The equilibrium position of a deformable drop in Couette and Poiseuille flows is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objective of this work is to study the motion of a non-neutrally buoyant drop in Couette and Poiseuille flows with different density ratios at finite Reynolds numbers. Couette flow: The equilibrium position of the lighter drops is higher than the heavier drops at each particle Reynolds number. Also, the equilibrium position height increases with increasing the Reynolds number at a fixed density ratio. At this equilibrium distance from the wall, the migration velocity is zero, while the velocity of the drop in the flow direction and rotational velocity of the drop is finite. It is observed that the equilibrium position is independent of the initial position of the drops and depends on the density ratio and the shear Reynolds number. Poiseuille flow: When the drop is slightly buoyant, it moves to an equilibrium position between the wall and the centerline. The equilibrium position is close to the centerline if the drop lags the fluid but close to the wall if the drop leads the fluid. As the Reynolds number increases, the equilibrium position of lighter drops moves slightly closer to the wall and the equilibrium position of heavier drops moves towards the centerline.

This paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

Structural Health Monitoring (SHM) takes advantage of the recent advances in nanotechnology and sensing in order to monitor the behavior of a structure, assess its performance and identify damage at an early stage. Monitoring the state of strain throughout an entire structure is essential to determine its state of stress, detect potential residual stresses after fabrication, and also to help to establish its integrity. The Carbon nanotube thread was integrated into three-dimensional braiding materials and used for the first time as a sensor to monitor strain and also to detect damage in the three-dimensional braided composite material.

In this paper a literature review about the application of carbon nanotubes thread for sensors and smart materials used for SHM of braiding structures is presented. The test data show the braided angle is important parameter for structural health monitoring of three-dimensional. The research will provide a new integrated and distributed technologies for the built-in carbon nanotube sensor to detect the health of composite. The subject will provide the new idea and method for the development of smart composite materials research and application.

Hall effects on the unsteady Couette flow between two infinite horizontal parallel plates in a rotating system under the boundary layer approximations have been studied. One of the plate is at rest and the other oscillates in its own plane with the velocity U(t). An exact solution of the governing equations has been obtained by the use of the Laplace transform technique. The numerical results for the velocity components and the shear stresses are depicted graphically. Asymptotic behavior of the solution has analyzed for large values of magnetic parameter, rotation parameter and frequency parameter to gain some physical insight into the flow pattern. It is observed that there exists thin boundary layer (s) is formed near the stationary plate for large values of rotation parameter, magnetic parameter and frequency parameter.

A thermoacoustic standing-wave prime mover with a quarter-wave resonator has been investigated experimentally. The working fluid is air at the barometric pressure. The holographic interferometry and hot-wire anemometry have been used. A special optical setup, based on a Michelson interferometer, has been developed and used. The setup exhibits a double sensitivity, in comparison with a common Mach-Zehnder holographic interferometer. The results have confirmed a proper function of the prime mover, and advantages of the present optical setup.

Mixed convection flow of second grade fluid bounded by a permeable stretching surface is discussed. Soret and Dufour effects are also present. Series solutions for the resulting problems are made using homotopy analysis method (HAM). Analysis has been carried out for the effects of embedded parameters on the velocity, temperature and concentration fields. Numerical values of Nusselt and Sherwood numbers are computed and discussed.

This paper studies the influence of mass transfer in the magnetohydrodynamic (MHD) boundary layer stagnation point flow of Burgers' fluid over a shrinking sheet. Analysis has been carried out in the presence of first order chemical reaction. The two-dimensional flow equations are modeled and then simplified using boundary layer approach. Similarity variables are used to transform the partial differential equations into nonlinear ordinary differential equation. The resulting system is computed using homotopy analysis method (HAM). It is noted that retardation time in Burgers' fluid enhances the magnitude of the flow. The gradient of mass transfer and surface mass transfer for various interesting parameters are also tabulated and analyzed.

This paper contributes to propose a 2D practical interface tracking algorithm of volume-of-fluid (VOF) method through the improved interface reconstruction, namely using both mixed Youngs centered column method (MYCCM) and the Lagrangian split advection scheme. A computationally efficiency and second-order accuracy for interface reconstruction method is presented and approximated by heuristic algorithms based on the piecewise linear interface calculation (PLIC) concept. The method can be accurately estimated by a regular structured mesh without any geometrical modifications. Besides, a linear mapping technique is implemented to improve the efficiency of numerical simulations with regard to the approximation for capturing the interface. The computational tests include widely used benchmark cases, such as the solid-body translations and rotations and the swirled single vortex of fluid body. Its performances of the improved algorithm are compared against other classical VOF advection methods. Good results are obtained by using present algorithm.

