Sharif Digital Repository

Atomic force microscope (AFM) can be used as nanorobotics manipulation tool for nano particle positioning, pushing, indenting, cutting and etc. control the vibration behavior of AFM and make the micro-cantilever tip track specified trajectory is very crucial to appropriately manipulate particles in nano-scales. The novel combined sliding mode approach has been investigated in this paper to obtain robust nonlinear control scheme for nanomanipulation. First (classical) and second order (SOSM) sliding mode techniques have been developed and applied to nonlinear dynamical and uncertain model of AFM cantilever beam to track the desired trajectories. The simulation results show chattering in... 

Carbon nanotubes (CNTs) are promising candidates for high-resolution mass nanosensors owing to their unique vibrational behavior. The structural characteristic (e.g. defect type and density) and working temperature have a significant effect on the natural frequency of CNT-based sensors. Herein, a stochastic approach based on novel finite element and molecular mechanics simulations is implemented to model the effect of temperature and structural characteristics of single-wall CNTs including defects (vacancy defect with different densities) and chirality (zigzag and armchair) on their vibrational behavior. The results show that the vacancy defects exert a significant deterioration of the... 

Vibrational analysis of single-walled carbon nanotubes (SWCNTs) is performed using a finite element method (FEM). To this end, the vibrational behavior of bridge and cantilever SWCNTs with different side lengths and diameters is modeled by three-dimensional elastic beams and point masses. The beam element elastic properties are calculated by considering mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as point masses at nodes coinciding with the carbon atoms. Implementing the atomistic simulation approach, the natural frequencies of zigzag and armchair SWCNTs are computed. It is observed that the... 

An important issue in the study of the nanostructures behaviors is the surface effects, which increases with the increase of the surface-to-volume ratio. Continuum theories are capable of modeling structures at micro and larger scales with enough precision and low computational costs. However, these theories are unable to predict the mechanical properties of nanostructures accurately. On the other hand, due to their high precision, atomistic modeling techniques are extensively employed for the study of systems at nanoscale; however, computational costs of these techniques are relatively high. In this research, we aim to study the vibrational behavior of nanobeams made of three FCC metals;... 

The governing differential equation and both classical and non-classical boundary conditions of strain gradient bars are derived using variational approach. A closed-form analytical solution is obtained for static torsion and the characteristic equation, which gives the natural frequencies, is derived and analytically solved for the free torsional vibrations of the strain gradient microbars. A fixed-fixed microbar is considered as a specific case to investigate the torsional size-dependent static and free-vibration behavior of strain gradient microbars. The results of the current model are compared to those of the modified couple stress and classical theories  

Accurate prediction of static and dynamic response of nano structures under external excitations has been one of the interests of scientists in the last decade. Several applications of nano machines make it necessary to analyze their components, such as nano bearing, precisely. In this paper, the static and vibrational behavior of a fullerene as a sensitive part of nano bearing under external forces is simulated by a newly designed spherical super element. This super element is designed in such a way that the user can select as many numbers of nodes as desired, so that it can be implemented in different desired precisions. In this study, a 228-node super element, which is similar to a hollow... 

In this study, several analytical expressions are obtained for the vibrational characteristics of a Jeffcott model for micro-rotor systems based on the strain gradient theory to investigate the small-scale effects on the model. The Jeffcott model consists of a massless microrotating shaft and a disk as a rotor with eccentricity. The disk is mounted on the middle of the shaft. Two second-order differential equations associated with the oscillating motion of the rotor in the plane perpendicular to the longitudinal axis are presented and transformed into a complex form. The stiffness of the system is determined by obtaining the deflection of a strain-gradient-based nonrotating microbeam... 

The instability of large diameter single-walled carbon nanotubes (SWCNTs) conveying fluid is investigated based on the molecular mechanics. Using the modal expansion for structural displacements, the governing equations of coupled fluid-structural dynamics of SWCNTs are derived. The natural frequencies and mode shape of the SWCNTs are obtained based on the molecular structural mechanics to account for the effect of chirality and discrete nature of SWCNTs. The results show that the vibrational behavior of large diameter SWCNTs conveying fluid is size dependent, but the effect of chirality is negligible. The obtained results are compared with the equivalent continuum-based model in the... 

