Influences of the Helical Strake Cross-Section Shape on Vortex-Induced Vibrations Suppression for A Long Flexible Cylinder

An experimental study on a bare flexible cylinder as well as cylinders fitted with two types of cross-sectioned helical strakes was carried out in a towing tank. The main purpose of this paper is to investigate the effects of strakes’ cross-section on the vortex-induced vibrations （VIV） suppression of a flexible cylinder. The square-sectioned and round-sectioned helical strakes were selected in the experimental tests. The uniform current was generated by towing the cylinder models along the tank using a towing carriage. The Reynolds number was in the range of 800–16000. The strain responses were measured by the strain gages in cross-flow （CF） and in-line （IL） directions. A modal analysis method was adopted to obtain the displacement responses using the strain signals in different measurement positions. The comparison of the experimental results among the bare cylinder, square-sectioned straked cylinder and round-sectioned straked cylinder was performed. The helical strakes can effectively reduce the strain amplitude, displacement amplitude, response frequencies and dominant modes of a flexible cylinder excited by VIV. And the mean drag coefficients of straked cylinders were approximately consistent with each other. In addition, the square-sectioned and round-sectioned strakes nearly share the similar VIV reduction behaviors. Sometimes, the strakes with round-section represent more excellent effects on the VIV suppression of response frequency than those with square-section.

The Optimal Cross-section Design of the “Trapezoid-V” Shaped Drainage Canal of Viscous Debris Flow

Debris flow drainage canal is one of the most widely used engineering measures to prevent and manage debris flow hazards.The shape and the sizes of the cross-section are important parameters when design debris flow drainage canal.Therefore,how to design the appropriate shape and sizes of the cross-section so that the drainage canal can have the optimal drainage capacity is very important and few researched at home and abroad.This study was conducted to analyze the hydraulic condition of a Trapezoid-V shaped drainage canal and optimize its cross-section.By assuming characteristic sizes of the cross-section,the paper deduced the configuration parameter of the cross-section of a Trapezoid-V shaped debris flow drainage canal.By theory analysis,it indicates that the optimal configuration parameter is only related to the side slope coefficient and the bottom transverse slope coefficient.For this study,the Heishui Gully,a first-order tributary of the lower Jinsha River,was used as an example to design the optimal cross-section of the drainage canal of debris flow.

Fabrication of High-Density Out-of-Plane Microneedle Arrays with Various Heights and Diverse Cross-Sectional Shapes

Out-of-plane microneedle structures are widely used in various applications such as transcutaneous drug delivery and neural signal recording for brain machine interface.This work presents a novel but simple method to fabricate high-density silicon(Si)microneedle arrays with various heights and diverse cross-sectional shapes depending on photomask pattern designs.The proposed fabrication method is composed of a single photolithography and two subsequent deep reactive ion etching(DRIE)steps.First,a photoresist layer was patterned on a Si substrate to define areas to be etched,which will eventually determine the final location and shape of each individual microneedle.Then,the 1st DRIE step created deep trenches with a highly anisotropic etching of the Si substrate.Subsequently,the photoresist was removed for more isotropic etching;the 2nd DRIE isolated and sharpened microneedles from the predefined trench structures.Depending on diverse photomask designs,the 2nd DRIE formed arrays of microneedles that have various height distributions,as well as diverse cross-sectional shapes across the substrate.With these simple steps,high-aspect ratio microneedles were created in the high density of up to 625 microneedles mm^(-2)on a Si wafer.Insertion tests showed a small force as low as~172μN/microneedle is required for microneedle arrays to penetrate the dura mater of a mouse brain.To demonstrate a feasibility of drug delivery application,we also implemented silk microneedle arrays using molding processes.The fabrication method of the present study is expected to be broadly applicable to create microneedle structures for drug delivery,neuroprosthetic devices,and so on.

Optimization of Cross-sectional Shapes of the Bi-2223/Ag Wires before Flat Rolling

Rolling process plays an important role in the manufacture of Bi-based high temperature superconductor tapes, and the plastic flow regularities of the superconducting wires during deformation will directly affect the ultimate quality of the tapes. In order to investigate the effect of cross-sectional shapes before fiat rolling on the performance and homogeneity of the tapes, some numerical models of Bi-2223/Ag wires with different cross-sectional shapes including circular, square, elliptical and racetrack cross-sections are constructed during the rolling process. By comparing the relative density, logarithmic strain ratio and length-width ratio on the filaments, it is revealed that Bi-2223/Ag wire with special-shaped cross-section can achieve better conductivity than the round wire, in particular, the racetrack cross-sectional wire has the second best performance among four wires. Based on material processability and experimental condition, tri-pass racetrack drawing technique is employed to optimize the process and obtain racetrack cross-sectional wire. The rolling process of Bi-2223/Ag wire with racetrack cross-section causes more intensive deformation of filaments in the center of the tape and achieves the filaments with larger length-width ratio. Also, the deformation distribution of filaments verifies the numerical results. Consequently, the racetrack drawing technique can be utilized for a reference during the mechanical processing and to increase the current transmission capacities of Bi-2223/Ag tapes.

