scholarly journals Unsteady Helical Flows of a Size-Dependent Couple-Stress Fluid

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Qammar Rubbab ◽  
Itrat Abbas Mirza ◽  
Imran Siddique ◽  
Saadia Irshad
Keyword(s):  
Stress Tensor ◽  
Couple Stress ◽  
Integral Transform ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Fluid Velocity ◽  
Axial Flow ◽  
Couple Stress Fluid ◽  
Stress Vector ◽  
Transform Method

The helical flows of couple-stress fluids in a straight circular cylinder are studied in the framework of the newly developed, fully determinate linear couple-stress theory. The fluid flow is generated by the helical motion of the cylinder with time-dependent velocity. Also, the couple-stress vector is given on the cylindrical surface and the nonslip condition is considered. Using the integral transform method, analytical solutions to the axial velocity, azimuthal velocity, nonsymmetric force-stress tensor, and couple-stress vector are obtained. The obtained solutions incorporate the characteristic material length scale, which is essential to understand the fluid behavior at microscales. If characteristic length of the couple-stress fluid is zero, the results to the classical fluid are recovered. The influence of the scale parameter on the fluid velocity, axial flow rate, force-stress tensor, and couple-stress vector is analyzed by numerical calculus and graphical illustrations. It is found that the small values of the scale parameter have a significant influence on the flow parameters.

Analysis of Micro-Cracks Using Modified Couple-Stress Elasticity under Anti-Plane Deformation

2016 ◽  
Vol 258 ◽  
pp. 182-185
Author(s):  
Jalil P. Vafa ◽  
Shahriar J. Fariborz
Keyword(s):  
Couple Stress ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Plane Deformation ◽  
Fourier Integral ◽  
Modified Couple Stress Theory ◽  
Elastic Plane ◽  
Transform Method ◽  
Micro Cracks ◽  
Modified Couple Stress

Based on the modified couple stress theory the solution to a screw dislocation is obtained, in an isotropic elastic plane, via Fourier integral transform method. The asymptotic analysis of displacement field at the tip of a stationary crack reveals that stress field is not singular. A crack under anti-plane deformation is modeled by the distribution of screw dislocations. The ensuing integral equations are solved numerically to determine the density of dislocation on a crack surface. The dislocation solution is used to study the interaction between two parallel non-collinear micro-cracks.

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

2021 ◽  
pp. 107754632110482
Author(s):  
J Ranjan Banerjee ◽  
Stanislav O Papkov ◽  
Thuc P Vo ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Dynamic Stiffness ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

Several models within the framework of continuum mechanics have been proposed over the years to solve the free vibration problem of micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified couple stress theories. Many of these models retain the basic features of the Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one or more material scale length parameters to tackle the problem. The work described in this paper deals with the free vibration problems of micro beams based on the dynamic stiffness method, through the implementation of the modified couple stress theory in conjunction with the Timoshenko–Ehrenfest theory. The main advantage of the modified couple stress theory is that unlike other models, it uses only one material length scale parameter to account for the smallness of the structure. The current research is accomplished first by solving the governing differential equations of motion of a Timoshenko–Ehrenfest micro beam in free vibration in closed analytical form. The dynamic stiffness matrix of the beam is then formulated by relating the amplitudes of the forces to those of the corresponding displacements at the ends of the beam. The theory is applied using the Wittrick–Williams algorithm as solution technique to investigate the free vibration characteristics of Timoshenko–Ehrenfest micro beams. Natural frequencies and mode shapes of several examples are presented, and the effects of the length scale parameter on the free vibration characteristics of Timoshenko–Ehrenfest micro beams are demonstrated.

scholarly journals On the effective properties of foams in the framework of the couple stress theory

2020 ◽  
Vol 32 (6) ◽  
pp. 1779-1801 ◽  
Author(s):  
Andrzej Skrzat ◽  
Victor A. Eremeyev
Keyword(s):  
Stress Tensor ◽  
Couple Stress ◽  
Elastic Moduli ◽  
Effective Properties ◽  
Couple Stress Theory ◽  
Volume Element ◽  
Open Cell ◽  
Stress Theory ◽  
Open Cell Foam ◽  
Cell Foam

Abstract In the framework of the couple stress theory, we discuss the effective elastic properties of a metal open-cell foam. In this theory, we have the couple stress tensor, but the microrotations are fully described by displacements. To this end, we performed calculations for a representative volume element which give the matrices of elastic moduli relating stress and stress tensors with strain and microcurvature tensors.

