The ribbing instability of forward roll coating is analyzed numerically by linear stability theory. The velocity ratio of two rolls is fixed to be 1/4 for practical surface coating processes. The base flows through the gap between two rolls are solved by use of powerful CFD-RC software package. A numerical program is developed to solve the ribbing instability for the package is not capable of solving the eigenvalue problem of ribbing instability. The effects of the gap between two rolls, flow viscosity, surface tension and average roll velocity on ribbing are investigated. The criterion of ribbing instability is measured in terms of critical capillary number and critical wave number. The results show that the surface coating becomes stable as the gap increases or as the flow viscosity decreases and that the surface coating is more stable to the ribbing of a higher wave number than to the ribbing of a lower wave number. The effect of average roll velocity is not determinant to the ribbing instability. There are optimum and dangerous velocities for each setup of rolling process.

Knowledge of the control of the musculoskeletal system in patients with knee osteoarthritis (OA) during gait is helpful for the development of intervention programs in the management of these patients. The current study aimed to investigate the leg and joint stiffness, aswell as the associated joint kinematics and kinetics, in patients with bilateral medial knee OA during gait. Joint angles, moments and stiffness, as well as leg stiffness from fifteen patients with bilateral knee OA and fifteen normal controls during level walking, were obtained and their values at the beginning and end of single leg stance were compared using a t-test.

Patients with knee OA were found to modulate their leg and joint stiffness through acquired specific biomechanical strategies in order to maintain normal temporal-spatial patterns of gait. During weight acceptance, they increased their leg stiffness with increased knee stiffness but unalterd hip and ankle stiffness. During weight release, they modulated their hip and ankle kinetics with increased knee and ankle stiffness to improve the control stability of the limb with unaltered leg stiffness. It is suggested that muscle strengthening exercise intervention and/or rehabilitation for patients with knee OA should focus on activities that develop and/or maintain functions not only of the knee, but also of the overall lower extremity.

This study theoretically and experimentally investigates the velocity distributions of the interface boundary layer region in a porous medium. By combining a quadratic non-Darcy law and a practical eddy viscosity model, an analytical solution is derived and presented. Three additional parameters, i.e., the depth of the interface boundary layer region, the slip velocity, and proportionality constant, are contained in the analytical solution. The measured experimental data show the depth of the interface boundary layer region only depends on the characteristics of the porous medium rather than the relative flow depth, bed slop, or Reynolds number. The values of the slip velocity are found to increase with increasing relative mean clear fluid velocities. The proportionality constant plays an important role in modeling the penetration of turbulence and the associated momentum transfer. The measured experimental velocity distribution is used to evaluate the accuracy of the analytical predicted profile. The analytical results obtained in this study are in agreement with the measured experimental results.

A fiber Bragg grating (FBG) sensor system which can simultaneously measure the point-wise, out-of-plane and in-plane dynamic displacements is proposed. A demodulation system based on the fiber Bragg grating filter is used. The steady-state responses of particle motions of a piezoceramic plate measured by the FBG out-of-plane and in-plane displacement sensors are simultaneously compared with those obtained by a laser Doppler vibrometer (LDV) and a surface-mounted FBG strain sensor, respectively. The integration of the FBG displacement sensor with a dynamic signal analyzer (FBG-DSA) forms a measurement system which has the ability to acquire the frequency response of a piezoceramic plate. An LDV-DSA system and an impedance analyzer are used to compare the results obtained from the dynamic signal analyzer combined with the out-of-plane FBG sensor (OFBG-DSA) and the in-plane FBG sensor (IFBG-DSA), respectively. The experimental results of the impulse excitation as well as the random excitation of the piezoceramic plate are also presented. To explain the experimental results, an optical full-field measurement technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and FEM numerical calculations are also used to provide full-field vibration mode shapes of the piezoceramic plate. These results indicate that the proposed displacement sensor system has the multiplexing capability to measure the dynamic displacements up to 45kHz.