Optimal Cross-Sectional Shape of Gas/Air Ducts

In industrial plants, ships, and buildings, a large amount of gas and air ducts are applied for equipment connection, HVAC, medium transport, and exhaust, etc. These ducts can be designed in varied cross-sectional shapes, such as round or rectangle. The author reveals through geometric calculation of the duct cross-sectional shapes and engineering experiences that the round cross-section is an optimal shape in the duct system. The round duct has the shorter perimeter than the other cross-sectional shape ducts and the stronger structure in the same working condition. The material saving of the round duct due to the shorter perimeter is quantitatively determined. In the pater, it is shown that the round duct is economically attractive. The economic analysis for the material cost saving is illustrated by an example. For a long duct system, the material and material cost savings are significant. It is suggested that the round duct in the gas and air duct system should have priority as long as the field conditions are allowed. In the paper, the material cost saving is also converted to PW, AW, and FW used for LCC economic analysis.

The recirculation flow after different cross-section shaped high-rise buildings with applications to ventilation assessment and drag parameterization

The building cross-section shape significantly affects the flow characteristics around buildings,especially the recirculation region behind the high-rise building.Eight generic building shapes including square,triangle,octagon,T-shaped,cross-shaped,#-shaped,H-shaped and L-shaped are examined to elucidate their effects on the flow patterns,recirculation length L and areas A using computational fluid dynamics(CFD)simulations with Reynolds-averaged Navier-Stokes(RANS)approach.The sizes and positions of the vortexes behind the buildings are found to be substantially affected by the building shapes and subsequently changing the recirculation flows.The recirculation length L is in the range of 1.6b-2.6b with an average of 2b.The maximum L is found for L-shaped building(2.6b)while the shortest behind octagon building(1.6b).The vertical recirculation area Av is in the range of 1.5b^(2)-3.2b^(2)and horizontal area Ah in 0.9b^(2)-2.2b^(2).The L,Av and Ah generally increase with increasing approaching frontal area when the wind direction changes but subject to the dent structures of the#-shaped and cross-shaped buildings.The area-averaged wind velocity ratio(AVR),which is proposed to assess the ventilation performance,is in the range of 0.05 and 0.14,which is around a three-fold difference among the different building shapes.The drag coefficient parameterized by Ah varies significantly,suggesting that previous models without accounting for building shape effect could result in large uncertainty in the drag predictions.These findings provide important reference for improving pedestrian wind environment and shed some light on refining the urban canopy parameterization by considering the building shape effect.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part I:Theory and Integral Formulae

The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components（velocity potential and streamfunction） can be constructed by applying Green＇s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential（or streamfunction） component to zero,the other component of the externally induced solution can be expressed by the imaginary（or real） part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction（or velocity potential） for the externally induced solution can also be expressed by the boundary integral of a double-layer（or singlelayer） density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part II:Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.

Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP

Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered;2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45- and the axial length of mushroom is considered.

SCATTERING OF PLANE SH-WAVE BY A CYLINDRICAL HILL OF ARBITRARY SHAPE

The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Furthermore appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method (FEM).

Anti-plane deformations around arbitrary-shaped canyons on a wedge-shape half-space:moment method solutions

The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.

Ultimate Load Capacity of Offshore Pipeline with Arbitrary Shape Corrosion Defects

A set of generalized solutions are proposed for estimating ultimate load capacity of pipeline with arbitrary corrosion shapes subjected to combined internal pressure, axial force and bending moment. Isotropic and anisotropic material characteristics in longitudinal and circumferential direction of pipeline are also considered in the proposed equations. Simplified numerical method is used to solve the generalized expressions. The comparisons of numerical results based generalized solutions and full-scale experimental results are carried out. The predicted results agree reasonably well with the experiment results. Meanwhile, the effects of corrosion shapes and locations on the ultimate load capacity are studied.

Scattering and diffraction of plane P-waves in a 2-D elastic half-space Ⅱ：shallow arbitrary shaped canyon

Scattering and Diffraction of elastic in-plane P-and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH waves on the same elastic canyon that is semi-circular in shape on the half-space surface is the first such problem that was solved by analytic closed form solutions over forty years ago by Trifunac. The corresponding case of in-plane P-and SV-waves on the same circular canyon is a much more complicated problem because, the in-plane P-and SV-scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattered and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape.

