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The paper presents size-dependant mechanical behaviors of carbon nanotubes under electrostatic actuation using modified couple stress theory. The behaviors of the carbon nanotubes with different geometries and boundary conditions are studied in detail. The results reveal that application of this theory results in higher pull-in voltages for both cantilever and doubly clamped boundary conditions  

This article presents a study on the thermal buckling behavior of two-dimensional functionally graded microbeams made of porous materials. The material composition varies along thickness and length of the microbeam based on the power law distribution. The microbeam is modeled within the framework of Euler–Bernoulli beam theory. The microbeam is considered having variable material composition along thickness. The equations are derived using the modified couple stress theory and the solving process is based on the generalized differential quadrature method. The validity of the results is shown through comparison of the results with the results of other published research. © 2017 Taylor &... 

The modified couple stress theory is employed in this paper in order to formulate the size-dependent strain energy release rate of Euler-Bernoulli and Timoshenko notched beams. As a case study, the normalized energy release rate of the aforementioned beams has been developed for three-point bending as a function of the ratio of material length scale parameter to the beam depth. The results of the current model are compared to the experimental data. The good agreement between the present results and the experimental values indicates that the current model can be successfully applied to evaluate size dependent energy release rate of structures  

The experimental observations indicate that the mechanical behavior of micro and nano scale structures is size-dependent. In this study, employing the modified couple stress theory the size-dependent strain energy release rate of notched Euler-Bernoulli beams made of functionally graded material (FGM) is formulated. The normalized energy release rate for the problem of three-point bending in notched FG beams is obtained using the procedure established by Kienzler and Herrmann [Kienzler R, Herrmann G, An elementary theory of defective beams. Acta Mech 1986; 62:37-46]. It is assumed that the material properties vary continuously along the beam thickness according to a power law distribution.... 

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... 

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  

In this paper, static behavior and pull-in of micro tweezers is studied. The micro tweezer is modelled as two cantilever beams. Static behavior of the micro tweezer under the effect of electrostatic actuation is modelled using the Euler-Bernoulli beam theory. In order to capture size effects on the behavior of micro tweezers, modified couple stress theory is utilized. It is shown when the voltage between two electrodes increased from some specific value, micro beams adhere to each other and it is observed that the pull-in voltage predicted by the modified couple stress theory considerably differs with that of the classical theory of elasticity. Results of this paper can be used for accurate... 

In this paper, the nonlinear forced-vibration of Euler-Bernoulli beams with large deflections is investigated based on the modified couple stress theory, a non-classical theory capable of capturing size effects. The classical theory is unable to predict the size effects. In systems with the dimensions in order of microns and sub-microns the size effects are very significant. For some specific beams subjected to a concentrated force at its middle as the harmonic exciter, the size-dependent responses are investigated for primary, super-harmonic and sub-harmonic resonances. The results show that the frequency-responses of the system are highly size-dependent  

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... 

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... 

On the basis of the modified couple stress theory, some analytical results are obtained for vibrational parameters of micro-spinning Rayleigh beams with an axial mass-eccentricity distribution. The modified couple stress theory is a nonclassical continuum theory capable to capture the size effects in small-scale structures. After writing the governing equations of motion, they are transformed to the complex form. Then by utilizing the Galerkin method, analytical expressions for natural frequencies of the micro-spinning beam in forward and backward whirl motions are obtained. Critical speeds are also analytically presented in the two whirl motions for different modes. Moreover, the... 

In this article, the size-dependent behavior of micro-beams with the thermoelastic damping (TED) phenomenon is studied. The coupled thermoelasticity equations are derived on the basis of the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model. By solving these coupled equations simultaneously, a closed-form expression for the TED parameter in micro-beams is presented which considers the small-scale effects incorporation. Then, the effect of various parameters on TED in micro-beams, such as micro-beam height, the type of material, boundary conditions, and aspect ratio is investigated. The results show that the influence of utilizing non-classical continuum and... 

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... 

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... 

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... 

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... 

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