Couple stress

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1 - Chaotic convection in couple stress liquid saturated porous layer‎
Vinod K&lrm;. &lrm;Gupta&lrm; A. K. &lrm;Singh&lrm; B. S. Bhadauria&lrm; I. Hasim&lrm; J. M. Jawdat&lrm;

&lrm;In this paper&lrm;, &lrm;we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity&lrm;, &lrm;heated from below and cooled from above&lrm;, &lrm;based on theory of dynamical system&lrm;. &lrm;A چکیده کامل

&lrm;In this paper&lrm;, &lrm;we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity&lrm;, &lrm;heated from below and cooled from above&lrm;, &lrm;based on theory of dynamical system&lrm;. &lrm;A low dimensional Lorenz&lrm;- &lrm;like model is obtained by using Galerkin-truncation approximation&lrm;. &lrm;We found that there is proportional relation between scaled couple stress parameter and rescaled Rayleigh number&lrm;. We analyzed that increase in level of couple stress parameter increases the level of chaos&lrm;. پرونده مقاله

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2 - Genetic Algorithm and ANN for Estimation of SPIV of Micro Beams
M. Heidari

In this paper, the static pull-in instability (SPIV) of beam-type micro-electromechanical systems is theoretically investigated. Herein, modified strain gradient theory in conjunction with Euler–Bernoulli beam theory have been used for mathematical modeling of the چکیده کامل

In this paper, the static pull-in instability (SPIV) of beam-type micro-electromechanical systems is theoretically investigated. Herein, modified strain gradient theory in conjunction with Euler–Bernoulli beam theory have been used for mathematical modeling of the size dependent instability of the micro beams. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two common beam-type systems including double-clamped and clamped-free cantilever have been investigated. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps and size effect, we identify the static pull-in instability voltage. Back propagation artificial neural network (ANN) with three functions have been used for modelling the static pull-in instability voltage of micro beam. Effect of the size dependency on the pull-in performance has been discussed for both micro-structures. The network has four inputs of length, width, gap and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. The number of nodes in the hidden layer, learning ratio and momentum term are optimized using genetic algorithms (GAs). Numerical data, employed for training the network and capabilities of the model in predicting the pull-in instability behaviour has been verified. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the back propagation neural network has the average error of 6.36% in predicting pull-in voltage of cantilever micro-beam. Resultant low relative error value of the ANN model indicates the usability of the BPN in this area. پرونده مقاله

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3 - Vibration Analysis of Rectangular Kirchhoff Nano-Plate using Modified Couple Stress Theory and Navier Solution Method
Behzad Bayati Chaleshtori Ali Hajiahmad Seyed Saeid Mohtasebi

10.30495/admt.2021.1916102.1230

In this study, the characteristics of rectangular Kirchhoff nano-plate vibrations are investigated using a modified couple stress theory. To consider the effects of small-scale, the modified couple stress theory proposed by Young (2002) is used as it has only one length چکیده کامل

In this study, the characteristics of rectangular Kirchhoff nano-plate vibrations are investigated using a modified couple stress theory. To consider the effects of small-scale, the modified couple stress theory proposed by Young (2002) is used as it has only one length scale parameter. In modified couple stress theory, the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor, and symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and kinetic energy equation and inserting them in the Hamilton principle, the main and auxiliary equations of nano-plate are obtained. Then, by applying the boundary and force conditions in the governing equations, the vibrations of the rectangular Kirschhof nano-plate with the thickness are investigated with simple support around. The solution method used in this study is the Navier method and the effects of material length scale, length and thickness of the nanoplate on the vibration are investigated and the results are presented and discussed in details. پرونده مقاله

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4 - Bending and Buckling Analysis of a Nth-Order Shear Deformation Nanoplate using Modified Couple Stress Theory
Majid Eskandari shahraki mahmoud shariati naser asiaban

10.30495/admt.2021.1915086.1229

In this paper a Nth order nanoplate model is developed for the bending and buckling analysis of a graphene nanoplate based on a modified couple stress theory. The strain energy, external work and buckling equations are solved. Also using Hamilton’ principle, main چکیده کامل

In this paper a Nth order nanoplate model is developed for the bending and buckling analysis of a graphene nanoplate based on a modified couple stress theory. The strain energy, external work and buckling equations are solved. Also using Hamilton’ principle, main and auxiliary equations of nano plate are obtained. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, the dimensionless critical force under a uniaxial surface force in x direction are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The governing equations are numerically solved. The effect of material length scale, length, width and thickness of the nanoplate on the bending and buckling ratios are investigated and the results are presented and discussed in details. پرونده مقاله

