Volume 21 (2016): Issue 4 (December 2016)

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

In this article, a new mathematical representation of the sinusoidal alternating velocity, force and power by means of some complex quantities, termed ‘holors’ is proposed. The word holor is a term to describe a mathematical entity that is made up of one or more independent quantities, and includes complex numbers, scalars, vectors, matrices, tensors and other hypernumbers. Holors, thus defined, have been known for centuries but each has been developed more or less independently, accompanied by separate nomenclature and theory.

This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

Beetle wings perform a flapping movement, consisting of the rotation relative to the two axes. This paper presents the results of observations and measurements of wings operating parameters in different planes of some beetle species. High speed photos and videos were used. The concept of the mechanism performing a complex wing movement was proposed and developed.

This paper presents a numerical analysis of the relationship between in-plane constraints and the crack tip opening displacement (CTOD) for single-edge notched bend (SEN(B)) specimens under predominantly plane strain conditions. It provides details of the numerical model and discusses the influence of external load and in-plane constraints on the CTOD. The work also reviews methods for determining the CTOD. The new formula proposed in this paper can be used to estimate the value of the coefficient d_n as a function of the relative crack length, the strain hardening exponent and the yield strength - d_n(n, σ₀/E, a/W), with these parameters affecting the level of in-plane constraints. Some of the numerical results were approximated using simple mathematical formulae.

Differential games are a combination of game theory and optimum control methods. Their solutions are based on Bellman's principle of optimality. In this paper, the zero-sum differential game theory has been used for the purposes of controlling a mechatronic object: a single-link manipulator. In this case, analytical solutions are unavailable, thus approximate solutions were used. Two approximation methods were compared with the use of numerical simulations and selected quality indicators. The results confirm previous assumptions and the connection between the differential game theory and H_∞ control problems.

Silicon <111> crystal is one of the crystal orientations, which shows potential for application in micro device developments of pressure diaphragms for measurement purposes. To date, no theoretical basis has been examined to develop the deflections for computational analysis purposes [1]. This paper presents the development of the diaphragm deflections for Silicon <111> Crystal in Cylindrical coordinates system. The Silicon <111> crystal possesses transverse isotropic properties. Thus, an anisotropic thin plate theory is used here to develop the plate deflection. A numerical example is given to compare the theoretical results with Finite Element Analysis (FEA) results.

We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.

A numerical solution of a transient natural convection flow past a semi-infinite inclined plate under the combined buoyancy effects of heat and mass transfer along with chemical reaction is presented herewith. The governing boundary layer equations for the above flow problem for a first order homogeneous chemical reaction are set up and non-dimensionalised. An implicit finite difference method is employed to solve the unsteady, nonlinear, integro and coupled partial differential equation. Numerical results are presented for various parameters occurring in the problem. The unsteady velocity, temperature and concentration profiles, local and average skin friction, Nusselt number and Sherwood number are studied for both a generative and destructive reaction.

In the paper, the problems of devices supporting functional rehabilitation of a human wrist were addressed. A literature review and a description of selected devices together with an indication of their advantages and disadvantages were conducted. The biomechanical structure of a human wrist was analyzed. On this basis and after taking into consideration ranges of motion of the selected joints the concept of a new mechanism was developed. A 3D model of the device was built in the Autodesk Inventor system. For the purpose of simulations another model was developed in the MSC Adams system. Issues of drives and sensors selection, as well as requirements for the control system, were examined.

