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modified-couple-stress
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Analysis of Forced Vibration of Micro-Plates Based On A Modified Couple Stress Theory
, M.Sc. Thesis Sharif University of Technology ; Asghari, Mohsen (Supervisor)
Abstract
Vibration analysis of micro-structures has been a major topic in recent years. Among them micro-plates play an important role in micro- and nano-electromechanical systems (MEMS and NEMS), e.g. micropumps, micromirrors, and microresonators. Some experimental observations revealed the size-dependent mechanical behavior in micro-scaled structures. Because of the incapability of the classical continuum theory to interpret the experimentally-detected small-scale effects in mechanical behavior of micro-scaled systems, non-classical theories should be used to deal with micron and sub-micron structures. Couple stress theory is one of the non-classical theories with only one length scale parameter. A...
A size-dependent yield criterion
, Article International Journal of Engineering Science ; Vol. 74, issue , Jan , 2014 , p. 151-161 ; Rahaeifard, M ; Ahmadian, M. T ; Sharif University of Technology
Abstract
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...
Buckling Analysis of Nano-Plates in the Context of Modified Couple Stress Theory Using RKPM
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor)
Abstract
In this research, a new Kirchhoff plate model based on the modified couple stress theory has been utilized to derive the corresponding closed-form expression for the buckling load. Moreover, a numerical mesh-less method, Reproducing Kernel Particle Method (RKPM), in combination with Corrected Collocation Method (CCM) has been employed to model the nano-plate and calculate its buckling load in the framework of the modified couple stress theory. To this end, two kinds of nano-plates have been modeled, the square nano-plates with all edges simply supported 1) in the presence of the nano-void and 2) without the nano-void. It should be noted that the analytical and numerical solutions for the...
Free Vibration Analysis of Circumferentially Stiffened Micro-Cylinder Made of the Functionally Graded Material
, M.Sc. Thesis Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor) ; Firouzbakhsh, Kekhosro (Co-Advisor)
Abstract
Micro-Structures, especially cylindrical shells, has been widely used in different high tech industries, that this extreme usage emphasis, analyze of the vibration behavior of these structures. For gain an appropriate characteristics for a known purpose we can stiffen cylindrical shells with some rings that lids to improvement in mechanical properties of them. With advent of new materials, such as Functionally Graded Materials (FGM) and unique properties of these materials investigation of vibration behavior and characteristics of micro cylinders which has been made of FGM can be very important and essential. By using FGM materials many mechanical characteristics of these structures can be...
Dynamic analysis of carbon nanotubes under electrostatic actuation using modified couple stress theory
, Article Acta Mechanica ; Vol. 225, Issue 6 , June , 2014 , pp. 1523-1535 ; Online ISSN: 1619-6937 ; Rastgoo, A ; Ahmadian, M. T ; Mashhadi, M. M ; Sharif University of Technology
Abstract
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
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...
Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection
, Article Microsystem Technologies ; Volume 25, Issue 8 , 2019 , Pages 3137-3150 ; 09467076 (ISSN) ; Mohasel Afshari, B ; Barati, M. R ; Hamouda, A. M. S ; Sharif University of Technology
Springer Verlag
2019
Abstract
Nonlinear free/forced vibration of a functionally graded graphene nanoplatelet (GNP) reinforced microbeam having geometrical imperfection which is rested on a non-linear elastic substrate have been studied in the present research. Graphene Platelets have been uniformly and non-uniformly scattered in the cross section area of the microbeam. Non-uniform distribution of GNPs is considered to be linear or non-linear type. Geometric imperfection is considered similar to the first vibration mode of microbeam. Size effects due to micro-rotations are captured in this study by means of modified couple stress elasticity. In the case of forced vibration, a uniform harmonic load is exerted to the top...
Size-dependent analysis of thermoelastic damping in electrically actuated microbeams
, Article Mechanics of Advanced Materials and Structures ; Volume 28, Issue 9 , 2021 , Pages 952-962 ; 15376494 (ISSN) ; Asghari, M ; Sharif University of Technology
Bellwether Publishing, Ltd
2021
Abstract
This paper presents an analytical expression for the thermoelastic damping (TED) in electrically actuated microbeams based on the nonclassical continuum theory of the modified couple stress (MSC) and the nonclassical heat conduction model of the dual-phase-lag (DPL). This expression for TED captures small-scale effects. The coupled equations of motion and heat conduction are first derived. Then, the set of coupled governing equations are analytically dealt, and the real and imaginary parts of frequency are extracted in the framework of the complex frequency approach. Next, a closed-form relation for describing TED in electrically actuated microbeams is obtained which captures the small-scale...
Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem
, Article Engineering with Computers ; 2021 ; 01770667 (ISSN) ; Hao, H ; Oslub, K ; Habibi, M ; Tounsi, A ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021
Abstract
In the current paper, vibrational and critical circular speed characteristics of a functionally graded (FG) rotary microdisk is examined considering a continuum nonlocal model called modified couple stress (MCS) model, for the first time in the literature. The generalized differential quadrature (GDQ) approach and variational method are used for deriving and solving the non-classical final relations. The FG size-dependent micro-sized disk’s final relations and corresponding boundary conditions (BCs) are achieved on the basis of the higher-order shear deformation (HSD) model. Then, a parametric analysis has been conducted to analyze the influences of the length scale factor, circumferential,...
Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties
, Article Engineering with Computers ; Volume 37, Issue 4 , 2021 , Pages 3629-3648 ; 01770667 (ISSN) ; Habibi, M ; Tounsi, A ; Safarpour, H ; Safa, M ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021
Abstract
The stability analysis of cantilevered curved microtubules in axons regarding various size elements and using the generalized differential quadrature method for solving equations is reported. The impacts of covering MAP Tau proteins along with cytoplasm are taken into account as the elastic medium. Curved cylindrical nanoshell considering thick wall is used to model the microtubules. The factor of length scale (l/R = 0.2) used in modified couple stress theory would result in more accuracy when it comes to comparison with experiments, while alternative theories presented in this paper provide less precise outcomes. Due to the reported precise results, at the lower value of the time-dependent...
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
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...
Polysilicon nano-beam model based on modified couple stress and Eringen's nonlocal elasticity theories
, Article Physica E: Low-Dimensional Systems and Nanostructures ; Vol. 63, issue , 2014 , p. 223-228 ; Pishkenari, H. N ; Yousefi-Koma, A ; Hoorzad, H ; Sharif University of Technology
Abstract
In recent years, extensive experiments have shown that classical continuum theory cannot predict the behavior of mechanical microstructures with small size. To accurately design and analyze micro- and nano-electro-mechanical systems, size-dependent continuum theories should be used. These theories model micro- and nano-electro-mechanical systems with higher accuracy because they include size-dependent parameters. In this paper, polysilicon nano-beam is modeled using modified couple stress and Eringen's nonlocal elasticity theories. First, partial differential equations governing the vibration of nano-beams are converted to a one D.O.F. differential equations using Galerkin method, resulting...
Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory
, Article International Journal of Engineering Science ; Volume 54 , May , 2012 , Pages 99-105 ; 00207225 (ISSN) ; Sharif University of Technology
2012
Abstract
In this paper an analytical solution for size-dependent response of cantilever micro-beams is presented. Using the modified couple stress theory, the small scale effects are accounted for. Employing the Modified Variational Iteration Method, efficient and accurate analytical expressions for the deflection of the micro-beam are presented. Very good agreement is observed between the present work results and available experimental data. This study may be helpful to characterize the size-dependent mechanical properties of MEMS. Consequently, the proposed analytical solution can be used as an efficient tool for studying the effects of the material or geometrical parameters on small scale devices...
Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro-plates
, Article International Journal of Engineering Science ; Volume 100 , 2016 , Pages 45-60 ; 00207225 (ISSN) ; Sharif University of Technology
Elsevier Ltd
2016
Abstract
In this study, the buckling and postbuckling analysis of FG micro-plates under different kinds of traction on the edges is investigated based on the modified couple stress theory. The static equilibrium equations of an FG rectangular micro-plate as well as the boundary conditions are derived using the principle of minimum total potential energy. The analytical solutions are developed for three case studies including: simply supported micro-plates subjected to uniform transverse load and biaxial tractions, clamped-simply supported micro-plates under uniform transverse load and axial traction, and simply supported micro-plates subjected to shear traction. All plate properties except the length...
Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams
, Article Computer Methods in Applied Mechanics and Engineering ; Volume 322 , 2017 , Pages 615-632 ; 00457825 (ISSN) ; Mirjavadi, S. S ; MohaselAfshari, B ; Rabby, S ; Kazemi, M ; Sharif University of Technology
Elsevier B.V
2017
Abstract
This study presents analysis on the vibration behavior of the two-dimensional functionally graded (2D-FG) nano and microbeams which are made of two kinds of porous materials for the first time, based on Timoshenko beam theory. The material of the nano and microbeams is modeled as 2D-FGMs according to the power law. The Eringen's nonlocal elasticity and the modified couple stress theories are used, respectively in case of nano and microbeams. The boundary conditions are considered as clamped (CC), simply supported (SS), clamped–simply supported (CS), and cantilever (CF). The governing equations are solved using the generalized differential quadrature method (GDQM). The effects of FG power...
The couple stress-based nonlinear coupled three-dimensional vibration analysis of microspinning Rayleigh beams
, Article Nonlinear Dynamics ; Volume 87, Issue 2 , 2017 , Pages 1315-1334 ; 0924090X (ISSN) ; Hashemi, M ; Sharif University of Technology
Springer Netherlands
2017
Abstract
The nonlinear coupled three-dimensional vibrations of microspinning Rayleigh beams are analytically studied utilizing the modified couple stress theory to take into account the small-scale effects. The considered nonlinearity is of geometrical type due to the mid-plane stretching. The rotary inertia and gyroscopic effects are both included in the formulation. Governing equations of motion are derived with the aid of the Hamilton Principle and then transformed into complex form. Then, the Galerkin and multiple scales methods are utilized to solve the nonlinear partial differential equation. Approximate analytical expressions for nonlinear natural frequencies of the spinning beams in forward...
Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory
, Article Scientia Iranica ; Volume 25, Issue 5B , 2018 , Pages 2598-2615 ; 10263098 (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
Sharif University of Technology
2018
Abstract
In this paper, free vibration of the micro-cylinder made by functionally graded material stiffened in circumferential direction was investigated based on modified couple stress and first-order shear deformation theories. Modified Couple Stress Theory (MCST) was used to catch size effects in micro scales. By using first-order shear deformation theory and Hamilton's principle, the general equations of motion and corresponding boundary conditions were derived. Free vibration of the structure was investigated by implementing simply-supported boundary condition as a common case. The effects of different parameters, such as dimensionless length scale parameter, distribution of FGM properties,...
Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale timoshenko beam
, Article JVC/Journal of Vibration and Control ; Volume 24, Issue 18 , 2018 , Pages 4211-4225 ; 10775463 (ISSN) ; Mohasel Afshari, B ; Shafiei, N ; Rabby, S ; Kazemi, M ; Sharif University of Technology
Abstract
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...
Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: a comparative study on modified couple stress theory and nonlocal elasticity theory
, Article Journal of Intelligent Material Systems and Structures ; Volume 29, Issue 11 , 2018 , Pages 2492-2507 ; 1045389X (ISSN) ; Saeidi Googarchin, H ; Mahinzare, M ; Eftekhari, S. A ; Sharif University of Technology
SAGE Publications Ltd
2018
Abstract
In this article, free vibration behavior of a rotating nano/microcircular plate constructed from functionally graded magneto-elastic material is simulated with the first-order shear deformation theory. For the sake of comparison, the nonlocal elasticity theory and the modified couple stress theory are employed to implement the small size effect in the natural frequencies behavior of the nano/microcircular plate. The governing equations of motion for functionally graded magneto-elastic material nano/microcircular plates are derived based on Hamilton’s principle; comparing the obtained results with those in the literature, they are in a good agreement. Finally, the governing equations are...
On buckling and post-buckling behavior of functionally graded micro-beams in thermal environment
, Article International Journal of Engineering Science ; Volume 128 , July , 2018 , Pages 63-78 ; 00207225 (ISSN) ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
This study provides an exact solution for the size dependent buckling and post-buckling behavior of functionally graded (FG) micro-beams with arbitrary boundary conditions which are subjected to combined thermo-mechanical loading. To this end, a theoretical formulation including the effects of size dependency, elastic foundation and uniform temperature distribution is first derived using the modified couple stress theory and through the principle of minimum total potential energy. Next, the nonlinear equations governing bending and stretching behavior of FG micro-beams are uncoupled to a fourth-order ordinary differential equation. Finally, the differential operator method is utilized to...