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On pull-in instabilities of microcantilevers
, Article International Journal of Engineering Science ; Volume 87 , February , 2015 , Pages 23-31 ; 00207225 (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
Elsevier Ltd
2015
Abstract
In this paper the static deflection and pull-in instability of electrostatically actuated microcantilevers is investigated based on the strain gradient theory. The equation of motion and boundary conditions are derived using Hamilton's principle and solved numerically. It is shown that the strain gradient theory predicts size dependent normalized static deflection and pull-in voltage for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. The results of strain gradient theory are compared with those of classical and modified couple stress theories and also experimental observations. According to this comparison, the...
Effect of size dependency on in-plane vibration of circular micro-rings
, Article Scientia Iranica ; Volume 24, Issue 4 , 2017 , Pages 1996-2008 ; 10263098 (ISSN) ; Ahmadian, M. T ; Rahaeifard, M ; Sharif University of Technology
Sharif University of Technology
2017
Abstract
In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam...
Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials
, Article Proceedings of the ASME Design Engineering Technical Conference, 30 August 2009 through 2 September 2009, San Diego, CA ; Volume 6 , 2009 , Pages 539-544 ; 9780791849033 (ISBN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
ASME
2009
Abstract
The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a...
A nonlinear strain gradient beam formulation
, Article International Journal of Engineering Science ; Volume 49, Issue 11 , 2011 , Pages 1256-1267 ; 00207225 (ISSN) ; Asghari, M ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
2011
Abstract
In this paper, a nonlinear size-dependent Euler-Bernoulli beam model is developed based on a strain gradient theory, capable of capturing the size effect. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, the governing nonlinear partial differential equation of motion and the corresponding classical and non-classical boundary conditions are determined using the variational method. As an example, the free-vibration response of hinged-hinged microbeams is derived analytically using the Method of Multiple Scales. Also, the nonlinear size-dependent static bending of hinged-hinged beams is evaluated numerically. The results of the new model are compared...
Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory
, Article International Journal of Engineering Science ; Volume 48, Issue 12 , 2010 , Pages 1985-1994 ; 00207225 (ISSN) ; Asghari, M ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
2010
Abstract
In this paper, the resonant frequency and sensitivity of atomic force microscope (AFM) microcantilevers are studied using the modified couple stress theory. The classical continuum mechanics is incapable of interpreting micro-structure-dependent size effects when the size of structures is in micron- and sub-micron scales. However, this dependency can be well treated by using non-classical continuum theories. The modified couple stress theory is a non-classic continuum theory which employs additional material parameters besides those appearing in classical continuum theory to treat the size-dependent behavior. In this work, writing differential equations of motion of AFM cantilevers together...
A strain gradient based yield criterion
, Article International Journal of Engineering Science ; Vol. 77 , 2014 , pp. 45-54 ; ISSN: 00207225 ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2014
Abstract
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...
Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Vol. 228, Issue. 5 , May , 2014 , pp. 896-906 ; ISSN: 09544062 ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2014
Abstract
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...
Vibration analysis of electrostatically actuated nonlinear microbridges based on the modified couple stress theory
, Article Applied Mathematical Modelling ; Volume 39, Issue 21 , November , 2015 , Pages 6694-6704 ; 0307904X (ISSN) ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
Elsevier Inc
2015
Abstract
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...
Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials
, Article Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, 30 August 2009 through 2 September 2009 ; Volume 6 , August , 2010 , Pages 539-544 ; 9780791849033 (ISBN) ; Kahrobaiyan, M. H ; Ahmadian, M.T ; Sharif University of Technology
2010
Abstract
The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a...
Investigation of the size effects in Timoshenko beams based on the couple stress theory
, Article Archive of Applied Mechanics ; Volume 81, Issue 7 , July , 2011 , Pages 863-874 ; 09391533 (ISSN) ; Kahrobaiyan, M. H ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
2011
Abstract
In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained...
Static pull-in analysis of microcantilevers based on the modified couple stress theory
, Article Sensors and Actuators, A: Physical ; Volume 171, Issue 2 , 2011 , Pages 370-374 ; 09244247 (ISSN) ; Kahrobaiyan, M. H ; Asghari, M ; Ahmadian, M. T ; Sharif University of Technology
2011
Abstract
This paper investigates the deflection and static pull-in voltage of microcantilevers based on the modified couple stress theory, a non-classic continuum theory capable to predict the size effects for structures in micron and sub-micron scales. It is shown that the couple stress theory can remove the gap between the experimental observations and the classical theory based simulations for the static pull-in voltage
On the size-dependent behavior of functionally graded micro-beams
, Article Materials and Design ; Volume 31, Issue 5 , May , 2010 , Pages 2324-2329 ; 02641275 (ISSN) ; Ahmadian, M. T ; Kahrobaiyan, M. H ; Rahaeifard, M ; Sharif University of Technology
2010
Abstract
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...
Optimization of first mode sensitivity of V-shaped AFM cantilever using genetic algorithm method
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings, 13 November 2009 through 19 November 2009 ; Volume 12, Issue PART A , 2010 , Pages 495-501 ; 9780791843857 (ISBN) ; Kahrobaiyan, M. H ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
2010
Abstract
Atomic force microscopes (AFM) are widely used for feature detection and scanning surface topography of different materials. Contrast of topography images is significantly influenced by the sensitivity of AFM micro cantilever which means enhancement of sensitivity leads to increase of topography images resolution So, in the last years numerous scientists interested in studying the effects of different parameters such as geometric one on the sensitivity of AFM micro cantilevers. V-shape micro cantilever types of AFMs probe are widely used to scan various types of surfaces. In V-shape micro cantilevers, there are many geometric and design parameters which influence the flexural sensitivity of...
