Sharif Digital Repository

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... 

In this paper, a size-dependent non-classical yield criterion is introduced on the basis of the modified couple stress theory in order to capture the size-dependency of the micro-scale structure yielding loads where the attempts of the classical yield criteria such as the von-Mises have been in vain. In order to develop the new yield criterion, the deviatoric part of the micro-scale structure strain energy density, including both classical and non-classical parts, is equated to the deviatoric strain energy density of a macro-size tensile-test sample at the yielding point. For bending of microbeams and torsion of microbars, the size-dependent yielding moments have been determined based on the... 

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  

The paper presents the effects of fluid flow on the static and dynamic properties of carbon nanotubes that convey a viscous fluid. The mathematical model is based on the modified couple stress theory. The effects of various fluid parameters and boundary conditions on the pull-in voltages are investigated in detail. The applicability of the proposed system as nanovalves or nanosensors in nanoscale fluidic systems is elaborated. The results confirm that the nanoscale system studied in this paper can be properly applied for these purposes  

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... 

This paper analyzes the deflection and pull-in behaviors of cantilever and doubly clamped carbon nanotubes (CNTs) under electrostatic actuation using the homotopy perturbation method. The effects of electrostatic force and interatomic interactions on the deflection and pull-in instabilities of CNTs with different lengths, diameters, and boundary conditions are investigated in detail. The results reveal that larger diameters and shorter lengths result in higher pull-in voltages. Moreover, CNTs with doubly clamped boundary conditions, in comparison with cantilever boundary conditions, are more resistant to pull-in  

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... 

In this paper, a nonlinear model is used to analyze the dynamic pull-in instability and vibrational behavior of a microcantilever gyroscope. The gyroscope has a proof mass at its end and is subjected to nonlinear squeeze film damping, step DC voltages as well as base rotation excitation. The electrostatically actuated and detected microgyroscopes are subjected to coupled flexural-flexural vibrations that are related by base rotation. In order to detune the stiffness and natural frequencies of the system, DC voltages are applied to the proof mass electrodes in drive and sense directions. Nonlinear integro differential equations of the system are derived using extended Hamilton principle... 

This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input... 

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton's second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of... 

In this paper, a mathematical modeling of a microcantilever gyroscope is presented considering the nonlinearities of the system due to electrostatic forces, fringing field, geometry and the inertial terms. The microgyroscope is actuated and detected by electrostatic methods and subjected to coupled bending oscillations. First a system of two nonlinear integro-differential equations is derived which describes flexural-flexural motion of electrostatically actuated and detected microbeam gyroscopes. Afterward, static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (driving and sensing) directions are studied for different parameters. The model's... 

The dynamic response analysis of a delaminated composite beam with a general lay-up traversed under an arbitrary moving/non-moving force is presented. By employing the energy method and introducing a new finite element, the global mass and stiffness matrices for a Laminated Composite Beam (LCB) of Timoshenko type are derived in which the material couplings (bending-tension, bending-twist, and tension-twist couplings) with the Poisson's effect are considered. In deriving the governing equation the non-penetration condition is imposed by employing the method of Lagrange multipliers. Out of a self-developed finite element program, the natural frequencies and time response of such LCB are... 

The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

In this article, the propagation of one-dimensional stress waves in a plate made of functionally graded materials excited by a harmonic force is studied. The material properties of the functionally graded material plate are assumed to be graded in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The governing equations are based on stress-strain relation and the equation of motion. Keeping generality, the functionally graded material plate is assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of aluminum and alumina is... 

The classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli beam element is developed based on the strain gradient theory. Compared to the classical Euler-Bernoulli beam element, the nodal displacement vector of the new Euler-Bernoulli beam element has an additional component, i.e. the... 

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  

The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that...