This paper deals with vibrational behaviors of blades with cracks which are key components in rotating machines. However, since modelling and analysis of real blade is a complex problem, a simplified cantilever beam with both chordwise (in X-Y plane) and flapwise (in X-Z plane) motion are modeled instead. Finite Element Method (FEM) is used to model beam and to investigate its natural frequencies with a crack. Finally a limit function using modal data is developed and reliability analysis of beam model is performed. © 2017 IEEE  

In this paper, assuming porosity varies only along thickness direction, its optimal distributions in functionally graded porous (FGP) beams are tailored. Two multi-objective optimization problems are defined. In the first one, critical buckling load and mass are optimized simultaneously while in the second one, we concentrate on simultaneous optimization of mass and fundamental frequency. Employing Timoshenko beam theory, we present governing equations for a FGP beam. For the solution, we use Ritz method and propose appropriate trial functions according to the boundary conditions (Hinged-Hinged, Clamped-Clamped, Clamped-Hinged and Clamped-Free). Since the porosity distribution along... 

In this paper, the size-dependent static and vibration behavior of micro-beams made of functionally graded materials (FGMs) are analytically investigated on the basis of the modified couple stress theory in the elastic range. Functionally graded beams can be considered as inhomogeneous composite structures, with continuously compositional variation from usually a ceramic at the bottom to a metal at the top. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Closed-form solutions for the normalized static deflection and natural frequencies are obtained as a function of the ratio of the beam characteristic size to the internal material... 

This article aims to study the buckling and free vibrational behavior of axially functionally graded (AFG) nanobeam under thermal effect for the first time. The temperature is considered to be constant and variable along thickness and different boundary conditions. The governing equation is developed using the Hamilton’s principle considering the axial force. The Euler–Bernoulli beam theory is used to model the nanobeam, and Eringen’s nonlocal elasticity theory is utilized to consider the nano-size effect. The generalized differential quadrature method (GDQM) is used to solve the equations. The small-scale parameter, AFG power index, thermal distribution, different functions of temperature... 

The non-linear flexural vibration for a dagger-shaped atomic force microscope cantilever has been investigated using the Timoshenko beam theory. In this article, the normal and tangential tip-sample interaction forces are found from Hertzian contact model and the effects of the geometry, normal and lateral contact stiffness, height of the tip, thickness of the beam, the angle between the cantilever and the sample surface and breadth and height taper ratios on the non-linear frequency to linear frequency ratio have been studied. The differential quadrature method (DQM) is employed to solve the non-linear differential equations of motion. The results show that the softening behaviour is seen... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions... 

Molecular structural mechanics approach is implemented to investigate vibrational behavior of single-layered graphene sheets. By using the atomistic modeling, mode shapes and natural frequencies are obtained. Vibration analysis is performed under different chirality and boundary conditions. Numerical results from the finite element technique are applied to develop empirical equations via a statistical multiple nonlinear regression model. With the proposed empirical equations, fundamental frequencies of single-layered graphene sheets under considered boundary conditions can be predicted within 3 percent accuracy. Copyright © 2007 by ASME  

The classical methods utilized for modeling nano-scale systems are not practical because of the enlarged surface e ects that appear at small dimensions. Contrarily, implementing more accurate methods is followed by prolonged computations as these methods are highly dependent on quantum and atomistic models, and they can be employed for very small sizes in brief time periods. In order to speed up the Molecular Dynamics (MD) simulations of the silicon structures, Coarse-Graining (CG) models are put forward in this research. The procedure involves establishing a map between the main structure's atoms and the beads comprising the CG model and modifying the parameters of the system so that the... 

Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then... 

In this paper, the effect of blade number on the vibration behavior of industrial fans has been studied experimentally and numerically. Two similar industrial fans with similar specifications and only different blade numbers were chosen in a plant. The vibration levels were measured on these fans and the results revealed that the blade passage phenomenon is the main cause of vibrations on both fans. Both fans and their structures were modeled numerically and the performance characteristics, vibratory forces and vibration response of structure were calculated. The results showed that the number of blade has small effect on vibratory forces compared to the performance characteristics. The... 

Influences of the tip mass, excitation mode of Frequency Modulated Atomic Force Microscope (FM-AFM) on the resonance frequency shift in force modulation (FM) mode are studied. Governing equations of motion are determined based on Timoshenko beam model with concentrated end mass. Approach point and base amplitude are set such that the FM-AFM remains just in FM mode. Either the linearized and nonlinear Derjaguin-Muller-Toporov (DMT) model are investigated. Then frequency shifts are determined for various interaction force regimes. It is showed the effect of tip mass on frequency shift is significant even for small tips. Nonlinear model shows lower frequency shifts in comparison with linearized... 

This work is aimed to present analysis on the thermal vibrational behavior of two-dimensional functionally graded porous microbeams based on Timoshenko beam theory. According to the power law function, the material composition and so the material properties are varying along thickness and axis of the microbeam. The governing equations are derived on the basis of the couple stress theory and the generalized differential quadrature method is used to solve the equations. The temperature gradient is considered to be uniform and nonuniform across the thickness of the microbeam. The results are presented to show the effect of temperature change, porosity, functionally graded and axially...