In the step-by-step solution of a linear elastic system, an appropriate time step can be selected based on analytical evaluation resultsHowever, there is no way to select an appropriate time step for accurate integration of a nonlinear system. In this study, numerical properties of the Newmark explicit method are analytically evaluated after introducing the instantaneous degree of nonlinearity. It is found that the upper stability limit is equal to 2 only for a linear elastic system. In general, it reduces for instantaneous stiffness hardening and it is enlarged for instantaneous stiffness softening. Furthermore, the absolute relative period error increases with the increase of instantaneous degree of nonlinearity for a given product of the natural frequency and the time step. The rough guidelines for accurate integration of a nonlinear system are also proposed in this paper based on the analytical evaluation results. Analytical evaluation results and the feasibility of the rough guidelines proposed for accurate integration of a nonlinear system are confirmed with numerical examples.

In this paper, an analytical approach for deriving the Green's function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noticed that all the improper integrals were avoided when the degenerate kernels were used. After determining the unknown Fourier coefficients, the displacement, slope, normal moment and effective shear force of the plate could be obtained by using the boundary integral equations. The present approach was seen as an “analytical” approach for a series solution. Finally, several analytical solutions were obtained. To see the validity of the present method, FEM solutions using ABAQUS were compared well with our analytical solutions. The displacement, radial moment and shear variations of radial and angular positions were presented.

In Taipei, many pile proof load tests were not conducted to failures but only to a multiple (e.g., 2) of the design load. This leads a difficulty of incomplete information: For these test results, the ultimate bearing capacities of the test piles are unknown. This paper addresses the issue of calibrating resistance factors of piles for the axial ultimate bearing capacities based on the incomplete information from these tests. A simplified probabilistic method is proposed to resolve this issue. A local pile test database of Taipei is presented, and the analysis results show that the inclusion of the incomplete pile load test data helps in calibrating the resistance factors. Moreover, it is found that the calibrated resistance factors for the axial ultimate bearing capacities are consistent to the safety factors that are adopted in the current Taiwan design code. This paper also addresses another important issue for the pile design in Taipei: the end bearing capacity in the sandstone layer is very uncertain. A maximum likelihood method is taken to identify the best estimate for this end bearing capacity. The conclusion of this paper may be useful for reliability-based designs for the axial ultimate bearing capacities of single bored piles in the Taipei region.

In this study an effective numerical approach is proposed for calculation of exhaust pipe flows. The flow inside an exhaust pipe is very complicated, since that flow involves pulsating hot gases with blast waves discharged from an internal combustion engine. In order to accurately simulate the complicated pulsating flow with the effects of heat transfer and friction at the duct wall, two systems of quasi-onedimensional model equations are employed, which resulted from the governing equations of the mass, momentum and energy conservation. One system of model equations with the terms of heat loss and wall friction results from the dimensionless governing equations based on dimensionless time variable t1 where t1 is defined as the dimensional time divided by the ratio of the pipe length to the time-average flow velocity at the pipe inlet. This system of model equations is numerically solved for a steady exhausted gas-flow without blast waves. The computed steady flow is referred as a basic flow. The other system of model equations without the terms of heat loss and wall friction results from the dimensionless governing equations based on dimensionless time variable t2, where t2 is defined as the dimensional time divided by the ratio of the pipe length to the speed of sound at the pipe inlet. The latter model is used for predicting exhausted gas-flows with blast waves. These two systems of model equations are solved by a th-order weighted essential non-oscillation scheme. It is found that the computed result of the peak pressures, temperature, and flow velocity at some check points for an exhaust pipe at different engine speeds agrees reasonably well with experimental data.

Some analytical formulas are presented for torsional analysis of homogeneous hollow tubes. The cross section is supposed to consist of straight and circular segments. Thicknesses of segments of the cross section can be different. The problem is formulated in terms of Prandtl's stress function. The derived approximate formulas are so simple that computations can be carried out by a simple calculator. Several examples are presented to validate the formulation. The accuracy of formulas is verified by accurate finite element method solutions. It is seen that the error of the formulation is small and the formulas can be used for analysis of thin to moderately thick-walled hollow tubes.