Weighted residual method for diffraction of plane P-waves in a 2-D elastic half-spaceⅢ:on an almost circular arbitrary-shaped alluvial valley

Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong motion seismologists for over forty years. The case of out-of- plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV- waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by Lee and Liu. This paper uses their technique of defining these stress-free scattered waves, which Brandow and Lee previously used to solve the problem of the scattering and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape, to the study of the scattering and diffraction of these in-plane waves on an almost circular arbitrary-shaped alluvial valley.

On-chip optical pulse shaper for arbitrary waveform generation

We propose and demonstrate a silicon-on-insulator （SOI） on-chip optical pulse shaper based on four-tap finite impulse response. Due to different width designs in phase region of each tap, the phase differences for all taps are controlled by an external thermal source, resulting in an optical pulse shaper. We further demonstrate optical arbitrary waveform generation based on the optical pulse shaper assisted by an optical frequency comb injection. Four different optical waveforms are generated when setting the central wavelengths at 1533.78 nm and 1547.1 nm and setting the thermal source temperatures at 23 ℃ and 33 ℃, respectively. Our scheme has distinct advantages of compactness, capability for integrating with electronics since the integrated silicon waveguide is employed.

Optical pulse shaper with integrated slab waveguide for arbitrary waveform generation using optical gradient force

Integrated optical pulse shaper opens up possibilities for realizing the ultra high-speed and ultra wide-band linear signal processing with compact size and low power consumption. We propose a silicon monolithic integrated optical pulse shaper using optical gradient force, which is based on the eight-path finite impulse response. A cantilever structure is fabricated in one arm of the Mach–Zehnder interferometer（MZI） to act as an amplitude modulator. The phase shift feature of waveguide is analyzed with the optical pump power, and five typical waveforms are demonstrated with the manipulation of optical force. Unlike other pulse shaper schemes based on thermo–optic effect or electro–optic effect, our scheme is based on a new degree of freedom manipulation, i.e., optical force, so no microelectrodes are required on the silicon chip,which can reduce the complexity of fabrication. Besides, the chip structure is suitable for commercial silicon on an insulator（SOI） wafer, which has a top silicon layer of about 220 nm in thickness.

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux.A conformal mapping function for the coating and matrix is introduced,which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane.Using analytic continuation,we derive a general solution in terms of two auxiliary functions.The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface.Once the two auxiliary functions have been obtained in the elementary-form,the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined.The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition.Finally,the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.

NUMERICAL ANALYSIS OF NONLINEAR WAVE FORCE ON LARGE BODY WITH ARBITRARY SHAPE

In this paper a nonlinear diffraction theory due to Stoke's 2nd-order wave for computing the wave force on the large body is presented. The radiation condition as r-∞ for 2nd-order scattered potential has been studied in connection with asymptotic solutions. A numerical procedure has been developed for the purpose of calculating the nonlinear wave force on the large body with arbitrary shape.

Dynamic Analysis of Nanosized Arbitrary Shape Inclusion under SH Waves

The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress and displacement are given by classical elastic theory. Secondly, the arbitrary shape inclusion in the two-dimensional plane is transformed into a unit circle domain by conformal mapping, the incident wave field and the scattered wave field are presented. Next, the stress and displacement boundary conditions are established by considering surface elasticity theory, The infinite algebraic equations for solving the unknown coefficients of the scattered and standing waves are obtained. Finally, the influence of surface effect, non-dimensional wave number, Shear modulus and hole curvature on the dynamic stress concentration factor are analyzed by some examples, the numerical results show that the surface effect weakens the dynamic stress concentration. With the increase of wave number, the dynamic stress concentration factor (DSCF) decreases. Shear modulus and hole curvature have significant effects on DSCF.

Voltage Generation by Rotating an Arbitrary-Shaped Metal Loop around Arbitrary Axis in the Presence of an Axial Current Distribution

A thin metallic wire loop of arbitrary curvature is rotated with respect to an arbitrary axis of its plane. The device is excited by an electric dipole of infinite length and constant current. The resistance of the loop is computed rigorously as function of the position of the source. In this way, the induced voltage along the wire, under any kind of axial excitation, is given in the form of a superposition integral. The measured response is represented for various shapes of the coil, with respect to the time, the rotation angle and the position of the source. These diagrams lead to several technically applicable conclusions which are presented, discussed and justified.