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5 - Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution
Majid Eskandari Shahraki Mahmoud Shariati naser asiaban

10.30486/admt.2021.1923209.1252

In this paper, a Mindlin rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress theory. In order to consider the small scale effects, the modified couple stress theory, with one length sc چکیده کامل

In this paper, a Mindlin rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress theory. In order to consider the small scale effects, the modified couple stress theory, with one length scale parameter, is used. In modified couple stress theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. After obtaining the strain and kinetic energy, external work and substituting them in the Hamilton’s principle, the main and auxiliary equations of the nanoplate are obtained. Then, by manipulating the boundary conditions the governing equations are solved using Navier approach for bending and vibration of the nanoplate. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load and different mode frequencies are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The effect of material length scale, length, width and thickness of the nanoplate on the bending and vibration ratios are investigated and the results are presented and discussed in details. پرونده مقاله

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6 - Influence of Viscoelastic Foundation on Dynamic Behaviour of the Double Walled Cylindrical Inhomogeneous Micro Shell Using MCST and with the Aid of GDQM
A Mohammadi H Lashini M Habibi H Safarpour

10.22034/jsm.2019.665264

In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a v چکیده کامل

In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelasticmedium. For the first time, in the present study, has been considered, FG length scale parameter in double walled cylindrical FG microshells, which this parameter changes along the thickness direction. Taking into consideration the first-order shear deformation theory (FSDT), double walled cylindrical FG microshell is modeled and its equations of motions are derived using Hamilton's principle. The novelty of this study is considering the effects of double layers and MCST, in addition to considering the various boundary conditions of double walled cylindrical FG microshell. Generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motions and boundary conditions. Also, for confirmation, the result of current model is validated with the results obtained from molecular dynamics (MD) simulation. Considering length scale parameter (l=R/3) on MCST show, the results have better agreement with MD simulation. The results show that, length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor have important role on the natural frequency of double walled cylindrical FG microshell. پرونده مقاله

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7 - Thermoelastic Damping and Frequency Shift in Kirchhoff Plate Resonators Based on Modified Couple Stress Theory With Dual-Phase-Lag Model
S Devi R Kumar

10.22034/jsm.2020.1896290.1569

The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dual-phase-lag model. The basic equations of motion and heat conduction equation are written with the he چکیده کامل

The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dual-phase-lag model. The basic equations of motion and heat conduction equation are written with the help of Kirchhoff-Love plate theory and dual phase lag model. The analytical expressions for thermoelastic damping and frequency shift of modified couple stress dual-phase-lag thermoelastic plate have been obtained. A computer algorithm has been constructed to obtain the numerical results. Influences of modified couple stress dual-phase-lag thermoelastic plate, dual- phase-lag thermoelastic plate and Lord-Shulman (L-S, 1967) thermoelastic plate with few vibration modes on the thermoelastic damping and frequency shift are examined. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically for clamped-clamped and simply-supported boundary conditions. It is observed from the results that the damping factor and frequency shift have noticed larger value in the presence of couple stress for varying values of length but opposite effect are shown for varying values of thickness in case of both vibration modes and boundary conditions. پرونده مقاله

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8 - Reflection and Transmission at the Boundary of Two Couple Stress Generalized Thermoelastic Solids
R Kumar K Kumar R.C Nautiyal

In this paper the reflection and transmission at a plane interface between two different couple stress generalized thermoelastic solid half spaces in context of Loard-Shulman(LS)[1967] and Green-Lindsay(GL)[1972] theories in welded contact has been investigated. Amplitu چکیده کامل

In this paper the reflection and transmission at a plane interface between two different couple stress generalized thermoelastic solid half spaces in context of Loard-Shulman(LS)[1967] and Green-Lindsay(GL)[1972] theories in welded contact has been investigated. Amplitude ratios of various reflected and transmitted waves are obtained due to incidence of a set of coupled longitudinal waves and coupled transverse waves. It is found that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the couple stress properties of the media. Some special cases are deduced from the present formulation. پرونده مقاله

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9 - Vibration and Stability Analysis of a Pasternak Bonded Double-GNR-System Based on Different Nonlocal Theories
A Ghorbanpour Arani R Kolahchi H Vossough M Abdollahian