In present research, improvement of a microbubble generator's performance via reliance on fluid dynamics characteristics is studied numerically, and then some experiments are executed. In an elementary cylindrical microbubble generator, water flow enters the device via six diagonal nozzles, and passes a rotational path around a central motionless hub. This flow breaks the big bubbles entering the device by gas injection from air nozzles. The high-intensity turbulence and shear flow in this device is the cause of the air bubble breaking process. These small bubbles can be used to reduce frictional drag on the contact surface of moving solid bodies in water flow. To improve the operation of the apparatus, some suggested geometrical shapes were investigated numerically and were optimized based on the bubbles' effective breaking-up parameters. The experimental results illustrated good performance of the recent apparatus for generating smaller bubbles.

Analytical study is conducted in this paper to understand the characteristics of sound transmission through cylindrical shell with free layer damping (FLD) treatment. It is assumed an infinitely long circular cylindrical shell subjected to a plane wave with uniform airflow in the external fluid medium. The damping layer applied on the surface of the shell is represented by HN model with frequency-dependent specifications. An exact solution is obtained by solving the Markus equations of FLD shells and acoustic wave equations simultaneously. As the pressure and displacement terms are expressed in series form, an iterative procedure is founded to cut them with an appropriatenumber of modes. Transmission losses obtained from the solution are compared with “modal-impedance method” for an especial case of untreated shell. Eventually, the numerical results show the effects of stiffness, loss factor and thickness of damping material, and also incident wave angles on TL curves.

This paper presents the results of numerical simulations on the characteristics of hydraulic shockwaves in an inclined chute contraction. A two-dimensional numerical hydraulic simulation model is used to simulate the hydraulic shockwaves, based on the finite-volume multi-stage (FMUSTA) scheme proposed by Guo et al. [1]. This numerical model has been proved having good ability in simulating hydraulic shockwaves through the comparison with the exact solution of idealized shockwaves in a horizontal contraction provided by Ippen and Dawson [2], and the comparison with experimental results provided in the companion paper by Jan et al. [3]. The simulated shockwave parameters such as the shock angle, maximum shockwave height and maximum shockwave position for various conditions are compared with those calculated by the empirical relations obtained in the companion paper. The numerical results validate the applicability of these empirical relations and also extend their applicability to higher approach Froude numbers.

An experimental study for determining the thermal contact conductance between two periodically contacting surfaces is presented. The influence of the frequency of contact upon the thermal contact conductance is investigated. Also, the results show that the thermal contactconductance decreases as the frequency of contact increases. The experimental results obtained from present work are in agreement with the previous published data.

The scattering of plane SH-wave from a partially debonded shallow cylindrical elastic inclusion in half space is investigated in this paper by complex function method and expansion method of wave function. The debonding regions are considered as multiple arc-shaped interface cracks with non-contacting faces. Firstly, in the inclusion district, the standing wave function in the elastic inclusion with unknown coefficients which satisfies the boundary condition is constructed and generated into the Fourier series; in the half space, the stress and displacement boundary condition around the elastic inclusion can be modeled as the same as the standing wave function in the elastic inclusion. Then, a set of infinite algebraic equations can be obtained around the same boundary and the solution of problem can be gained. In the end, numerical examples of the surface displacement are provided and discussed. It is found that the interface cracks can raise the surface displacement amplitudes to a certain degree.

The stability and possible chaotic vibrations of a fluid-conveying pipe with additional combined constraints are investigated. The pipe, restrained by motion constraints somewhere along the length of the pipe, is modeled by a beam clamped at the left end and supported by a special device (a rotational elastic constraint plus a Q-apparatus) at the right end. The motion constraints are modeled by both cubic and trilinear models. Based on the Differential Quadrature Method (DQM), the nonlinear dynamical equations of motion for the system are formulated, and then solved via a numerical iterative technique. Calculations of bifurcation diagrams, phase portraits, time responses and Poincare maps of the oscillations establish the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations. It is found that the effect of spring constant of the rotational elastic constraint on the dynamics is significant. Moreover, the critical fluid velocity at the Hopf bifurcation point for the cubic model is higher than that for the trilinear model.