The present paper investigates the propagation of time harmonic circumferential waves in a two-dimensional hollow poroelastic cylinder with an inner shaft (shaft-bearing assembly). The hollow poroelastic cylinder and inner shaft are assumed to be infinite in axial direction. The outer surface of the cylinder is stress free and at the interface, between the inner shaft and the outer cylinder, it is assumed to be free sliding and the interfacial shear stresses are zero, also the normal stress and radial displacements are continuous. The frequency equation of guided circumferential waves for a permeable and an impermeable surface is obtained. When the angular wave number vanish the frequency equation of guided circumferential waves for a permeable and an impermeable surface degenerates and the dilatational and shear waves are uncoupled. Shear waves are independent of the nature of surface. The frequency equation of a permeable and an impermeable surface for bore-piston assembly is obtained as a particular case of the model under consideration when the outer radius of the hollow poroelastic cylinder tends to infinity. Results of previous studies are obtained as a particular case of the present study. Nondimensional frequency as a function of wave number is presented graphically for two types of models and discussed. Numerical results show that, in general, the first modes are linear for permeable and impermeable surfaces and the frequency of a permeable surface is more than that of an impermeable surface.

The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated with a lubricant being a viscoplastic fluid of a Herschel-Bulkley type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Herschel-Bulkley lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze films in a step bearing (modeled by two parallel disks) is discussed in detail.

Based upon a Prandtl fluid flow model, a curvilinear squeeze film bearing is considered. The equations of motion are given in a specific coordinate system. After general considerations on the Prandtl fluid flow these equations are used to derive the Reynolds equation. The solution of this equation is obtained by a method of successive approximation. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of the Prandtl fluid flow in gaps of two simple bearings are presented.

The article presents a description of ion migration in a concrete pore liquid caused by an external electric field. The equation of the flow of aggressive chloride ions is formulated on the basis of partial equations of mass balance. It is assumed that electrochemical potential is in classical form, then an attempt is made to determine the average diffusion coefficient using the inverse diffusion Eq.(3.9).

The issues addressed in the paper present a part of the scientific research conducted within the framework of the automation of the aircraft engine part manufacturing processes. The results of the research presented in the article provided information in which tolerances while using a robotic control station with the option of force control we can make edge deburring.

The present study analyzes the operation length of internal forces (DDSW) understood as the length of the flow of internal forces along the shortest possible internal routes. The operation length of internal forces is determined on the basis of stresses and the given volume in the constructional space. The minimum DDSW of the structure satisfies the criterial conditions of the most rigid structure, where the potential energy of deformation and the deformation energy potential is the same in the whole volume and thus the potential gradient is zero.

One of the major work safety issues involves the investigations of machine vibrations and the way they affect the machine operators. These investigations can be performed in the laboratory conditions in a setup in which the seat vibrations are induced by a motion platform. A complex mechanism is proposed implementing 3 translations and 2 rotation movements, and actuated by three electric motors. This study investigates the design structure of the real motion platform mechanism and provides the synthesis of link dimensioning. Kinematic dependencies are formulated and the Jacobian matrix is derived accordingly to solve the equations of motion. Computer simulation procedure yields the critical seat vibration frequency and amplitudes for the available asynchronous motors.

The numerical calculations results of torsional vibration of the multi-cylinder crankshaft in the serial combustion engine (MC), including a viscous damper (VD), at complex forcing, were shown. In fact, in the MC case the crankshaft rotation forcings spectrum is the sum of harmonic forcing whose amplitude can be compared with the amplitude of the 1st harmonic. A significant impact, in the engine operational velocity, on the vibration damping process of MC, may be the amplitude of the 2^nd harmonic of a forcing moment. The calculations results of MC vibration, depending on the amplitude of the 2^nd harmonic of the forcing moment, for the first form of the torsional vibration, were shown. Higher forms of torsional vibrations have no practical significance. The calculations assume the optimum damping coefficient VD, when the simple harmonic forcing is equal to the base critical velocity of the MC crankshaft.

In this paper, the technical data provided by the sellers of an exercise bike FALCON SG-911B SAPPHIRE have been verified. After dismantling the bike, the dimensions of the components of the transmission of motion were measured and the mass parameters of the flywheel were set. In order to increase the mass moment of inertia reduced to an axis of the crankshaft, construction changes were proposed. The values of the braking torque of the magnetic brake at subsequent resistance levels were measured. The cycling test was performed and the distance, calories burned and heart rate read from the counter were verified computationally.