It is difficult to obtain the derivative values from most mesh dependent numerical procedures in general. This study proposes an efficient computational tool to accurately evaluate the multi-order derivatives by the radial basis functions and local differential quadrature (LRBF-DQ) algorithm. Most of the traditional derivative calculations can be only adopted to evaluate the differential values with the regular meshes. Moreover, the traditional numerical schemes are very restricted by the order of the shape functions. The present technique can be applied to both the structured and unstructured meshes as well as meshless numerical algorithms – such as RBFs and LDQ method. In addition, the proposed model can be also used to estimate multi-order or mixed partial derivative values because its test function using RBFs is a multi-order differentiable function. All of the evaluation of derivative results will be compared with the exact solutions and other numerical techniques. Consequently, this study provides an effective algorithm of post process to accurately calculate the multi-order derivative values for any numerical schemes.

This paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

This paper concentrates on theoretical and experimental nonlinear stiffness study of milling machine tool spindle angle contact ball bearing. The theoretical study allows us to build an analytical model to define nonlinear stiffness of angle contact ball bearings based on geometrical and physical parameters. Modifications were done on literature's models (e.g. Balls deformations) having positives impacts on conformity of models to experimental results.

FEM model using ANSYS is constructed to analyze the different parameters affecting the nonlinear stiffness of ball bearing. Among those parameters are physical including the geometry, friction coefficient and the boundary conditions of the model and Numerical parameters such as mesh density and penetration.

Experimental tests were done on the spindle ball bearing 7014, to measure the rigidity. Universal tensile testing machine is used to achieve load displacement curves. The developed theoretical model, constructed finite element model and experimental results showed good conformity.

This article presents the results from a study of drainage rates and groundwater pressure distributions surrounding a horizontal drain pipe. The pipe is assumed to be applied on a retaining wall and reached a steady state condition. The optimized design pattern for horizontal drain pipes on a retaining wall is deeply related to the efficiency of dissipation of groundwater and the pore pressure behind the wall. Therefore, simulations of groundwater flow through a single horizontal drain pipe with different sizes (diameters and lengths) and depths by a 3-D finite element program model would lead us to find out the mechanism of the drainage pattern. The study has revealed the equalized water pressure contours surrounding the horizontal drain pipe exhibited horn shapes distributions. The biggest but still has a closed shape of horn was named Characterized Iso-pressure Surface (CIPS) in this research. It was found to be a good object to reflect the effects of single drain pipe so as to explore the mechanisms of drainage pattern. This research conducted a series study of dimension factor influence. It could be a help in developing assessment and design methods for horizontal drain pipes applied to the retaining wall.

The double side approach method combines the method of weighted residuals (MWR) with mathematical programming to solve the differential equations. Once the differential equation is proved to satisfy the maximum principle, collocation method and mathematical programming are used to transfer the problem into a bilateral inequality. By utilizing Genetic Algorithms optimization method, the maximum and minimum solutions which satisfy the inequality can be found. Adopting this method, quite less computer memory and time are needed than those required for finite element method.

In this paper, the incompressible-Newtonian, fully-developed, steady-state laminar flow in equilateral triangular, rectangular, elliptical and super-elliptical ducts is studied. Based on the maximum principle of differential equations, the monotonicity of the Laplace operator can be proved and the double side approach method can be applied. Different kinds of trial functions are constructed to meet the no-slip boundary condition, and it was demonstrated that the results are in great agreement with the analytical solutions or the formerly presented works. The efficiency, accuracy, and simplicity of the double side approach method are fully illustrated in the present study to indicate that the method is powerful for solving boundary value problems.

Hamiltonian system is a special case of dynamical system. Mostly it is used for potential shaping of mechanical systems stabilization. In our present work, we are using Hamiltonian dynamics to study and control the fuel slosh inside spacecraft tank. Sloshing is the phenomenon which is related with the movement of fluid inside a container in micro and macro scale as well. Sloshing of fluid occurs whenever the frequency of container movement matches with the natural frequency of fluid inside the container. Such type of synchronization may cause the structural damage or could be a reason of moving object's attitude disturbance. In spacecraft technology, the equivalent mechanical model for sloshing is common to use for the representation of fuel slosh. This mechanical model may contain a model of pendulum or a mass attached with a spring. In this article, we are using mass-spring mechanical model coupled with rigid body to derive the equations for Hamiltonian system. Casimir functions are used for proposed model. Conditions for the stability and instability of moving mass are derived using Lyapunov function along with Casimir functions. Simulation work is presented to strengthen the derived results and to distribute the stable and unstable regions graphically.

