The shapes of a growing or decaying bubble entrapped by a solidification front are predicted in this work. The bubble results from supersaturation of a dissolved gas in the liquid ahead of the solidification front. Pore formation and its shape in solid are one of the most critical factors affecting properties, microstructure, and stresses in materials. In this study, the bubble and pore shapes entrapped in solid can be described by a three-dimensional phase diagram, obtained from perturbation solutions of Young-Laplace equation governing the tiny bubble shape in the literature. The predicted growth and entrapment of a microbubble as a pore in solid are found to agree with experimental data. This work thus provides a realistic prediction of the general growth of the pore shape as a function of different working parameters.

Using a piezoelectric unimorph vibrator with constraint-tuning modified-mode (CTMM) mechanism, a novel design of a thin-disc ultrasonic actuator was developed to drive an optical sled. The theoretical estimation of in-plane wave propagation on a thin disc is introduced to explain the novel actuating mechanism, via a modal expansion technique and modal participation factors. Furthermore, the approximate wave propagations could be illustrated by the practical estimated wave equations in this study. Applying four screws at the exact distribution of angles on the thin-disc vibrator, the actuating mechanism of ultrasonic modified modes is generated and propagated. The in-plane vibration modes could be tuned by these desired screw constraints on the piezoelectric vibrator. The ultrasonic actuator offers the output force to drive an optical sled by friction contact in bilateral motions. To implement the equilibrium structure force in bilateral directions, natural and forced analysis as well as impedance comparison of FEM software ANSYS are also introduced into the constrained design. Hence, there are two various modified modes chosen at the different resonant frequencies within the electromechanical coupling of piezoelectric material to pursue more efficiency in energy conversion. Experimental results have demonstrated consistency with the approximate theoretical approach of the in-plane wave propagation and simulations based on the concept of constrained-tuning modified modes.

This paper proposes a complete basis set for analyzing elastic wave scattering in half-space. The half-space is an isotropic, linear, and homogeneous medium except for a finite inhomogeneity. The wave bases are obtained by combining buried source functions and their reflected counter-waves generated from the infinite-plane boundary. The source functions are the vector wave functions of infinite-space. Based on the source functions expressed in the Fourier expansion form, the reflected counter-waves are easily obtained by solving the infinite-plane boundary conditions. Few representations adopt Wely's integration, but the Fourier expansion is developed from it and applied to decouple the angular-differential terms of the vector wave functions. In addition to the scattering of the finite inhomogeneity, the transition matrix method is extended to express the surface boundary conditions. For the numerical application in this paper, the P- and the SV- waves are assumed as the incoming fields. As an example, this paper computes stress concentrations around a cavity. The steepest-descent path method yielding the optimum integral paths is used to ensure the numerical convergence of the wave bases in the Fourier expansion. The resultant patterns from these approaches are compared with those obtained from numerical simulations.

A series solution based on the mild-slope equation is produced in this study of wave scattering produced by a circular cylindrical island mounted on an axi-symmetrical shoal. The solution is presumed to be a Fourier cosine expansion with variable coefficients in the radial direction on account of the symmetric scattering field, which translates the original 2-D boundary-value problem to a 1-D one in which an ordinary differential equation is in effect treated. Approximations to the coefficients of the governing equation with the Taylor expansions enable the use of the Frobenius method, and consequently the solution is obtained in a combined Fourier and power series. For verification, the present method is mainly compared with Zhu and Zhang's [1] analytical solution of the linearised shallow water equation for a conical shoal, and with a different analytical solution of the mild-slope equation developed by Liu et al. [2] for a paraboloidal shoal. Fine agreements are achieved. The present method is then used to investigate the variation pattern of the wave run-up when the shoal profile varies from conical to paraboloidal, and some interesting phenomena are observed.

In this study, a spray cooling device for electronic components was investigated. Dielectric fuid (FC-72) was sprayed at 50°C through five nozzles (4.243mm spacing). The nozzles are of diameters 0.17, 0.23 or 0.41mm. Volume flow rate varied from 24.5 to 99.1ml/min. Two grooved surfaces and a smooth surface were tested, and the heated area was 12 × 12mm2. The larger nozzles yielded greater heat transfer coefficients at high heat fluxes (300 ∼ 600kW/m2). However, smaller nozzles result in greater dry-out heat fluxes and greater heat transfer coefficients at heat flux < 300kW/m2. The C4 surface, having parallel grooves of 0.4mm depth, improved the spray cooling performance by up to 80% as compared with the smooth suface. Its thermal resistance is 0.11 ∼ 0.12K/W at 99.1ml/min flow rate, in the range of 85 ∼ 130W heat input. A new correlation of spray cooling, accounting for the contributions of nucleate boiling and spray convection, is proposed. For data of FC-72 in the range of Re = 856 ∼ 6188, Bo = 0.19 ∼ 5.70, We = 25.2 ∼ 3541.3, the predicted h-values agree with experimental data of the smooth surface within ±25%.

A hybrid differential transformation / finite difference scheme is used to analyze the complex nonlinear behavior of an electrostatically-actuated micro cantilever beam which high aspect ratios (length/width). The validity of the proposed method is confirmed by comparing the numerical results obtained for the tip displacement and pull-in voltage of the cantilever beam with the analytical and experimental results presented in the literature. The hybrid scheme is then applied to analyze both the steady-state and the dynamic deflection behavior of the cantilever beam as a function of the applied voltage. Overall, the results confirm that the hybrid method provides an accurate and computationally-efficient means of analyzing the complex nonlinear behavior of both the current micro cantilever beam system and other micro-scale electrostatically-actuated structures.

An analytical study on entropy generation considering viscous dissipation effect in the circular microchannel is reported. The fluid flow is steady, laminar, hydrodynamically fully developed and thermally developing. In the first law analysis, appropriate dimensionless variables are applied to solve the energy equation in the thermal entrance region of microchannel. Subsequently the obtained temperature field is used to derive an expression for entropy generation rate. The effect of Knudsen number and Brinkman number on the entropy generation rate and Bejan number in different axial location is presented.

To realize the relationship between flow structures of wingtip vortices and post stall characteristics of low aspect-ratio wings, this paper experimentally studies the aerodynamic characteristics and the corresponding flow structures of the rectangular thin-plate wings at Reynolds numbers between 104 and 105. The aerodynamic properties to be studied include lift, drag, slopes at linear and nonlinear range of the lift curves and lift-to-drag ratios of the tested wings with the aspect ratio varying from 1.0 to 3.0. The flow structures regarding the leading-edge separation vortices and wingtip vortices at upper surface and near-wake regions of the wings are also investigated by smoke-wire visualization. Results indicate that the high stall angle of attack and vortex lift are clearly manifested to induce the nonlinear increase in the lift curves as the aspect ratio reaches less than 1.6. This phenomenon is specifically observed to augment the aerodynamic properties with the decrease of the aspect ratio. Additionally, the corresponding flow visualization also indicates that the wingtip vortices and the areas of highly affected regions are duly increased with the increase of the angle of attack up to 40°, which makes certain that the extra increase of the nonlinear lift results from these vortices. This result can be practically applied to the planform design for unmanned aerial vehicles.

The present study utilized audio recordings of snoring during natural sleep to analyze characteristics related to the snoring duration at the soft palate, epiglottis, and tongue base. 10 subjects were recruited for the study, with an average age of 23.7 years. These audio files were then used to analyze the characteristics of snoring duration at the soft palate, epiglottis, and tongue base responsible for sound generation. Findings indicated that snoring duration was 3.7 seconds at the soft palate, 2.2 seconds at the epiglottis and 1.29 seconds at the tongue. Since the soft palate is the softest structure of the three, snoring sound by vibration was most easily induced at this structure, leading to the longest snoring duration. This was followed by the epiglottis and the tongue base respectively. Of the 10 subjects, 6 had BMI in the overweight range, and snoring durations for these individuals were seen to be lengthened by 0.13 seconds, with the tongue base snoring duration lengthened by 0.11 seconds but unchanged for the epiglottis. Prior studies from this laboratory have established a non-invasive system for measuring snoring. This can be used to analyze the sound frequency, amplitude and duration of snoring. Snoring duration was found to be the longest at the soft palate, followed by the epiglottis and tongue base in the present investigation. Clinically, this finding has implications in snoring assessments prior to uvula-palato-pharyngoplasty procedures. Snoring duration may also be used as a parameter in post-operative monitoring.