This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. چکیده کامل

This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the coupled system. The three vibrational states including out-of-phase vibration, in-phase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient theory is higher than the Eringen's and modified couple stress theories. Moreover, the small scale effect in the case of in-phase vibration is higher than that in the other cases. This study might be useful for the design of nano-devices in which GNRs act as basic elements. پرونده مقاله

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10 - Study on the Pull-In Instability of Gold Micro-Switches Using Variable Length Scale Parameter
M Fathalilou M Sadeghi G Rezazadeh M Jalilpour A Naghilou S Ahouighazvin

In this paper, the size dependent behavior of the gold micro-switches has been studied. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. The size dependent effect چکیده کامل

In this paper, the size dependent behavior of the gold micro-switches has been studied. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. The size dependent effect is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. On the other hand, in some types of micro-beams like gold base, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. In this study, by obtaining the equilibrium positions or fixed points of the gold micro-beam, a considerable difference between the obtained fixed points using classic beam theory and modified couple stress theory has been shown. In addition, it has been shown that the calculated pull-in voltages using modified couple stress theory are much closer to the experimental results than those obtained by classic beam theory. Finally, it has been shown that considering a unique value of length scale parameter, especially for the smallest values of the beam thicknesses, may leads to inaccurate results and variable length scale parameter should be considered. پرونده مقاله

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11 - Axisymmetric Problem of Thick Circular Plate with Heat Sources in Modified Couple Stress Theory
R Kumar Sh Devi V Sharma

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have چکیده کامل

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. The displacements, stress components, temperature change and chemical potential are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of couple stress on the resulting quantities are shown graphically. Some particular cases of interest are also deduced. پرونده مقاله

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12 - Dynamic Instability of Visco-SWCNTs Conveying Pulsating Fluid Based on Sinusoidal Surface Couple Stress Theory
A Ghorbanpour Arani R Kolahchi M Jamali M Mosayyebi I Alinaghian

In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic چکیده کامل

In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip boundary condition and small size effect of nano flow are considered using Knudsen number. The Gurtin–Murdoch elasticity theory is applied for incorporation the surface stress effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The motion equations are derived based on the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is used in order to calculate the dynamic instability region (DIR) of visco-SWCNTs induced by pulsating fluid. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of SWCNTs. The results depict that increasing magnetic field and considering surface effect shift DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems. پرونده مقاله

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13 - Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension
H Safarpour M.M Barooti M Ghadiri

10.22034/jsm.2019.665254

In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuato چکیده کامل

In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell. پرونده مقاله

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14 - The Effect of Modified Couple Stress Theory on Buckling and Vibration Analysis of Functionally Graded Double-Layer Boron Nitride Piezoelectric Plate Based on CPT
M Mohammadimehr M Mohandes

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is چکیده کامل

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of motion are obtained by applying a modified couple stress and von Karman nonlinear strain for piezoelectric material and Kirchhoff plate. These equations are coupled for the FG double-layer plate using Pasternak foundation and solved using Navier’s type solution. Then, the dimensionless natural frequencies and critical buckling load for simply supported boundary condition are obtained. Also, the effects of material length scale parameter, elastic foundation coefficients and power law index on the dimensionless natural frequency and critical buckling load are investigated. The results demonstrate that the dimensionless natural frequency of the piezoelectric plate increases steadily by growing the power law index. ‌‌Also, the effect of the power law index on the dimensionless critical buckling load of double layer boron nitride piezoelectric for higher dimensionless material length scale parameter is the most. پرونده مقاله

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15 - Thermo-elastic Damping in a Capacitive Micro-beam Resonator Considering Hyperbolic Heat Conduction Model and Modified Couple Stress Theory
M Najafi G Rezazadeh R Shabani

In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected micro-beam resonator has been investigated. The thermo-elastic coupled equations for the deflected micro-beam have been derived using variational and Hamilton principles based چکیده کامل

In this paper, the quality factor of thermo-elastic damping in an electro-statically deflected micro-beam resonator has been investigated. The thermo-elastic coupled equations for the deflected micro-beam have been derived using variational and Hamilton principles based on modified couple stress theory and hyperbolic heat conduction model. The thermo-elastic damping has been obtained discretizing the governing equations over spatial domain and applying complex frequency approach. The effects of the applied bias DC voltage, playing simultaneously role of an external force and softening parameter, on the quality factor have been studied. The obtained results of the modified couple stress and classic theories are compared and the effects of the material internal length-scale parameter on the differences between results of two theories have been discussed. In addition, the effects of different parameters such as beam length and ambient temperature on the quality factor have been studied. پرونده مقاله