Four helical-grooved cones were installed behind an unconfined combustion nozzle to increase the bluff-body effect and turbulence intensity (T.I.). The cone configurations included a smooth cone and the other three cones cut with 1, 2 and 3 helical v-grooves. Experimental results showed that the helical v-grooves transformed the axial momentum (or the axial velocity) to the angular momentum (or the angular velocity). The T.I. was enhanced by increasing the tangential component of fuel-jet momentum. The direct photography and thermocouple were utilized to observe the flame structures and to delineate the characteristic flame modes, flame length, temperature distribution, and combustion intensity. The flame modes were classified as jet flame, flickering flame, bubble flame, recirculation flame, lifted flame and ring flame. The flame length decreases as the groove number increases. The increased T.I. and groove number (or bluff-body effect) improve the fuel-air mixing. The total combustion intensity increases with annular-air jet and with the groove number.

The problem of a layered structure containing an arbitrarily oriented crack crossing the interface in anti-plane elasticity is considered in this paper. The fundamental solution of displacements and stresses is obtained in a series form via the method of analytical continuation in conjunction with the alternating technique. A dislocation distribution along the prospective site of a crack is used to model a crack crossing the interface and the singular integral equations with logarithmic singular kernels for a line crack are then established. The crack is approximated by several line segments and the linear interpolation equation with undetermined coefficients was applied for the dislocation function along line segments. Once the undetermined dislocation coefficients are solved, the mode-III stress intensity factors KIII at two crack tips can be obtained for various crack inclinations with different material property combinations. All the numerical results are checked to achieve a good approximation that demonstrates the accuracy and the efficiency of the proposed method.

Theoretical and experimental investigations of the stiffness of non-clearance linear guideways without preload were conducted. A theoretical approach that applied Hertz's contact theory to steel balls to derive the contact angle equation was proposed. The theoretical analysis showed that the stiffness of the linear guideway under variable vertical loads changes nonlinearly with the external load. Therefore, an experimental setup was proposed in which the stiffness curves of three blocks, differing in geometrical shape and assembled with steel balls, were measured under increased vertical load until the guideway began to plastically deform. The results showed that variation in both the width and the thickness of the block does not significantly affect stiffness. A comparison of the theoretical and experimental results revealed a relative error of 4.5%, indicating the correctness of the theoretical model. Based on theoretical equations, the main parameters that affect stiffness are conformity fm, coefficient of contact deformation cδ, reference diameter of the ball Dw, number of load-carrying rows i, number of load-carrying balls in one row Z, and initial contact angle α0. The results are useful for determining the static/dynamic behavior and rigidity of linear guideways in the design stage.

Anti-plane interaction of an elliptically cylindrical layered media with an arbitrarily oriented crack embedded in an infinite matrix, intermediate layer, or inner inclusion under a remote uniform shear load is considered in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation in the inclusions and the matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack can easily be obtained by using the screw dislocation solutions as the Green's function together with the principle superposition. The stress intensity factors, which can properly reflect the interaction between a crack and an elliptically cylindrical layered media, are then obtained numerically in terms of the values of the dislocation density functions of the integral equations. The effects of material property combinations and geometric parameters on the normalized mode-III stress intensity factors are discussed in detail and shown in graphic form.

Clearances in the joints of mechanism cause vibrations and noise in mechanical systems. The contact force model is the important factor in dynamic analysis of mechanical systems with clearance. This paper presents a nonlinear contact force model for revolute joint with clearance, which is a hybrid model of the Lankarani-Nikravesh model and the improved elastic foundation model. The framework of the Lankarani-Nikravesh model is used with the nonlinear stiffness coefficient derived using the improved elastic foundation model and the damping applied in introducing the ratio of the nonlinear stiffness coefficient of the improved elastic foundation model and contact stiffness of Lankarani-Nikravesh model. Finally, the nonlinear hybrid contact force model is analyzed and discussed. The hybrid contact force model presented in this paper is a nonlinear continuous contact force model, which extends contact modeling of joints with clearance and has a greater applicable scope.

A Plate Infinite Element Method (PIEM) formulation based on Reissner-Mindlin theory is proposed for the stress analysis of cracked plates under bending and tension. The validity of the proposed formulation is demonstrated by comparing the results obtained for the normalized Stress Intensity Factor (SIF) under various loading conditions with the solutions presented in the literature. Importantly, the proposed formulation enables the effects of different crack lengths to be analyzed without the need to re-mesh the computational domain for each simulation/analysis. Overall, the PIEM formulation provides an accurate and computationally-efficient means of analyzing a wide variety of plate bending problems.