作者： Junhua Xiao Jie Wang Department of Engineering Mechanics Yanshan UniversityQinhuangdao 066004China Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures Yanshan UniversityQinhuangdao 066004China

Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in *** using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into *** equations for nonlinear vibrations are obtained though the balance of *** Galerkin method is employed to obtain the approximate solutions for nonlinear free and forced vibrations of the FGM *** results show that considering surface effects changes the equivalent Young’s modulus and bending stiffness of FGM sandwich *** addition,the influences of surface effects are related to the geometric size of the *** examples are proposed to verify the effectiveness of the present results.

关键词： Functionally graded material Sandwich nanoplates surface effects Nonlinear vibration

TRANSVERSE VIBRATION OF A HANGING NONUNIFORM NANOSCALE TUBE BASED ON NONLOCAL ELASTICITY THEORY WITH surface effects

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Acta Mechanica Solida Sinica 2014年第2期27卷 202-209页

作者： Hossein Roostai Mohammad Haghpanahi Department of Mechanical Engineering Iran University of Science & Technology (IUST)

The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.

关键词： nonlocal elasticity theory vibration surface effects nanoscale tube

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

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Acta Mechanica Sinica 2018年第4期34卷 676-688页

作者： Hai-Sheng Zhao Yao Zhang Seng-Tjhen Lie School of Civil and Environmental Engineering Nanyang Technological University

Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions： hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.

关键词： Fredholm integral equation Natural frequency Nonlocal elasticity surface effects Timoshenko beam

Analytical Solutions for an Isotropic Elastic Half-Plane with Complete surface effects Subjected to a Concentrated/Uniform surface Load

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Acta Mechanica Solida Sinica 2024年第3期37卷 371-384页

作者： Xia-Hui Pan School of Civil Engineering Henan Polytechnic UniversityJiaozuo454003China

Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface *** the effects of residual surface stress and surface elasticity are *** stress function method and Fourier integral transform technique are *** solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at *** results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the *** elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally *** the remaining situations,combined effects of surface elasticity and residual surface stress should be *** results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface *** solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.

关键词： surface effects Residual surface stress surface elasticity Half-plane Analytical solutions

THREE-DIMENSIONAL MODELING FOR THIN PLATE-LIKE STRUCTURES INCLUDING surface effects BY USING STATE SPACE METHOD

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Acta Mechanica Solida Sinica 2010年第3期23卷 260-270页

作者： Hongyu Sheng Pin Lu Institute of Civil Engineering Hefei University of Technology Hefei 230009 China Institute of Materials Research and Engineering A ^＊STAR (Agency for Science Technology and Research) 3 Research Link Singapore 117602

A three-dimensional （3-D） approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. State equations, including the surface properties of the structure, can be established on the basis of 3-D fundamental elasticity to analyze the size-dependent static characteristics of the thin plate-like structure. Compared with two-dimensional plate theories based size-dependent models for thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of 2-D plate theories and various numerical approaches. To show the feasibility of the proposed approach, a 3-D analytical solution for a simply supported plate-like thin structure including surface layers is derived. An algorithm is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Numerical examples are carried out to exhibit the surface effects and some discussions are provided based on the results obtained.

关键词： micro-structures surface effects size-dependence state equation three-dimensional modeling

surface-effects-dominated thermal and mechanical responses of zinc oxide nanobelts

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Acta Mechanica Sinica 2006年第3期22卷 217-224页

作者： A. J. Kulkarni. M. Zhou The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta Georgia

t Molecular dynamics （MD） simulations are carried out to characterize the mechanical and thermal responses of [011^-1]-oriented ZnO nanobelts with lateral dimensions of 21.22A × 18.95 A, 31.02A× 29.42 A, and40.81A ×39.89A over the temperature range of 300-1000 K. The Young＇s modulus and thermal conductivity of the nanobelts are evaluated. Significant surface effects on properties due to the highsurface-to-volume ratios of the nanobelts are observed. For the mechanical response, surface-stress-induced internal stress plays an important role. For the thermal response, surface scattering of phonons dominates. Calculations show that the Young＇s modulus is higher than the corresponding value for bulk ZnO and decreases by -33% as the lateral dimensions increase from 21.22 A × 18.95A to 40.81 A × 39.89A. The thermal conductivity is one order of magnitude lower than the corresponding value for bulk ZnO single crystal and decreases with wire size. Specifically, the conductivity of the 21.22 A × 18.95 A belt is approximately （31-18）% lower than that of the 40.81 A × 39.89 A belt over the temperature range analyzed. A significant dependence of properties on temperature is also observed, with the Young＇s modulus decreasing on average by 12% and the conductivity decreasing by 50% as temperature increases from 300 K to 1000 K.

关键词： Zinc oxide nanobelts surface effects Size dependence Young's modulus Thermal conductivity

Small-scales effects on the electromechanical coupling behavior of piezoelectric nanowires with surface energy

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Small-scales effects on the electromechanical coupling behav...

Vibration and Buckling Analysis of Piezoelectric Nanowires Based on surface Energy Density

2011年全国压电和声波理论及器件应用研讨会

作者： K.F.Wang B.L.Wang~(1,*) 1 Graduate School at Shenzhen,Harbin Institute of Technology,Harbin 150001

＜正＞Based on the Euler-Bernoulli beam theory,the combined influence of the surface energy and nonlocal effect on electromechanical coupling behavior of a cantilever piezoelectric nanobeam was *** formula for electro... 详细信息

关键词： surface effects nonlocal elastic piezoelectric nanowires EMC coefficient

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Acta Mechanica Solida Sinica 2021年第3期34卷 425-436页

作者： Liyuan Wang Hongjun Han Key Laboratory of Mechanics on Disaster and Environment in Western China the Ministry of EducationCollege of Civil Engineering and MechanicsLanzhou UniversityLanzhou 730000China Longqiao College of Lanzhou University of Finance and Economics Lanzhou 730101China

In this paper,the influences of surface effects on free transverse vibration and buckling of piezoelectric nanowires are investigated by surface energy density elasticity *** relations are given for the natural frequencies of nanowires by taking into account the effects of surface energy density and surface relaxation *** implementing this theory with consideration of surface effects under clamped-clamped boundary conditions,the natural frequencies of nanowires are *** is shown that the natural frequency depends on both the surface effects and piezoelectricity.A closed-form solution is also obtained to calculate the critical buckling *** study is expected to provide useful insights for the design of piezoelectric nanowire-based nanodevices.

关键词： surface effects Piezoelectric nanowires Vibration Buckling Natural frequency Critical electric potential