Surface and Thermal Effects on the Pull-In Behavior of Doubly-Clamped Graphene Nanoribbons Under Electrostatic and Casimir Loads

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Hossein Rokni ◽  
Wei Lu
Keyword(s):  
Surface Tension ◽  
Analytical Model ◽  
Graphene Nanoribbons ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Variable Coefficients ◽  
Experimental Models ◽  
Multilayer Graphene ◽  
Casimir Forces ◽  
Special Cases

In this study, a comprehensive analytical model is established based on Euler–Bernoulli beam theory with von Kármán geometric nonlinearity to investigate the effect of residual surface tension, surface elasticity, and temperature on the static pull-in voltages of multilayer graphene nanoribbon (MLGNR) doubly-clamped beams under electrostatic and Casimir forces and axial residual stress. An explicit closed-form analytical solution to the governing fourth-order nonlinear differential equation of variable coefficients is presented for the static pull-in behavior of electrostatic nanoactuators using a Fredholm integral equation of the first kind. The high accuracy of the present analytical model is validated for some special cases through comparison with other existing numerical, analytical, and experimental models. The effects of the number of graphene nanoribbons (GNRs), temperature, surface tension, and surface elasticity on the pull-in voltage and displacement of MLGNR electrostatic nanoactuaotrs are investigated. Results indicate that the thermal effect on the pull-in voltage is significant especially when a smaller number of GNRs are used. It is found that the surface effects become more dominant as the number of GNRs decreases. It is also demonstrated that the residual surface tension exerts a greater influence on the pull-in voltage in comparison with the surface elasticity.

Hydrophobic Ferrocene Derivatives as Potential Standards in Electrochemistry

1997 ◽  
Vol 62 (2) ◽  
pp. 185-198 ◽  
Author(s):  
Jaroslav Podlaha ◽  
Petr Štěpnička ◽  
Róbert Gyepes ◽  
Vladimír Mareček ◽  
Alexander Lhotský ◽  
...  
Keyword(s):  
Surface Tension ◽  
Cyclic Voltammetry ◽  
Redox Potential ◽  
Diffusion Coefficients ◽  
Carbon Electrodes ◽  
X Ray Diffraction ◽  
Ferrocene Derivatives ◽  
X Ray ◽  
Special Cases ◽  
As Solubility

Ferrocene (FcH) derivatives monosubstituted by palmitoyl (1), hexadecyl (2), 1-adamantoyl (3) or 1-adamantylmethyl (4) groups were sythesized and characterized by NMR, mass and 57Fe Mossbauer spectroscopy. The structure of 1-adamantoylferrocene was determined by single-crystal X-ray diffraction. Cyclic voltammetry on gold and glass-like carbon electrodes demonstrated that the compounds can serve as electrochemical standards for special cases since their ferrocene/ferricinium redox potential remains stable and reversible, while the properties such as solubility, diffusion coefficients and surface tension are strongly solvent-dependent.

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

scholarly journals Nonlinear Analytical Model of Two Weakly Coupled MEMS Cantilevers for Mass Sensing Using Electrostatic Actuation

Proceedings ◽  
2018 ◽  
Vol 2 (13) ◽  
pp. 1084
Author(s):  
Toky Rabenimanana ◽  
Vincent Walter ◽  
Najib Kacem ◽  
Patrice Le Moal ◽  
Joseph Lardiès
Keyword(s):  
Analytical Model ◽  
Beam Theory ◽  
Continuous System ◽  
Mode Localization ◽  
Dc Voltage ◽  
Weakly Coupled ◽  
Flexible Supports ◽  
Nonlinear Analytical Model ◽  
Mems Mass Sensor ◽  
Mems Cantilevers

This paper presents a nonlinear analytical model of MEMS mass sensor, which is composed of two cantilevers of 98 µm and 100 µm length, 20 µm width and 1.3 µm thick. They are connected by a coupling beam and only the shortest cantilever is actuated by a combined AC-DC voltage. The DC voltage is used to equilibrate the system and the phenomenon of mode localization is investigated when a mass perturbation is applied. The sensor is modeled as a continuous system with beam theory and non-ideal boundary conditions are considered by using flexible supports. With a low AC voltage of 10 mV, a DC voltage of 5.85 V can counterbalance the length difference. This DC voltage decreases at 5.60 V when we increase the AC voltage, due to the effect of electrostatic nonlinearities. For a relative added mass of 0.1%, the amplitude change in the two cantilevers is more important when the coupling is weaker.

