A systematic procedure is developed to calculate ground vibration at any specific location in layered medium due to harmonic loadings applied at a circular plate on the medium. In the procedure, the technique decomposing the interaction tractions between excited plate and layered medium will be employed. The decomposed tractions will automatically match boundary values of general solutions of three dimensional wave equations in cylindrical coordinates. In numerical results, the effect of layered stratum on ground vibration will be investigated and how ground vibration in layered medium decreases with depth will be presented. Also, from the numerical results, one can observe ground vibration may not decay monotonically along distance away from vibration source. The presented scheme is proved to be effective and efficient for accurately predicting near-field ground response to harmonic loadings applied at a rigid circular plate on layered medium. Comments on the presented scheme and numerical results will be given.

This paper studies the behavior of second grade viscoelastic fluid past a cavity in a horizontal channel. The effects of Reynolds number, fluid elasticity and the aspect ratio of the cavity on the flow field are simulated numerically. The equations are converted into the vorticity and stream function equations. The solution is obtained by the finite difference method.

The behavior of viscoelastic fluids is quite different from the Newtonian fluid, due to the effects of fluid elasticity. Only one flow pattern appears when the Newtonian fluid past the cavity. However, three kinds of flow patterns appear while the viscoelastic fluids past the cavity by increasing Reynolds number from 20 to 300. The flow field is affected by the fluid elasticity as well as the aspect ratio of the cavity. The transitional flow pattern appears at lower Reynolds number as the higher elasticity fluid past the cavity with larger aspect ratio.

The boundary layer flow of an Eyring-Powell fluid over a stretching surface subject to the convective boundary condition is investigated. Nonlinear problem is computed and a comparative study is presented with the existing results in viscous fluid. The constructed differential systems have been solved for homotopic solutions. Convergence of series solutions has been discussed. Special emphasis has been given to the effects of material parameters of fluid (ε), (δ), Biot number (γ) and Prandtl number (Pr) on the velocity and temperature profiles. Tabulated values of Nusselt number and skin friction for different emerging parameters are also illustrated. It is noted that the boundary layer thickness is an increasing function of (ε) and decreasing function of (δ). However the temperature and thermal boundary layer thickness decrease when the values of (ε) and (δ) are increased.

Despite the analysis of muffler performance for many years, most works focus mainly on reducing inlet sound and fail to consider the flow effect. Most of their results correlate well with the experimental measurements. Subsequent works have considered the mean flow effect. Owing to Doppler's effect, transmission loss curve of the muffler will shift in its corresponding frequency. However, the correlation is worse than the experimental results since the flow induced noise does not include in the analysis. This work elucidates how flow induced noise affects muffler performance by analyzing a uniform flow that passes through perforated mufflers. The flow field is calculated with the CFD method, followed by evaluation of the aerodynamic noise based on the simulation results. Additionally, the procedure is simplified by computing and comparing only the total sound power induced by the flow in the muffler interior. Two muffler types, Helmholtz resonator and plug perforated tube muffler, are analyzed and discussed.

Analytical solutions are presented for time periodic EOF flow of linear viscoelastic fluids through a cylindrical micro-pipe. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluid and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. The velocity expressions of these two layers were obtained, respectively. By numerical computations, the influences of the periodic EOF electric oscillating Reynolds number Re, Deborah number De, depletion layer thickness δ and the viscosity ratio γ of Maxwell to Newtonian fluids on velocity profile are presented. For a prescribed De, the increasing Re will cause large changes of the EOF velocity with decreasing velocity magnitude. For a given Re, large De gives large EOF velocity magnitude. Increasing γ will lead to larger velocity amplitude for a given lower Re. However, at higher Re, the velocity amplitude decreases with the viscosity ratio γ, especially within the depletion layer. In addition, large depletion layer thickness gives small EOF velocity magnitude for fixed Re and De. Finally, the influence of De on energy dissipation is studied. These results provide a detail insight of the flow characteristic of this flow configuration.

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.

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.

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.

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.

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.

In the paper, nonlinear dynamic analysis of a circular plate composed of functionally graded material (FGM) is presented. Considering a transverse shear deformation and geometric nonlinearity, the von Karman geometric relation of the FGM circular plate is established. Based on the theory of the first-order shear deformation, a new set of equilibrium equations is developed by the principle of minimum total energy. Applying the finite difference method and Newmark scheme, the nonlinear transient problem is solved by the iterative method. To validate the presented method, the transient problem of the FGM circular plate is compared with those of the existed literature, and good agreement is observed. The effects of the volume fraction index, boundary conditions, mechanical load and the ratio of thickness to radius on the nonlinear transient problem of the FGM circular plate are investigated.

This study investigates the influences of constant compensations which are produced by capillary or constant flow pump on the dynamic characteristics of a circular worktable supported by a closed-type hydrostatic thrust bearing. The dynamic behaviors of this worktable are analyzed by using Runge-Kutta method to solve the coupled motion equation of worktable and pressure equations of hydrostatic film flow. For various supply pressure parameters, external loads, and varieties of design parameters, the dynamic responses of worktable subjected to both external excitations of harmonic force and step force are simulated, respectively. The results reveal the influences of both constant compensations on the dynamic characteristics of hydrostatic bearing by the different responses of worktable and make the appropriate parameters of design can be found for the worktable-bearing system. The accomplishments of this study will help the designers who deal with the hydrostatic- bearing compensated by constant restrictions to select the design parameters to approach the optimum condition.

