Sharif Digital Repository

This paper presents new exact 3-D (three-dimensional) elasticity closed-form solutions for out-of-plane free vibration of thick rectangular single layered FG (functionally graded) plates and thick rectangular homogeneous plate coated by a functionally graded layer with simply supported boundary conditions. It is assumed that the plate is on a Winkler- Pasternak elastic foundation and elasticity modulus and mass density of the FG layer vary exponentially through the thickness of the FG layer, whereas Poisson's ratio is constant. In order to solve the equations of motion, a proposed displacement field is used for each layer. Influences of stiffness of the foundation, inhomogeneity of the FG... 

Miniaturized culture systems of hepatic cells are emerging as a strong tool facilitating studies related to liver diseases and drug discovery. However, the experimental optimization of various parameters involved in the operation of these systems is time-consuming and expensive. Hence, developing numerical tools predicting the function of such systems can significantly reduce the associated cost. In this paper, a perfusion-based three dimensional (3D) bioreactor comprising encapsulated human liver hepatocellular carcinoma (HepG2) spheroids are analyzed. The flow and mass transfer equations for oxygen as well as different metabolites such as albumin, glucose, glutamine, ammonia, and urea were... 

The classical yield criteria do not describe the yield size-dependency that has been observed in micro-scale structures (Fleck, Muller, Ashby, & Hutchinson, 1994; Stolken and Evans 1998; Moreau et al. 2005), and may also significantly underestimate the yield loads of structures at micron and sub-micron scales (Son, Jeong, & Kwon, 2003; Liu et al., 2013). The present paper suggests a specific size-dependent yield criterion based on the strain gradient theory that is aimed at addressing this inadequacy. In order to develop the strain gradient based yield criterion, the deviatoric part of the strain energy is calculated based on this theory and equated to the deviatoric strain energy of a... 

In this paper, the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of a micro/nano cantilever gyroscope with proof mass at its end are investigated. The micro/nano gyroscope is subjected to coupled bending motions which are related by base rotation and nonlinearities due to the geometry and the inertial terms. It is actuated and detected by capacitance plates which are placed on the proof mass. The extended Hamilton principle is used to find the equations governing the static behavior of the clamp-free micro/nano gyroscopes under electrostatic, Casimir and van der Waals forces. The equations of static motion are discritized by Galerkin's... 

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... 

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... 

This paper investigates the dynamic behavior of microcantilevers under suddenly applied DC voltage based on the modified couple stress theory. The cantilever is modeled based on the Euler-Bernoulli beam theory and equation of motion is derived using Hamilton's principle. Both analytical and numerical methods are utilized to predict the dynamic behavior of the microbeam. Multiple scales method is used for analytical analysis and the numerical approach is based on a hybrid finite element/finite difference method. The results of the modified couple stress theory are compared with those from the literature as well as the results predicted by the classical theory. It is shown that the modified... 

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... 

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 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... 

In this paper natural frequency of electrostatically actuated microbridges is investigated based on the modified couple stress theory. Nonlinear formulation of Euler-Bernoulli microbeam is derived using Hamilton's principle. By considering the von-Karman strain, the nonlinearities caused by the mid-plane stretching are included in the formulation. To confirm the model, results of static deflection and natural frequency of microbeams are calculated using modified couple stress theory and compared to those evaluated based on the classical theory and experimental observations. At first, from experimental results of static deflection of a microcantilever, estimation for length scale parameter of... 

In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam affected by an electric field, including the fringing field effect, was obtained based on strain gradient elasticity, couple stress, and classical theory. Influences of different parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear differential equation was also solved by using the Homotopy Analysis Method (HAM). The influence... 

In this paper, the mechanical properties of graphene nanosheets are evaluated based on the nonlinear modified Morse model. The interatomic interactions including stretching and bending of the covalent bonds between carbon atoms, are replaced by nonlinear extensional and torsional spring-like elements. The finite element method is implemented to analyze the model under different loading conditions and linear characteristics of the graphene structure including the Young's modulus, surface modulus, shear modulus and Poisson's ratio are evaluated for various geometries and chirality where these properties are shown to be size and aspect ratio dependent. It is also found that when the dimensions... 

A viscoelastic microcantilever beam is analytically analyzed based on the modified strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening effect theory and discretized by Galerkin method. Inner damping, nonlinear curvature effect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and stiffness, as well... 

Dual-axis micromirrors are considered as the crucial components used for light deflection and control, which can be employed for arbitrary-direction optical beam steering with a low operating voltage. In order to achieve large scanning angles with a low driving voltage and presenting high resolution and scanning speeds, micromirrors are excited at their corresponding resonance frequencies. In addition, a bias DC voltage is also provided in order to scan around a desired nonzero tilt angle. Therefore, a comprehensive understanding of the mirror’s response to a DC-shifted primary resonance excitations is crucial. In this study, various design conditions including the primary resonances and the...