Using conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yang et al.'s simplified geometric stiffness matrix [kg]12×12 of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14 of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14 matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14 matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

This work integrates the Taylor theorem and the method of fundamental solutions to develop a numerical tool for estimating the added mass coefficient tensor for a solid object of any convex shape moving in potential flow. In potential flow theory, the Taylor theorem calculates the added mass coefficient tensor for a Rankine body with algebraic manipulations of the properties of the internal singularities employed to generate the corresponding flow. To apply this theorem for objects in other shapes, the singularity strength and locations are required information which is facilitated numerically in this work by the method of fundamental solutions (MFS). The developed scheme is tested on a circle, an ellipse, a square, and a rhombus and the numerical results are in good agreement with the corresponding analytical values. A final example of a Cassini oval is also considered to show the potential applications on bio-engineering problems.

The present study is concerned with a theoretical analysis of the photophoresis of a microsized long cylinder in a perpendicular optical field. Different from previous studies of photophoresis, thermal stress slip usually neglected is taken into account in the analysis. The gaseous fluid relative to the microparticle in photophoretic motion falls into slip-flow regime. Asymmetric distribution of the absorbed heat energy within the particle becomes the driving force for photophoretic motion of the cylinder-shaped particle. By evaluating heat source function distributions at various conditions, the study focuses on the effects of particle size and optical properties on the energy distribution and the resultant influences on the photophoresis. The photophoretic mobility is developed by the slip flow model with consideration of thermal stress slip. The results reveal that the photophoretic mobility decreases with the increase of particle thermal conductivity (k*) and increases with Knudsen number (Kn). The thermal stress slip effect on photophoretic velocity is more noticeable at high Kn, but disappears at the continuum limit. A long cylinder-shaped particle has higher photophoretic velocity than a spherical particle at low k*, while the situation reverses at high k*. With thermal stress slip considered, the critical condition for crossing of the photophoretic velocity curves of cylindrical and spherical particles is mildly influenced by Kn.

The reliability of the impeller-spindle with respect to the effects of abnormal vibrations and noises is relative to the whirl rotation in notebook (NB) computers, all-in-one (AIO) desktop systems, and tablet PCs. This study experimentally investigates the stability of a herringbone-microgrooved journal bearing in an impeller-spindle under static radial forces.The experimental device operated at 2700, 3600, 4200, and 4900rpm, with a static load ranging from 0.4, 0.8, and 1.6N. The experiment obtained the stiffness and damping coefficients, and the study involved analyzing the stability. Results show that the dimensionless threshold speed of rotation decreased as the Sommerfeld number increased. The proposed impeller-spindle is stable when the Sommerfeld number is less than 59, indicating that the impeller-spindle should not operate at an eccentricity ratio below 0.18.

This paper deals with the optimal design for a twin die stacked package. Firstly, the numerical model is built up in terms of a three-dimensional slice model along the diagonal direction of the package. The material behavior of the solder balls is a consequence of the viscoplastic property which can be described by the Anand's model. Secondly, the Darveaux model is applied to predict the solder ball reliability of the stacked die package under a cyclic temperature loading. Since simulation analysis found an obvious relation is found between the fatigue life of the solder ball and the distribution of the accumulated strain energy density (SED) on the critical solder ball of the package through the simulation analysis, the average value of the strain energy density for all solder balls is adopted as the optimization indicator of reliability. With such a viewpoint, the critical solder ball position can be ignored, and accordingly an efficient analysis can be obtained. Finally, the Box-Behnken regression model is adopted to construct all the experiments. Each experiment analyzes the reliability of the package under varying parameters. Subsequently, the pattern search algorithm is applied to search for optimal factors.

Through optimal analysis with the fatigue reliability indicator of an average SED, the fatigue life is found to be 59% lower than that of the original design. The fatigue life had clearly improved and the lowest ball fatigue life is found to be 2.859 times longer than the original one.

Complex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

The purpose of this study is to examine the acoustic performance of parallel simple expansion mufflers by a new approach for an acceleration of computational time required. The fast multipole method separated the field points and source points into two terms by means of addition theorem. When the boundary is divided into uniform meshes, the integration of source element can be calculated fast. Therefore, the fast multipole method, when compared with the boundary element method, reduces CPU time from an order of N2 to NlogγN, where N is the number of unknowns and γ is a constant. The numerical results have been compared with experiments and analytical approaches based on pressure and velocity continuity, as well as the modal meshing approach; the results clearly show that the agreements are good.

