Sharif Digital Repository

In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under... 

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are... 

Modified couple stress theory is a size-dependent theorem capturing the micro/nanoscale effects influencing the mechanical behaviors of the micro- and nanostructures. In this paper, it is applied to investigate the nonlinear vibration of carbon nanotubes under step DC voltage. The vibration, natural frequencies and dynamic pull-in characteristics of the carbon nanotubes are studied in detail. Moreover, the effects of various boundary conditions and geometries are scrutinized on the dynamic characteristics. The results reveal that application of this theory leads to the higher values of the natural frequencies and dynamic pull-in voltages  

The paper presents size-dependant mechanical behaviors of carbon nanotubes under electrostatic actuation using modified couple stress theory. The behaviors of the carbon nanotubes with different geometries and boundary conditions are studied in detail. The results reveal that application of this theory results in higher pull-in voltages for both cantilever and doubly clamped boundary conditions  

The paper deals with scrutinizing the vibration and dynamic pull-in behaviours of carbon nanotubes with different dimensions and boundary conditions. The strain gradient theory as a nonclassical elasticity theorem is applied in this research to compensate the limitations of the classical theories in predicting the mechanical behaviours of the micro- and nanostructures in general and carbon nanotubes, in particular under electrostatic actuation. The results reveal that the mechanical properties of carbon nanotube (CNTs) computed using the strain gradient theory differ significantly with those obtained from the classical theory. The strain gradient theory leads to higher stiffness and pull-in... 

The mechanism of gold nanowire (AuNW) and nanotube (AuNT) electrodeposition in a cyanide-free solution is investigated for the first time based on the analytical model of Szabo et al. (A. Szabo et al., J. Electroanal. Chem. 217 (1987) 417) for recessed cylindrical ultramicroelectrode (UME). Track-etched Polycarbonate Template (PCT) is served as cylindrical UME ensemble/arrays. Firstly, Au is nucleated through a charge transfer step and when the Nernst thickness exceeds the pore length, the radial diffusion is established around pore mouths. By overlapping of these domains, the planar diffusion toward the whole PCT surface is obtained. An analytic expression for global diffusion coefficient... 

This study investigates influence of fringing field effect on the voltage dependent behavior of electrostatically actuated micro-beams. For this purpose, the size dependent beam model is used. Strain gradient formulation is utilized to consider size effects. The effect of fringing field effect on the beam's behavior is investigated and it is shown that lack of considering the fringing field effect in the formulation of the problem may lead to considerable error in predicting the size dependent micro-beams behavior under the effect of electrostatic actuation. The results of this research can be used for safe and stable design of electrostatically actuated micro-beams  

In this paper the static deflection and pull-in instability of electrostatically actuated microcantilevers is investigated based on the strain gradient theory. The equation of motion and boundary conditions are derived using Hamilton's principle and solved numerically. It is shown that the strain gradient theory predicts size dependent normalized static deflection and pull-in voltage for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. The results of strain gradient theory are compared with those of classical and modified couple stress theories and also experimental observations. According to this comparison, the... 

Present study is devoted to investigate the size effect on chaotic behavior of a micro-electro-mechanical resonator under external electrostatic excitation. Using Galerkin's decomposition method, approximating the actuation force with a new effective lumped model, and neglecting higher order terms in the Taylor-series expansion, a simplified model of the main system is developed. By utilizing the Melnikov's method and based on the new form of the electrostatic force, an expression in terms of the system parameters is developed which can be used to rapidly estimate the chaotic region of the simplified system. Based on the analysis of the simple proposed model, it is shown that the effect of... 

Strike of a lightning stroke to the high voltage terminal of a power transformer results in an impulse stress on its windings. The magnitude of the series capacitance of the windings has an important effect on the impulse voltage distribution and the stresses along the windings. Increasing the series capacitances of the windings, the impulse voltage distribution becomes more linear and the stress on the winding is reduced. So interleaved windings rather than disc windings are used in power transformer windings to increase the series capacitances. In this paper, the electrostatic shielding, used in disc windings to increase the windings series capacitance, and for linearization of its impulse... 

Developing a transient fully-meshed model of coupled-domain microsystems is of paramount importance not only for accurate simulation and design but also for creating more accurate low-order or macro dynamic models. So in this paper, a complete nonlinear finite element model for coupled-domain MEMS devices considering electrostatic and squeeze film effects is presented. For this purpose, we use the Galerkin weighted-residual technique for developing the finite element model that capture the original microsystem's nonlinear behaviors, such as the structural dynamics, the squeeze-film damping, the electrostatic actuation and the geometric nonlinearity caused by inherent residual stresses. In... 

In this paper, we have studied the effect of annealing under slightly oxidizing ambient (N2+O2) on the structural and electrical characteristics of a limited number of silicon nanoparticles embedded in an ultra-thin SiO2 layer. These nanoparticles were synthesized by ultra-low-energy (1 keV) ion implantation and annealing. Specific experimental methods have been used to characterize the ncs populations. They include transmission electron microscopy (TEM) Fresnel imaging for evaluating the distances and widths of interest and spatially resolved electron energy loss spectroscopy (EELS) using the spectrum-imaging mode of a scanning transmission electron microscope (STEM) to measure the size... 

The nonlinear dynamic and static deflection of a micro/nano gyroscope under DC voltages and base rotation are investigated. The gyroscope undertakes two coupled bending motions along the drive and sense directions and subjected to electrostatic actuations and intermolecular forces. The nonlinear governing equations of motion for the system with the effect of electrostatic force, intermolecular tractions and base rotation are derived using extended Hamilton principle. Under constant voltage, the gyroscope finds the preformed shape. First, the deflection of the micro/nano gyroscope under electrostatic forces is obtained by static and dynamic analyses. Furthermore, the static and dynamic... 

In non-classical micro-beams, the strain energy of the system is determined by the non-classical continuum mechanics. In this study, we consider a closed-loop control methodology for suppressing the vibration of non-classical microscale Euler-Bernoulli beams with nonlinear electrostatic actuation. The non-dimensional form of the governing nonlinear partial differential equation of the system is introduced and converted into a set of ordinary differential equations using the Galerkin projection method. In addition, we prove the observability of the system and we design a state estimation system using the extended Kalman filter algorithm. The effectiveness and performance of the proposed... 

This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators  

In non-classical micro-beams, the strain energy of the system is determined by the non-classical continuum mechanics. In this study, we consider a closed-loop control methodology for suppressing the vibration of non-classical microscale Euler-Bernoulli beams with nonlinear electrostatic actuation. The non-dimensional form of the governing nonlinear partial differential equation of the system is introduced and converted into a set of ordinary differential equations using the Galerkin projection method. In addition, we prove the observability of the system and we design a state estimation system using the extended Kalman filter algorithm. The effectiveness and performance of the proposed... 

Molecular surface electrostatic potential was used to predict the solvent effect on the reaction rate, endo/exo selectivity and diastereomeric excess of a Diels-Alder reaction. It is shown that these quantities can be expressed in terms of molecular surface electrostatic potentials of solvents which are obtained computationally by the HF/6-31++G* procedure. Regression analyses and an experimental database are used to obtain analytical representation of rate constant, endo/exo selectivity and diastereomeric excess. The models obtained show that the hydrogen bond donor ability of solvents on the above mentioned properties is substantial, whereas solvophobicity only affects the reaction rate... 

The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton's principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling...