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EN
Dispersion curves employed for designing Love wave based liquid sensing devices may provide more accurate information if due consideration is given to parameters describing microstructural behavior of the substrate. The present study involves mathematical modelling of Love waves propagating in a hybrid structure consisting of an elastic layer in the middle overlying a size dependent substrate, loaded with a viscous liquid (Newtonian) half space. Numerical computations are carried out to graphically demonstrate the effects of various parameters: characteristic length of the substrate, thickness of the elastic layer, viscosity and density of the overlying viscous liquid (Newtonian) on dispersion characteristics.
EN
Shear wave based acoustic devices are being used in gaseous and liquid environments because of their high-sensitivity. The theoretical study of horizontally polarized shear (SH) waves in a layered structure consisting of a piezoelectric ceramic of P ZT − 5H or BaT iO3 material overlying a couple stress substrate is presented in this paper. The considered substrate is supposed to be exhibiting microstructural properties. The closed form expression of dispersion relations are derived analytically for electrically open and short conditions. The effects of internal microstructures of the couple stress substrate, thickness of P ZT − 5H or BaT iO3 ceramic, piezoelectric and dielectric constants are illustrated graphically on the phase velocity of the piezoelectric layer under electrically open and short conditions.
EN
The reflection of elastic waves at the surface of a couple-stress elastic half-space with a viscoelastic support is studied in this paper. Different from the classical elastic solid, there are: a non-dispersive dilatational propagating wave, a dispersive transverse propagating wave and a dispersive evanescent wave in a couple-stress elastic solid. The boundary conditions at the visco-elastically supported surface of a couple-stress elastic half-space include the couple-stress vector and the rotation vector, which disappear in the classical elastic solid. They are used to obtain a set of linear algebraic equation, from which the amplitude ratios of reflection waves with respect to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. At last, the influence of the boundary parameters that reflect the mechanical behavior of a viscoelastic support on the amplitude ratio, the phase shift and the energy partition of reflection waves are discussed based on the numerical results. Both the incident longitudinal displacement wave (the P-wave) and incident transverse displacement wave (the SV-wave) are considered. It is found that the instantaneous elasticity and the delayed viscosity of a viscoelastic support have different influences on the reflection waves.
EN
A study of magnetohydrodynamic (MHD) flow with viscous dissipation and heat transfer in an electrically conducting laminar steady viscous incompressible micropolar fluid between two infinite uniformly stretching disks is presented. The transformed self similar nonlinear ODEs are first linearized using a quasi linearization method and then solved by employing a combination of a direct and an iterative method. The study may be beneficial to flow and thermal control of polymeric processing.
EN
For understanding the effects of an internal microstructure, generalised microcontinuum theories with additional microstructural parameters are developed. One such a parameter, called the characteristic length of the material comparable with the internal cell size of the material is involved in the couple stress theory. The problem of propagation of Lamb waves in a plate with an internal microstructure and loaded with an inviscid liquid on both sides is studied using the couple stress theory. The dispersion equation of Lamb waves with the liquid loadings is derived. The impact of the liquid loadings is studied on the propagation of Lamb waves. The effect of the characteristic length is also studied on the phase velocity of Lamb waves in the plate for various modes in the presence of liquid loadings.
EN
We present the numerical study of hydromagnetic (MHD) flow and heat transfer characte- ristics of a viscous incompressible electrically conducting micropolar fluid in a channel with one wall shrinking and the other at rest in the presence of a transverse applied magnetic field. Different from the classical shooting methodology, we employ a combination of a di- rect and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigation may be beneficial to the flow and thermal control of polymeric processing.
7
Content available remote Biomechanical couple interactions
EN
Micropolar continuous medium theory from the beginning was modeling theory. It predicted in that medium existing of mass angular momentum, asymmetrical stress forces, stress moments and mass force momentum. On the beginning there was no able to interpret angular momentum, stress moments and mass force momentum on physical matter known base. In 70’s of XX age there were provided an examples for ferromagnetic, paramagnetic and dielectric bodies. This paper gives attention to interpret those effects in biological structures. On example of human blood there is showed application of Langevin’s paramagnetism classical theory and its mechanical results. In the paper there are presented interesting examples of biological structures which had mechanical results using electric dipole moments.
EN
The present paper is concerned with the propagation of waves in a couple stress elastic half space lying under an inviscid liquid layer in the context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. It is observed that shear waves get decoupled from the rest of the motion. After developing the formal solution, the secular equations for surface wave propagation are derived. The dispersion curve giving the phase velocity and attenuation coefficient related to wave number are plotted graphically to depict the effect of thermal relaxation times. The amplitude ratios of displacement components and temperature distribution are also computed numerically and shown graphically to depict the effect of thermal relaxation times. Some special cases are also deduced from the present investigation.
EN
Three-dimensional dispersion of a passive solute in a couple stress fluid through a channel of rectangular cross section is studied using the generalized miscible dispersion theory of Gill and Sankarasubramanian (1970) and Doshi et al. (1978). The effects of couple stress on the velocity and thereby the convective and dispersion coefficients are discussed. The time-dependent dispersion coefficient and mean concentration distribution are computed and the results are represented graphically for various values of the aspect ratio and couple-stress.
10
Content available remote Surface effects of coupled fields in micropolar continuous media
EN
In mechanics of continuous media, one of the sub areas is the coupled field theory describing interactions of mechanical, thermal, diffusion and electromagnetic field. All this physical fields are represented in the tensors introduced in this theory. Taking into consideration the momentum and angular momentum of the electromagnetic field in medium requires introduction of the fields: couple stress, mass angular momentum and mass couple in balance equations. From the vectorial nature of momentum, angular momentum, force and couple it appears that the stress tensor and couple stress tensor are the second order. Bearing in mind the importance for modern technology of the physical properties of the surface and surface layer of a solid, the conception of balance equations will be applied to describe the material surface interacting with an electromagnetic field.
EN
On the basic of Christensen's stochastic model of rough surfaces, different forms of Reynolds equation with rotational inertia effect are obtained for various types of surface roughness pattern and for couple stress lubricant. As results one obtained the formulae expressing the mean film pressure distribution for externally pressurized bearings and for bearings with a squeeze film. An example of step bearing is considered.
12
EN
The present investigation deals with the deformation of a micropolar thermoelastic medium with voids due to distributed mechanical thermal sources acting on the plane surface. The analytic expressions of displacement components, force stress, couple stress, change in volume fraction field and temperature distribution are obtained in the physical domain for Green-Lindsay (G-L) theory of thermoelasticity after applying the integrai transforms. These expressions are then inverted by using a numerical inversion method. The numerical results are presented graphically for a mechanical/ thermal uniformly distributed source. Some particular cases have also been deduced.
EN
On the basis of Christensen’s stochastic model of rough surfaces, different forms of Reynolds equation with rotational inertia effect are obtained for various types of surface roughness pattern and for couple stress lubricant. As results one obtained the formulae expressing the mean film pressure distribution for externally pressurized bearings and for bearings with a squeeze film. Examples of spherical and step bearings are considered.
EN
A variational formulation of initial-boundary value problems for the nonlinear elasticity theory of couple stresses is formulated using Hamilton functional. The local model equations are obtained. It is considered the model variants for theories of dynamical uncouple stress, quasistatic couple and uncouple stress elasticity as particular cases. The partial Hamilton functional is specified for the linear couple stress elasticity theory.
EN
The stability of two superposed couple-stress fluids of uniform densities, permeated with suspended particles, in a porous medium is considered. A stability analysis is carried out and for mathematical simplicity we consider two highly viscous fluids of equal kinematic viscosities and equal couple-stress kinematic viscosities. The system is found to be stable for a potentially stable configuration under certain condition whereas a potentially unstable configuration remains unstable for the couple-stress fluid permeated with suspended particles in a porous medium. The growth rates of perturbation are found to be both increasing (for some wave numbers) and decreasing (for other wave numbers) with the increase in medium permeability.
16
Content available remote Moving load response at thermal conducting fluid and micropolar solid interface
EN
The steady state response of a micropolar elastic solid with an overlying semi-infinite thermal conducting fluid subjected at the plane interface to a moving point load is determined. The analytic expressions of displacement components, force stress, couple stress and temperature distribution are obtained in the physical domain for Lord-Shulman (L-S), Green-Lindsay (G-L), coupled theory (C-T) and Green-Naghdi (G-N) theories of thermoelasticity by the use of Fourier transform technique and are shown graphically for magnesium crystal like material. The integral transform has been inverted by using a numerical technique.
17
Content available remote Couple stress and surface roughness effects in curvilinear thrust bearings
EN
On the basis of Christensen's stochastic model of rough surfaces, different forms of Reynolds equation with rotational inertia effect are obtained for various types of surface roughness pattern and for couple stress lubricant. As results one obtained the formulae expressing the mean film pressure distribution for externally pressurized bearings and for bearings with a squeeze film. A spherical squeeze film bearing is discussed as an example.
18
Content available remote Analysis of plane Couette flow using micropolar fluid theory
EN
In this study, fluid flow behavior in microchannel is examined because of its relevance to the design and development of micro-devices. Previous research has indicated that micropolar fluid theory may provide a better model of fluid flow in microfluidic devices than classical Navier-Stokes theory. An analysis of the plane Couette flow between two parallel plates of a viscous, incompressible, micropolar fluid is presented. The effects of non-zero values of micro-gyration vector and pressure gradient on the flow fields and skin friction are studied. Numerical results of velocity profiles of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Analytical results show that the skin friction increases by increasing the parameter of micro-gyration vector on the wall (n), and decreases by increasing values of micropolar parameter (b). It is also seen that the value of couple stress coefficient decreases as the model parameter (m) increases.
19
Content available remote Shear band development in modified DEM: importance of couple stress
EN
Numerical simulation tests were carried out using the distinct element method (DEM) with great interest in how large couple stress is actually generated in a shear band. To do this, the conventional DEM was modified slightly, so that the effect of rolling resistance at contact points can be taken into account (called MDEM). It has been found that MDEM provides a powerful tool in simulating not only the generation of large voids inside a shear band but also the high gradient of particle rotation along the shear band boundaries, in a quite similar manner to those of natural granular soils; and that couple stress, although it is very small, is certainly developed in a consistent manner with the particle relation gradient developed in a shear band.
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