Sharif Digital Repository

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... 

In this work, the dynamic and vibrational behavior of a micro/nano-manipulator has been studied. The manipulator comprises three links attached serially. While the connection of the links is rigid, which makes the whole body a monolithic structure, the movement of the manipulator is derived from the links deflection. Piezoelectric layers were employed as an actuator to impose deflection on the links, thereby moving the manipulator. After defining the dynamic behavior of each link, manipulator equations of motion were developed. To evaluate the validity of the mathematical model, two FEM models were constructed. The observed results showed a good agreement between the models, and they... 

Molecular structural mechanics is implemented to model vibrational behavior of defect free single-layered graphene sheets (SLGSs) at constant temperature. To mimic these two-dimensional layers, zigzag and armchair models with cantilever and bridge boundary conditions are adopted. Fundamental frequencies of these nano structures are calculated, and it is perceived that they are independent of the chirality and aspect ratio. Effects of point mass and atomistic dust on the fundamental frequencies are also considered in order to investigate the possibility of using SLGSs as sensors. Results of exhibit the principle frequencies are highly sensitive to the added mass in the order of 10-6 fg.... 

In this work, the dynamic and vibrational behavior of a micro/nano-manipulator has been studied. The manipulator comprises three links attached serially. While the connection of the links is rigid, which makes the whole body a monolithic structure, the movement of the manipulator is derived from the links deflection. Piezoelectric layers were employed as an actuator to impose deflection on the links, thereby moving the manipulator. After defining the dynamic behavior of each link, manipulator equations of motion were developed. To evaluate the validity of the mathematical model, two FEM models were constructed. The observed results showed a good agreement between the models, and they... 

In this paper, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The plate properties can arbitrarily vary through the thickness. The governing differential equations of motion are derived for functionally graded (FG) plates with arbitrary shapes utilizing a variational approach. Moreover, the boundary conditions are provided at smooth parts of the plate periphery and also at the sharp corners of the periphery. Utilizing the derived formulation, the free-vibration behavior as well as the static response of a rectangular FG micro-plate is investigated  

The geometrically nonlinear governing differential equations of motion and the corresponding boundary conditions are derived for the mechanical analysis of Timoshenko microbeams with large deflections, based on the strain gradient theory. The variational approach is employed to achieve the formulation. Hinged-hinged beams are considered as an important practical case, and their nonlinear static and free-vibration behaviors are investigated based on the derived formulation  

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  

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... 

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... 

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  

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... 

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;... 

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... 

The free linear vibration of an adaptive sandwich beam consisting of a frequency and field-dependent magnetorheological fluid core and an axially functionally graded constraining layer is investigated. The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. The Rayleigh-Ritz method is used to derive the frequency-dependent eigenvalue problem through the kinetic and strain energy expressions of the sandwich beam. In order to deal with the frequency dependency of the core, the approached complex eigenmodes method is implemented. The validity of the formulation and solution method is confirmed through comparison... 

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... 

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... 

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... 

The geometrically nonlinear governing differential equation of motion and corresponding boundary conditions of small-scale Euler-Bernoulli beams are achieved using the second strain gradient theory. This theory is a non-classical continuum theory capable of capturing the size effects. The appearance of many higher-order material constants in the formulation can certify that it appropriately assesses the behavior of extremely small-scale structures. A hinged-hinged beam is chosen as an example to lay out the nonlinear size-dependent static bending and free vibration behaviors of the derived formulation. The results of the new model are compared with the previously obtained results based on... 

This paper presents a nonlinear size-dependent Timoshenko beam model based on the modified couple stress theory, a non-classical continuum theory capable of capturing the size effects. The nonlinear behavior of the new model is due to the present of induced mid-plane stretching, a prevalent phenomenon in beams with two immovable supports. The Hamilton principle is employed to determine the governing partial differential equations as well as the boundary conditions. A hinged-hinged beam is chosen as an example to delineate the nonlinear size-dependent static and free-vibration behaviors of the derived formulation. The solution for the static bending is obtained numerically. The solution for...