Sharif Digital Repository

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior... 

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)... 

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... 

Design and development of FGMs as the heat treatable materials for high-temperature environments with thermal protection require understanding of exact temperature and thermal stress distribution in the transient state. This information is primary tool in the design and optimization of the devices for failure prevention. Frequently FGMs are used in many applications that presumably produce thermal energy transport via wave propagation. In this study, transient non-Fourier temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined. Hyperbolic heat conduction equation in terms of heat flux is used for obtaining temperature... 

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... 

The paper investigates the influences of fluid flow on static and dynamic behaviours of electrostatically actuated carbon nanotubes (CNTs) using strain gradient theory. This nonclassical elasticity theory is applied in order to obtain more accurate results possessing higher agreement with the experimental data. The effects of various fluid parameters such as the fluid viscosity, velocity, mass and temperature on the pull-in properties of the CNTs with two cantilever and doubly clamped boundary conditions are studied. The results reveal the applicability of the proposed nano-system as nano-valves or nano-fluidic sensors  

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... 

This paper presents vibration and buckling analysis of functionally graded beams with different boundary conditions, using reproducing kernel particle method (RKPM). Vibration of simple Euler-Bernoulli beam using RKPM is already developed and reported in the literature. Modeling of FGM beams using theoretical method or finite element technique is not evolved with accurate results for power law form of FGM with large power of "n" value so far. Accuracy of the RKPM results is very good and is not sensitive to n value. System of equations of motion is derived using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of the beam are taken into account using... 

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... 

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 deals with investigation of the effects of vacancy defects on the pull-in behaviors of the carbon nanotubes. The influences of single, double and triple vacancies in different peripheral and longitudinal positions are studied. The results reveal that the vacancy defects drastically reduce the pull-in charge because they weaken the nanostructure. Moreover, the effects of residual stresses on the pull-in and vibrational properties of the carbon nanotubes are scrutinized. The influences of the angular deviations from the parallel positions of the CNT and ground plate during the fabrication process are also reported. Copyright  

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 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... 

Human body is constantly under the influence of acceleration loads in environments such as combat flying. This study investigates the effect of body acceleration on human heart function by using finite element analysis. The nonlinear mechanical behavior of myocardium is modeled by Yeoh hyperelastic model. Stress-strain curves of myocardium are determined based on uniaxial compression tests on bovine heart samples. Nonlinear least square curve fitting is conducted in order to obtain material parameters. Heart geometrical modeling in threedimension is done by segmentation of cardiac MRI images. Obtained material coefficients are assigned to the constructed heart model and appropriate pressure... 

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