Flexure-Based Two Degree-of-Freedom Legs for Walking Microrobots

2006 ◽  
Author(s):  
Ankur M. Mehta ◽  
Kristofer S. J. Pister
Keyword(s):  
Analytical Model ◽  
Design Space ◽  
Beam Theory ◽  
Degree Of Freedom ◽  
Bernoulli Beam ◽  
Comb Drive ◽  
Walking Gait ◽  
Euler Bernoulli Beam ◽  
Force Displacement ◽  
Two Degree Of Freedom

This work examines the design of legs for a walking microrobot. The parameterized force-displacement relationships of planar serpentine flexure-based two degree-of-freedom legs are analyzed. An analytical model based on Euler-Bernoulli beam theory is developed to explore the design space, and is subsequently refined to include contact between adjacent beams. This is used to determine a successful leg geometry given dimensional constraints and actuator limitations. Standard comb drive actuators that output 100 μN of force over a 15 μm bi-directional throw are shown able to drive a walking gait with three legs on a 1 cm2 silicon die microrobot. If the comb drive suspensions cannot withstand the generated reaction moments, an alternate pivot-based leg linkage is proposed.

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.

scholarly journals Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

2014 ◽  
Vol 51 (A) ◽  
pp. 213-226 ◽  
Author(s):  
Bernt Øksendal ◽  
Leif Sandal ◽  
Jan Ubøe
Keyword(s):  
Continuous Time ◽  
Variable Coefficients ◽  
Uncertain Demand ◽  
Uhlenbeck Process ◽  
Delayed Information ◽  
Equilibrium Prices ◽  
Special Cases ◽  
Explicit Formulae ◽  
Contracting Model ◽  
Vertical Contracting

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

Nanoindentation hardness of a Steigmann–Ogden surface bounding an elastic half-space

2018 ◽  
Vol 24 (9) ◽  
pp. 2754-2766 ◽  
Author(s):  
Xiaobao Li ◽  
Changwen Mi
Keyword(s):  
Surface Tension ◽  
Half Space ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Indentation Hardness ◽  
Bending Rigidity ◽  
Size Dependent ◽  
Significant Difference ◽  
Nanoindentation Hardness ◽  
Membrane Stiffness

Previous studies demonstrate that, for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads. Therefore, in addition to the conventional residual surface tension and membrane stiffness, the curvature dependence of surface energy is desired for inhomogeneously strained nanostructures. In this paper, we aim to reevaluate the size-dependent nanoindentation hardness of an elastic half-space subjected to nanosized frictionless traction, through the use of both the curvature-independent Gurtin–Murdoch and the curvature-dependent Steigmann–Ogden models of surface elasticity. The nanoindentation problem is solved by the integration of Boussinesq’s method of displacement potentials and Hankel integral transforms. As examples, the effects of residual surface tension, membrane stiffness, and bending rigidity of the half-space boundary are parametrically analyzed in detail for a uniform circular pressure and a concentrated normal force. The observations in semianalytical calculations suggest a significant difference in the nanoindentation hardnesses predicted from the two popular models of surface mechanics. In most cases, the inclusion of bending rigidity results in smaller displacements and stresses, and therefore higher indentation hardness. Based on physically interpretable numerical values of surface material properties, we show that a curvature-dependent model of surface elasticity is required in order to characterize the size-dependent feature of nanoindentation problems correctly.

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