Flexural Vibration of an Atomic Force Microscope Cantilever Based on Modified Couple Stress Theory

2015 ◽  
Vol 15 (07) ◽  
pp. 1540025 ◽  
Author(s):  
Li-Na Liang ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang ◽  
Jie Yang ◽  
Sritawat Kitipornchai
Keyword(s):  
Size Effect ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Flexural Vibration ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Stress Theory ◽  
Atomic Force ◽  
Modified Couple Stress

This paper is concerned with the flexural vibration of an atomic force microscope (AFM) cantilever. The cantilever problem is formulated on the basis of the modified couple stress theory and the Timoshenko beam theory. The modified couple stress theory is a nonclassical continuum theory that includes one additional material parameter to describe the size effect. By using the Hamilton's principle, the governing equation of motion and the boundary conditions are derived for the AFM cantilevers. The equation is solved using the differential quadrature method for the natural frequencies and mode shapes. The effects of the sample surface contact stiffness, length scale parameter and location of the sensor tip on the flexural vibration characteristics of AFM cantilevers are discussed. Results show that the size effect on the frequency is significant when the thickness of the microcantilever has a similar value to the material length scale parameter.

Effects of the Length Scale Parameter on the Thermoelastic Damping of a Microbeam Considering the Couple Stress Theory

2016 ◽  
Vol 08 (06) ◽  
pp. 1650083 ◽  
Author(s):  
Mohammad Fathalilou ◽  
Ghader Rezazadeh
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Theory Of Elasticity ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Complex Frequency ◽  
Thermoelastic Damping ◽  
Stress Theory ◽  
Ambient Temperatures

This paper studies the thermoelastic damping in microbeams considering the couple stress theory with microstructure. This theory includes the microinertia effects, coming from the kinetic energy due to the velocity gradient through the differential macroelements. A Galerkin-based reduced order model and complex frequency approach have been used to determine the quality factor. For a gold microbeam as a case study, the obtained results for different ambient temperatures, beam lengths and thicknesses are compared to those obtained using the classic theory of elasticity. The comparison has been made for different values of the length scale parameter. The effects of the microinertia term on the magnitude of the thermoelastic damping have also been investigated and shown that for which conditions these effects are significant.

Thermal Effect on Static Bending, Vibration and Buckling of Reddy Beam Based on Modified Couple Stress Theory

2013 ◽  
Vol 332 ◽  
pp. 331-338 ◽  
Author(s):  
Ali Reza Daneshmehr ◽  
Mostafa Mohammad Abadi ◽  
Amir Rajabpoor
Keyword(s):  
Thermal Effect ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Bending Vibration ◽  
Stress Theory ◽  
Micro Scale ◽  
Modified Couple Stress

A microstructure-dependent Reddy beam theory (RBT) which contain only one material length scale parameter and can capture the size effect in micro-scale material unlike the classical theory is developed .using the variational principle energy the governing equation of motion is derived based on modified couple stress theory for the simply supported beam. the equations obtained are solved by Fourier series and the influence of the length scale parameter and thermal effect on static bending, vibration and buckling analysis of micro-scale Reddy beam is investigated.

scholarly journals Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

2020 ◽  
Vol 64 (2) ◽  
pp. 97-108
Author(s):  
Mehdi Alimoradzadeh ◽  
Mehdi Salehi ◽  
Sattar Mohammadi Esfarjani
Keyword(s):  
Differential Equation ◽  
Forced Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

Buckling analysis of functionally graded sandwich cylindrical micro/nanoshells based on the couple stress theory

2017 ◽  
Vol 21 (3) ◽  
pp. 917-937 ◽  
Author(s):  
Hamid Zeighampour ◽  
Milad Shojaeian
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length

Buckling of functionally graded sandwich cylindrical microshell under axial load is investigated. For this purpose, Donnell shell theory as well as material length scale parameter as considered by the couple stress theory is used, and equations of motion of the functionally graded sandwich cylindrical microshell along with boundary conditions are developed using Hamilton’s principle. Finally, dimensionless critical buckling load is determined for three functionally graded sandwich cylindrical microshells using the Navier procedure. Results of the new model are compared with the classical theory. The results indicate that the rigidity of the functionally graded sandwich cylindrical microshell in the couple stress theory is higher than that in the classical theory, which leads to increased dimensionless critical buckling load. Besides, the effect of material length scale parameter on dimensionless critical buckling load of the functionally graded sandwich cylindrical microshell in different wavenumbers is considerable.

Sign in / Sign up

Export Citation Format

Share Document