This paper studies the characteristics of a proposed reliability-dependent hazard rate function for composites under fatigue loading. The hazard rate function, in terms of reliability R, is in the form of e+c (1-R)p called (ecp) model, where e denotes the imbedded defects of material strength, c the coefficient of strength degradation, and p the memory characteristics of distributions of both applied stress and fatigue strength during the cumulative damage process. By taking a typical residual strength model in Monte Carlo simulation, this paper presents the time changing of the residual strength distribution and hazard rate of composite under various constant-amplitude cyclic stresses. The values of (e, c, p) are decided by fitting hazard rate function to the data generated in simulation. The results show that, under a suitable suggested value of e, p is a constant depending on the characteristics of stress distribution as well as the residual strength model used in Monte Carlo stimulation, and c is correlated to the maximum cyclic stress in a power-law relationship. Only by knowing the initial strength distribution and the maximum cyclic stress, the fatigue life can be easily estimated by integrating the reliability with time or its equivalent, i.e., the reciprocal of hazard rate function with reliability. Finally, by a proposed approximated equation of fatigue life, the (ecp) model is checked to be highly consistent with S-N curve in both the physical means and the equation form. The analysis presented here may be helpful in designing and maintenance planning of composite under fatigue loading.

An evolution equation for the Cauchy stress tensor is proposed, taking into account the elastic, viscous and plastic characteristics of complex fluids. Hypoplasticity, in particular, is incorporated to model the plastic features. The model is applied to investigate time-dependent Poiseuille flows between two parallel plates to simulate non-Newtonian behavior of complex rheological fluids. Results show that while different degrees of elastic and viscous features can be indexed by varying the values of the model parameters, hypoplasticity is capable of simulating the plastic characteristics. The fluid tends to be divided into different parallel layers as hypoplastic effects enhance gradually. Applications of the model may be found in geomorphic fluid motions involved granular materials.

In this study, a small two-medium duct with blast-wave propagation is numerically investigated by a high-resolution Euler/Navier-Stokes solver. The solver has a feature of treatment of the Tait equations of state for two media. One of the two media is water which is envisaged as a blood. The second medium is another liquid, used to simulate body's clot or tissue. The duct wall has a mass diffusion effect in addition to viscous effects. Since two different media are considered, the reflection and transmission of an underwater blast wave passing through the interfaces of the two media with different sound impedances are inevitable. The different properties of liquids may cause numerical oscillation at interfaces for very weak blast waves for a high-resolution scheme such as a 5th-order WENO scheme. In order to overcome this difficulty of numerical fictitious oscillation, a third-order WENO scheme was used. It was found that computed pressures of the transmitted blast wave for four kinds of simulated tissues are in good agreements with those obtained by the acoustic principle. Moreover, for the case of a simulated clot, the pressure force and impulse acted on the clot surface are investigated for different intensities of blast waves.

The stress state of a magnetized elastic half-plane with a uniformly pressurized crack parallel to the free surface subjected to a uniform magnetic induction Bo is considered. The linear theory for a soft ferromagnetic elastic solid with muti-domain structure, which has been developed by Pao and Yeh [1] is adopted to investigate this problem. A numerical method is developed to determine the magnetoelastic stress intensity factor. The effect of the magnetic field and the boundary conditions on the magnetoelasitc stress intensity factor are shown graphically and numerically.

This work studied the Rayleigh-Bénard convection under the first-order slip boundary conditions in both hydrodynamic and thermal fields. The variation principle was applied to find the critical Rayleigh number of instability. The exteneded relations of the critical Rayleigh number (Rc) and the wavenumber (ac) under partially slip boundary conditions were derived. The numerical results showed that both Rc and ac are decreasing with increasing the Knudsen number. The dependence of Rc on the Knudsen number (K) shows that when K≤10−3, the boundary can be considered as nonslip, while K≥10, it can be considered as free boundaries. The maximum change rate occurs when the Knudsen number is around 0.1, indicating that the system would be affected significantly in that range.