By the approaches of the theory of complex functions, dynamic problem concerning mode I semi-infinite crack propagation was studied. Analytical solutions are very easily obtained by application of the measures of self-similar functions. The problems researched can be changed into Riemann-Hilbert problems and analytical solutions to semi-infinite crack under the condition of impulse loads and increasing loads Pt located at the origin of the coordinates, respectively, are attained.

By application of the theory of complex variable functions, asymmetrical dynamic propagation problem on the edges of mode III interface crack subjected to superimpose loads was studied. Analytical solutions of the stresses displacements and dynamic stress intensity factors are obtained by means of self- similar functions. The problems researched can be facilely transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple according to this measure. After those solutions are utilized by superposition theorem, the solutions of arbitrarily complex problems can be gained.

This paper presents a static and linear dynamic model to simulate the performance of a Micro Gas Turbine (MGT). The static model is obtained using thermodynamic equations and maps of the components to determine off design performance of the MGT with constant output power. The linear dynamic model is developed using linearized static and dynamic nonlinear equations around an operating point as state-space model to predict the behaviour of the MGT in transient conditions. To validate the results of the static model, important information such as fuel flow, fuel to air ratio, and turbine inlet temperature are compared with the results of Aspen-HYSYS software during an increase in ambient temperature. In addition, static model results are compared with experimental data of the MGT test by previous studies. Also, the compressor equilibrium running line of the MGT is derived in constant ambient condition. In order to evaluate the linear dynamic model, the verification is performed using the results of nonlinear model of previous studies. The comparison between the results confirms the ability of proposed dynamic model to simulate a MGT while decreasing the computational effort and complexity of equations. Moreover, a comparison is carried out between static model results and steady state values predicted by dynamic model.

The unsteady hydromagnetic flow due to torsional oscillations of a rotating disc in a viscous incompressible electrically conducting fluid which is also rotating is studied taking the effects of the Hall current and ion-slip into consideration. The governing equations are solved analytically. The results show that the inclusion of the Hall current and ion slip have important effects on the velocity distributions as well as shear stresses at the disc. The flow is characterized by two opposite circularly polarized waves, travelling with different velocities. It is found that there is a formation of two-deck boundary layers, thicknesses of which increase with increase in either Hall parameter or ion-slip parameter. The radial velocity increases with an increase in Hall parameter and the azimuthal velocity increases with an increase in either Hall parameter or ion-slip parameter. Further, it is found that the amplitude of the transverse shear stress at the disc decreases with an increase in either Hall parameter or ion-slip parameter.

This paper presents a two dimensional asymptotic model of counterflow diffusion flame in the presence of radiation heat loss. The fuel and oxidizer, respectively, are injected from left and right hand side of the flame. The effects of burning rate, Lewis and Damkohler number on the structure and extinction of the flame is studied using perturbation method. To do so, the structure of the flame is considered to be composed of reaction zone with a thickness of O(ε) and radiation heat loss zone, of O(δ) thickness, that sandwiches the reaction zone. The effect of burning rate is illustrated by burning pre-exponential parameter, B. It is found that with the increase of the parameter, the flame temperature is also increased, and flame location moves toward the fuel side. In addition, the variation of Lewis number of fuel and oxidizer has a significant effect on the location and temperature of the flame.

In this paper, Laplace transformation method is used to solve the velocity profile and pressure gradient of the unsteady unidirectional flow of Bingham fluid. Between the parallel microgap plates, the flow motion is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Due to the rarefaction, the wall slip condition is existed; therefore, the complexity of solution is also increased. In order to understand the flow behavior of Bingham fluid, there are two basic flow situations are solved. One is a suddenly started flow and the other is constant acceleration flow. Furthermore, linear acceleration and oscillatory flow are also considered. The result indicates when the yield stress τ0 is zero; the solution of the problem reduces to Newtonian fluid.

In this paper, the modified collocation Trefftz method (MCTM) and the exponentially convergent scalar homotopy algorithm (ECSHA) are adopted to analyze the inverse boundary determination problem governed by the biharmonic equation. The position for part of the boundary with given boundary condition is unknown and the position for the rest of the boundary with overspecified Cauchy boundary conditions is given a priori. Since the spatial position for portion of boundary is not given a priori, it is extremely difficult to solve such a boundary determination problem by any numerical scheme. In order to stably solve the boundary determination problem, the MCTM will be adopted in this study owing to that it can avoid the generation of mesh grid and numerical integration. When this problem is modeled by MCTM, a system of nonlinear algebraic equations will be formed and then be solved by ECSHA. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. In addition, the stability of the proposed meshless method will be tested by adding some noise into the prescribed boundary conditions and then to see how does that affect the numerical results.

In this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.