The Kastner formula for cavity contraction is one of the commonly used formulae for the cavity contraction problem in tunnel excavation, and it is based on the assumption of small displacement around the cavity with no volume change in the plastic zone. In this paper, the errors arising from these assumptions are discussed, and the volume change of the plastic zone is considered. It can be seen that this assumption is reasonable for normal situations, but for rock with weak shear strength, the Kastner formula should be used with care, especially in situations where there will be relatively large volume changes in the plastic zone.

Convective flow and heat transfer in an inclined channel bounded by two rigid plates is studied, where the lower plate is fixed and upper plate is moving with a constant velocity. One of the regions filled with clear viscous fluid and the other region filled with the porous matrix saturated with a viscous fluid different from the fluid in the first region are considered. The coupled nonlinear equations are mainly solved numerically using finite difference method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Both the velocity and temperature profiles enhance as the values of buoyancy parameter GP, height ratio h, Brinkman number Br, density ratio n and thermal expansion ratio b increase but reduce as the values of porous parameter σ, viscosity ratio λand thermal conductivity ratio λT increase. The Nusselt numbers at upper plate diminish as GP, h and Br increase, whereas they increase as σ, λ and λT increase. The lower plate Nusselt numbers are reversely affected by the relevant parameters. The effect of σ and GP on shear stress profiles are drawn and discussed.

In this paper, the deflection, natural frequency and damping quality factor of a viscoelastic microplate under an electrostatic actuation are investigated. The microplate is assumed as a CNT-reinforced nanocomposite microplate, and an electrostatic actuation is applied on it. The nonlinear equations of motion are derived using the Von-Karman plate theory, and the Kelvin-Voigt viscoelastic model. In order to obtain the material properties of the nanocomposite microplate, the Eshelby–Mori–Tanaka method is implemented. The static pull-in instability of the microplate is obtained. It is shown that the nanocomposite microplate can both increase the deflection and natural frequency of the micro devices. So, one may have a nanocomposite microplate with the same deflection of the SiO2 microplate, while its frequency would be 1.45 times of the SiO2 microplate. This characteristic is highly desirable in microswitches. Also, it is shown that the damping quality factor of the nanocomposite microplate is much greater than SiO2 microplate. This fact limits the implementation of a nanocomposite microplate as a vibrating element of the micro devises. So, there are great beneficial static and frequency response characteristics for nanocomposite microplates. But, it is not recommended for microresonators due to high damping characteristics.

This paper presents the flow structure under a partially inundated bridge deck measured by using particle image velocimetry (PIV) and flow visualization techniques. The approaching flow was subcritical having Froude number F in the range 0.12 ∼ 0.55. The proximity ratio Pr (= ratio of clearance below the bridge deck h to the total depth of deck D) was varied from 0.57 to 2. Depending upon the Froude number F and proximity ratio Pr, four types of flow structures under the bridge deck were recognized. In flow Type I, the water surface elevation on the downstream side of bridge deck is slightly lower than the counterpart on the upstream side, and the shear layer formed at the bottom of upstream girder continuously fluctuates and touches soffit of all girders. In the case of flow Type II, the water surface on downstream side of bridge deck is lower than that on the upstream side and the shear layer originating from the upstream girder impinges near the third cavity between girders. However, in both the cases, the cavities between the girders are completely occupied by vortices. On the contrary, in the cases of flow Type III and flow Type IV, the flow is separated from the upstream girder edge. However, in flow Type III, the separated flow impinges on successive girders and cavities are partially filled by water; while in flow Type IV, the flow is totally separated from the deck bottom like orifice flow. The phenomena of vortex formation within the cavities are discussed for the cases of flow Type I and flow Type II. Also, for the vertical distribution of mean streamwise velocity in the shear layer below bridge deck, the nonlinear regression equations are developed. Using the distributions of measured mean streamwise velocity within the shear layer below the bridge deck at different streamwise distances, the similarity profile is obtained. The mean velocity deficit (usl – usu) and representative thickness bs are considered as the appropriate characteristic velocity and length scales for developing similarity profile. The proposed characteristic scales provided unique similarity profiles having promising regression coefficient. The similarity profile proposed is suitable for more general case of bridge deck having different bridge girders and even for rectangular block without girder. Further, the turbulence characteristics for the flow below the bridge deck are also presented.