Sharif Digital Repository

In this study tracking problem of tip of a micro cantilever, actuated by electrostatic, is investigated. Dynamic model of the system is a PDE. Using electrostatic actuation.introduced significant nonlinearity in dynamic model of the system. Control goals are achieved by means of backstepping for SI and feedback linearization for MI system. Performance of control system is inspected for some assumptions and simplifications. The results are in according to numerical simulations  

In this paper, vibration suppression of micro-or nano-scale beams subjected to nonlinear distributed electrostatic force is studied. For the sake of precision, we use the beam model derived from strain gradient elasticity theory aimed at prediction of size effect. In addition, the electrostatic force is considered with first order fringing field correction. The continuous model of the strain gradient beam is truncated by using Kantorovich method as a semi-analytical finite element method. A boundary control feedback law is proposed to suppress forced vibrations of the beam. Both measurements and actuations are taken place in the boundary to avoid spillover instabilities. Simulation results... 

This paper aims to explore the dynamic behaviour of a nano-resonator under ac and dc excitation using strain gradient theory. To achieve this goal, the partial differential equation of nano-beam vibration is first converted to an ordinary differential equation by the Galerkin projection method and the lumped model is derived. Lumped parameters of the nano-resonator, such as linear and nonlinear springs and damper coefficients, are compared with those of classical theory and it is demonstrated that beams with smaller thickness display greater deviation from classical parameters. Stable and unstable equilibrium points based on classic and non-classical theories are also compared. The results... 

In this study, dynamic response of a micro- and nanobeams under electrostatic actuation is investigated using strain gradient theory. To solve the governing sixth-order partial differential equation, mode shapes and natural frequencies of beam using Euler–Bernoulli and strain gradient theories are derived and then compared with classical theory. Galerkin projection is utilized to convert the partial differential equation to ordinary differential equations representing the system mode shapes. Accuracy of proposed one degree of freedom model is verified by comparing the dynamic response of the electrostatically actuated micro-beam with analogue equation and differential quadrature methods.... 

The classical continuum theory not only underestimates the stiffness of microscale structures such as microbeams but is also unable to capture the size dependency, a phenomenon observed in these structures. Hence, the non-classical continuum theories such as the strain gradient elasticity have been developed. In this paper, a Timoshenko beam finite element is developed based on the strain gradient theory and employed to evaluate the mechanical behavior of microbeams used in microelectromechanical systems. The new beam element is a comprehensive beam element that recovers the formulations of strain gradient Euler–Bernoulli beam element, modified couple stress (another non-classical theory)... 

In this paper, the classical and nonlocal elasticity are applied to investigate the deflection and instability of electrostatically actuated carbon nanotubes. The results are presented for different geometries and boundary conditions. They reveal that increasing radius and gap and decreasing length confine to increasing pull-in voltages of the carbon nanotubes. The results prove that application of the nonlocal elasticity theorem leads to stiffer structures with higher pull-in voltages. Thus, in order to obtain more accurate results about the mechanical and electromechanical behaviors of the carbon nanotubes, one should apply the nonclassical elasticity theories such as that applied in this... 

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... 

Since the classical continuum theory is neither able to evaluate the accurate stiffness nor able to justify the size-dependency of micro-scale structures, the non-classical continuum theories such as the modified couple stress theory have been developed. In this paper, a new comprehensive Timoshenko beam element has been developed on the basis of the modified couple stress theory. The shape functions of the new element are derived by solving the governing equations of modified couple stress Timoshenko beams. Subsequently, the mass and stiffness matrices are developed using energy approach and Hamilton's principle. The formulations of the modified couple stress Euler-Bernoulli beam element... 

Electrostatic torsional micromirrors, as instances of Micro Electro Mechanical Systems (MEMS), have many optical network applications; such as optical wavelength-selective switches, optical cross-connects, etc. For all these applications, the micromirror needs to have minimal overshoot and settling time in order to minimize the time between two successive switching operations. Moreover, the controllability and stability of a torsional micromirror are major challenges due to high nonlinearities in its dynamic characteristics. In this paper, a robust adaptive critic-based neurofuzzy controller is proposed for electrostatic torsional micromirrors, which can improve the performance of the mirror... 