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16 - Modified Couple Stress Theory for Vibration of Embedded Bioliquid-Filled Microtubules under Walking a Motor Protein Including Surface Effects
A Ghorbanpour Arani M Abdollahian A.H Ghorbanpour Arani

Microtubules (MTs) are fibrous and tube-like cell substructures exist in cytoplasm of cells which play a vital role in many cellular processes. Surface effects on the vibration of bioliquid MTs surrounded by cytoplasm is investigated in this study. The emphasis is place چکیده کامل

Microtubules (MTs) are fibrous and tube-like cell substructures exist in cytoplasm of cells which play a vital role in many cellular processes. Surface effects on the vibration of bioliquid MTs surrounded by cytoplasm is investigated in this study. The emphasis is placed on the effect of the motor protein motion on the MTs. The MT is modeled as an orthotropic beam and the surrounded cytoplasm is assumed as an elastic media which is simulated by Pasternak foundation. In order to consider the small scale effects, the modified couple stress theory (MCST) is taken into account. An analytical method is employed to solve the motion equations obtained by energy method and Hamilton’s principle. The influence of surface layers, bioliquid, surrounding elastic medium, motor proteins motion, and small scale parameter are shown graphically. Results demonstrate that the speed of motor proteins is an effective parameter on the vibration characteristics of MTs. It is interesting that increasing the motor proteins speed does not change the maximum and minimum values of MTs dynamic deflection. The presented results might be useful in biomedical and biomechanical principles and applications. پرونده مقاله

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17 - Effects of Hall Current and Rotation in Modified Couple Stress Generalized Thermoelastic Half Space due to Ramp-Type Heating
R Kumar Sh Devi V Sharma

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic rotating medium in the presence of Hall current and magnetic field due to a ramp-type thermal source. The generalized theories of thermoelasticity developed by Lord چکیده کامل

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic rotating medium in the presence of Hall current and magnetic field due to a ramp-type thermal source. The generalized theories of thermoelasticity developed by Lord Shulman (L-S, 1967) and Green Lindsay (G-L, 1972) are used to investigate the problem. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacements, stress components, temperature change and mass concentration are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of Hall current and rotation are shown in a resulting quantities. Some special cases of interest are also deduced. پرونده مقاله

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18 - Torsion in Microstructure Hollow Thick-Walled Circular Cylinder Made up of Orthotropic Material
S Yadav S Sharma

In this paper, a numerical solution has been developed for hollow circular cylinders made up of orthotropic material which is subjected to twist using micro polar theory. The effect of twisting moment and material internal length on hollow thick-walled circular cylinder چکیده کامل

In this paper, a numerical solution has been developed for hollow circular cylinders made up of orthotropic material which is subjected to twist using micro polar theory. The effect of twisting moment and material internal length on hollow thick-walled circular cylinder made up of micro polar orthotropic material is investigated. Finite difference method has been used to exhibit the influence of shear moduli and material internal length on shear stresses and couple stresses. It is found that the effect of small characteristic length on shear stresses is negligible and couple stresses present its significance when characteristic length is large in solid particle. The behavior of couple stresses are nonlinear for large internal length while for small internal length couple stresses are linear in nature except near the free boundaries. Torsion in hollow cylinder made up of micro polar orthotropic play vital role in the presence of cracks and holes. Therefore, torsional analysis of hollow cylinder plays important role in the field of biomechanics. پرونده مقاله

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19 - Damping and Frequency Shift in Microscale Modified Couple Stress Thermoelastic Plate Resonators
S Devi R Kumar

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the چکیده کامل

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode analysis. The solutions for the free vibrations of plates under clamped-simply supported (CS) and clamped-free (CF) conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for couple stress generalized thermoelastic and coupled thermoelastic plates. A computer algorithm has been constructed to obtain the numerical results. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically in the absence and presence of couple stress for (i) clamped-simply supported, (ii) clamped-free boundary conditions. Some particular cases are also presented. پرونده مقاله

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20 - Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation
M Goodarzi M Mohammadi M Khooran F Saadi

In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. The effect of in-plane pre-load and temperature change are investigated on the vibrati چکیده کامل