Size-dependent pull-in phenomena in nonlinear microbridges
, Article International Journal of Mechanical Sciences ; Volume 54, Issue 1 , January , 2012 , Pages 306-310 ; 00207403 (ISSN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2012
Abstract
This paper investigates the deflection and static pull-in of microbridges based on the modified couple stress theory, a non-classic continuum theory able to predict the size effects for structures in micron and sub-micron scales. The beam is modeled using EulerBernoulli beam theory and the nonlinearities caused by mid-plane stretching have been considered. It is shown that modified couple stress theory predicts size dependent normalized deflection and pull-in voltage for microbeams while according to classical theory the normalized behavior of microbeams is independent of the size of the beam. According to results, when the thickness of the beam is in order of length scale of the beam...
Strain gradient formulation of functionally graded nonlinear beams
, Article International Journal of Engineering Science ; Volume 65 , 2013 , Pages 49-63 ; 00207225 (ISSN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2013
Abstract
In this paper size-dependent static and dynamic behavior of nonlinear Euler-Bernoulli beams made of functionally graded materials (FGMs) is investigated on the basis of the strain gradient theory. The volume fraction of the material constituents is assumed to be varying through the thickness of the beam based on a power law. As a consequence, the material properties of the microbeam (including length scales) are varying in the direction of the beam thickness. To develop the model, the usual simplifying assumption which considers the length scale parameter to be constant through the thickness is avoided and equivalent length scale parameters are introduced for functionally graded microbeams...
Vibration analysis of a rotating FGM cantilever ARM
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings, 13 November 2009 through 19 November 2009 ; Volume 15 , 2010 , Pages 359-365 ; 9780791843888 (ISBN) ; Moeini, S. A ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
2010
Abstract
Functionally graded materials (FGMs) are inhomogeneous composites which are usually made of a mixture of metals and ceramics. Properties of these kinds of materials vary continuously and smoothly from a ceramic surface to a metallic surface in a specified direction of the structure. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are induced when two dissimilar materials with large differences in material properties are bonded. FGMs have extracted much attention as advanced structural materials in recent years. In this paper, free vibration of a rotating FGM cantilever...
Flexural sensitivity of a V-shaped AFM cantilever made of functionally graded materials
, Article ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, 12 July 2010 through 14 July 2010 ; Volume 1 , 2010 , Pages 495-501 ; 9780791849156 (ISBN) ; Kahrobaiyan, M. H ; Moeini, S. A ; Ahmadian, M. T ; Hoviattalab, M ; Sharif University of Technology
2010
Abstract
In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of...
Spindle speed variation for regenerative chatter suppression in turning process with tool wear effect
, Article ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, 12 July 2010 through 14 July 2010 ; Volume 4 , 2010 , Pages 619-626 ; 9780791849187 (ISBN) ; Vossoughi, G ; Rahaeifard, M ; Movahhedy, M ; ASME Turkey Section ; Sharif University of Technology
2010
Abstract
Chatter suppression in machining processes results in more material removal rate, high precision and surface quality. In this paper, a single degree of freedom model of orthogonal turning process is used to set up the delay differential equation of motion with considering the tool wear effect as a contact force between the workpiece and tool flank surfaces. Sinusoidal spindle speed variations with different frequencies around the mean speed are modulated to disturb the regenerative mechanism. The optimal amplitudes of the speed modulations are found based on a genetic algorithm such that the input energy to the turning process is minimized. Results of the stability analysis and the...
Mechanical behavior analysis of micro-scaled functionally graded timoshenko beams by the strain gradient theory
, Article Proceedings of the ASME Design Engineering Technical Conference ; Volume 5 , 2012 , Pages 67-73 ; 9780791845042 (ISBN) ; Kahrobaiyan, M. H ; Rahaeifard, M ; Ahmadian, M. T ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
2012
Abstract
In this paper, a size-dependent formulation is developed for Timoshenko beams made of functionally graded materials (FGM). The developed formulation is based on the strain gradient theory;a non-classical continuum theory able to capture the size-effect in micro-scaled structures. Considering the material length scale parameters of the FG beams vary through the thickness, the new equivalent length scale parameters are proposed as functions of the constituents' length scale parameters to describe the size-dependent static and dynamic behavior of FG microbeams. The governing differential equations of equilibrium and both classical and nonclassical sets of boundary conditions are derived for the...
Dynamic and Vibration Analysis of Functionally Graded Microswitches and Microresonators Based on the Strain Gradient Theory
,
Ph.D. Dissertation
Sharif University of Technology
;
Ahmadian, Mohammad Taghi
(Supervisor)
;
Firoozbakhsh, Keikhosrow
(Supervisor)
Abstract
In this research, based on the strain gradient theory, mechanical behavior of functionally graded microbeams is analyzed and the results are used to investigate the static and dynamic responses of electrostatically actuated microswitches and microresonators.
The nonlinear governing equations of motion of functionally graded microbeams are derived using Hamilton’s principle. Afterward, the nonlinear model is implemented to analyze the mechanical response of electrostatically actuated microswitches and microresonators. Pull-in instability and nonlinear vibration of these components are investigated considering the effects of squeeze film damping, mid-plane stretching and initial curvature...
The nonlinear governing equations of motion of functionally graded microbeams are derived using Hamilton’s principle. Afterward, the nonlinear model is implemented to analyze the mechanical response of electrostatically actuated microswitches and microresonators. Pull-in instability and nonlinear vibration of these components are investigated considering the effects of squeeze film damping, mid-plane stretching and initial curvature...