Mixing in droplets is an essential task in a variety of microfluidic systems. Inspired by electrokinetic mixing, electric field-induced hydrodynamic flow inside a charged droplet embedded in an unbounded polyelectrolyte hydrogel is investigated theoretically. In this study, the polyelectrolyte hydrogel is modeled as a soft, and electrically charged porous solid saturated with a salted Newtonian fluid, and the droplet is considered an incompressible Newtonian fluid. The droplet-hydrogel interface is modeled as a surface, which is located at the plane of shear, with the electrostatic potential ζ. The fluid inside the droplet attains a finite velocity owing to hydrodynamic coupling with the... 

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  

Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss–Seidel iteration methods are used. Both clamped-free and clamped–clamped micro- and nano-beams under electrostatical actuation are considered where... 

Propagation of a chirped laser pulse with a circular polarization through an uprising plasma density profile is studied by using 1D-3V particle-in-cell simulation. The laser penetration depth is increased in an overdense plasma compared to an unchirped pulse. The induced transparency due to the laser frequency chirp results in an enhanced heating of hot electrons as well as increased maximum longitudinal electrostatic field at the back side of the solid target, which is very essential in target normal sheath acceleration regime of proton acceleration. For an applied chirp parameter between 0.008 and 0.01, the maximum amount of the electrostatic field is improved by a factor of 2.... 

Electrical behavior of hybrid conductive composites made of phenolic resin, graphite woven, glass woven and graphite nano powder has been studied for the first time in the present research to apply as collecting plates in electro static precipitators. To this purpose, two types of four-layer composites smeared with phenolic resin by different amounts of graphite nano powder then produced at 120°C and 200 bars with proper curing cycle. Finally, electrical resistivity of all the plates undergoing impact loading after different rapping cycles was measured by means of a repetitive rapping tester system particularly manufactured for this task. This study performs changes in mechanical behavior of... 

Dynamic behavior of a electrostatically actuated MEMS resonator is investigated. A double clamped micro-beam under distributed DC and AC actuation is used. Corresponding single degree of freedom model is derived using Galerkin's decomposition method. Homotopy Perturbation Method (HPM) is implemented in order to derive analytical expression for frequency response of the micro-resonator. Comparison of the obtained results with the numerical simulations confirms that HPM agrees very well with numerical simulations for a wide range of parameters. Obtained analytical solution can be used for design and optimization of MEMS resonators  

Effects of fringing electrostatic fields on the behavior of a double clamped initially curved microbeam are investigated. Galerkin's decomposition method is applied on the governing Euler-Bernoulli equation with distributed electrostatic force to obtain the lumped-parameter model of the system. The resulting single degree of freedom model is obtained with the Palmer's formula as a model for the fringing field effects. To derive an applied form of the fringing field effect in lumped model, we have used Genetic Algorithms as an optimization method. Then using the lumped model, we have investigated the system nonlinear dynamics. Comparison of the obtained bifurcation diagrams with the... 

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... 

The paper deals with studying the deflection and pull-in voltages of the carbon nanotubes under electrostatic actuation with various dimensions and boundary conditions. The size-dependent behaviors of the carbon nanotubes (CNTs) are considered via application of the strain gradient theory. The results obtained from the strain gradient theory are compared to those estimated using the classical elasticity. The outcomes reveal that the classical elasticity theory underestimates the pull-in voltages of the carbon nanotubes and strain gradient theorem results in stiffer nano-structures with higher pull-in voltages. Increasing of the deflection due to the higher voltages increases the differences... 

This paper deals with investigation of fluid flow on static and dynamic behaviors of carbon nanotubes under electrostatic actuation. The effects of various fluid parameters including fluid viscosity, velocity, pressure and mass ratio on the deflection and pull-in behaviors of the cantilever and doubly clamped carbon nanotubes are studied. Furthermore, the effects of temperature variation on the static and dynamic pull-in voltages of the doubly clamped carbon nanotubes are reported. The results reveal that altering the fluid parameters significantly changes the mechanical and pull-in behaviors. Hence, the proposed system can be applied properly as a nano fluidic sensor to sense the various... 

The paper deals with the investigation of nonlinear static and dynamic behaviors of electrostatically actuated carbon nanotubes with different geometries and boundary conditions. The deflection and pull-in properties are studied in detail in the presence of DC and combined DC+AC electrostatic voltages accompanying the interatomic interactions. The considered nano system can be applied in a wide range of nanoelectronics devices such as nano switches, nano resonators, nano transistors, nano capacitors and random access memories. Moreover, a useful mathematical model of the nano sensor application of the studied nano system to sense the stiffness of the nano particles is presented