In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in a Visco-Pasternak foundation and coupled with temperature change is studied. The effect of in-plane pre-load and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanoplate, two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST), the governing equation is derived for FG circular and annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent, the in-plane pre-load, the temperature change, the power index parameter, the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and annular nanoplate. The temperature change also play an important role in the mechanical behavior of the FG circular and annular nanoplate. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplate پرونده مقاله

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21 - A FSDT model for vibration analysis of Nano rectangular FG plate based on Modified Couple Stress Theory under moving load
یونس امین

In present paper, vibration of Nano FGM plate based on modified couple stress and First Order Shear Deformation Theories (FSDT) under moving load has been developed. Basic equations and linear strains are introduced by first order shear deformation theory and Mori Tanak چکیده کامل

In present paper, vibration of Nano FGM plate based on modified couple stress and First Order Shear Deformation Theories (FSDT) under moving load has been developed. Basic equations and linear strains are introduced by first order shear deformation theory and Mori Tanaka’s model is used for the plate. The module of elasticity and density are assumed to vary only through thickness of plate. Governing Equations are derived according to the modified couple stress theory and Hamilton’s principle. Constitutive equations are also derived based on modified couple stress and finally, analytical solution for simply supported Nano rectangular FG plate is obtained by using of Navier solution. Examples of length scales parameter and power law index are presented to show effect of this parameter on plate behaviors. Results show that plate’s deflection enhances with power law index increasing and by increasing of length scale parameter, deflection decreases, and for frequencies, the deflection with both raising of power law index and length parameter scales, are reduced پرونده مقاله

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22 - Influence of an external magnetic field on the peristaltic flow of a couple stress fluid through a porous medium.
Ajaz Dar K Elangovan

Magnetohydrodynamic(MHD) peristaltic flow of a Couple Stress Fluid through a permeable channel is examined in this investigation. The flow analysis is performed in the presence of an External Magnetic Field. Long wavelength and low Reynolds number approach is implemente چکیده کامل

Magnetohydrodynamic(MHD) peristaltic flow of a Couple Stress Fluid through a permeable channel is examined in this investigation. The flow analysis is performed in the presence of an External Magnetic Field. Long wavelength and low Reynolds number approach is implemented. Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained. Pressure rise, frictional force and pumping phenomenon are portrayed and symbolized graphically. The elemental characteristics of this analysis is a complete interpretation of the influence of Couple Stress Parameter, magnetic number, non dimensional amplitude ratio and permeability parameter on the velocity, pressure gradient, pressure rise and frictional forces. پرونده مقاله

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23 - Vibration Analysis of FG Micro-Beam Based on the Third Order Shear Deformation and Modified Couple Stress Theories
Mehdi Alimoradzadeh Mehdi Salehi Sattar Mohammadi Esfarjani

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and n چکیده کامل

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-beam follow a power law form through thickness. The motion equations are solved by employing Furrier series in conjunction with Galerkin method. Also, effects of aspect ratio, power index and dimensionless length scale parameter on the natural frequencies and amplitude-excite frequency curves are investigated. Findings indicate that dimensionless frequencies are strongly dependent on the values of the material length scale parameter and power index. The numerical results of this study indicate that if the thickness of the beam is in the order of the material length scale parameter, size effects are more significant. پرونده مقاله

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24 - Free Vibration Analysis of Sandwich Micro Beam with Piezoelectric Based on Modified Couple Stress Theory and Surface Effects
Mohammad khajekhabaz Ali Eftekhari Mohammad Hashemian

In this paper, the free vibration analysis of sandwich micro beam with piezoelectric layers based on the modified couple stress and surface elasticity theories are investigated. The Hamilton’s principle is employed to derive the sandwich micro beam with piezoelect چکیده کامل

In this paper, the free vibration analysis of sandwich micro beam with piezoelectric layers based on the modified couple stress and surface elasticity theories are investigated. The Hamilton’s principle is employed to derive the sandwich micro beam with piezoelectric based on modified couple stress theory incorporating with Gurtin- Murdoch surface theory. The generalized differential quadrature method is used to discretize the partial differential equation into the ordinary differential equation. The effect of various parameters such as thickness to material length scale parameter ratio, the surface residual stress, Young's modulus of surface layer, surface mass density and surface piezoelectric constant are investigated by comparing the results obtained using the modified couple and classical theories. Numerical results of this problem evaluate the effect of micro length scale parameters on natural frequency. The results show that surface parameter effects are significant when the model is small, but can be neglected with increasing model size. پرونده مقاله

فهرست مقالات Couple stress

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