Triangular Bars Research Articles

Flexible, lightweight, tunable robotic arms enabled by X-tensegrity inspired structures

Robotic arms have remarkable applications in diverse fields such as medical rehabilitation, disaster relief, and space exploration. Enhancing their rigidity, load-bearing capacity, and motion simplicity is key to broadening their usage. Utilizing the admirable flexibility and strength of tensegrity structures, made of rigid bars and elastic strings, we introduce a new type of flexible robotic arm. This arm is constructed using a sequence of two-dimensional X-tensegrity inspired modules. Each module comprises two sets of triangular bars linked by three strings, enhancing the arm’s ability to deform and resist impact forces. The joints between modules are stiff, allowing for angular adjustments to create three-dimensional configurations with adjustable stiffness and curvature. Through theoretical analysis, simulations, and experiments, we have shown that this tensegrity-based robotic arm exhibits superior stability, flexibility, and scalability.

Quantitative Expression of the Modified Bragg's Law for Bragg resonances of water waves excited by five types of artificial bars

For Class I Bragg resonance excited by five types of finite periodic array of widely spaced bars (rectangular, parabolic, rectified cosinoidal, trapezoidal, and triangular bars), the average phase velocity between any two adjacent bars in each type of bar field has been specifically calculated by employing a mathematical transformation, and therefore, the excitation condition of Class I Bragg resonance excited by each bar field is clarified and the modified Bragg's law established by Xie and Liu becomes a quantitative form. On one hand, if the incident surface wavelength, L, is fixed in advance, then according to the excitation condition, we can directly obtain the critical bar spacing, d, at which Class I Bragg resonance occurs. On the other hand, if the bar spacing, d, is fixed, then according to the excitation condition, we can use an iteration scheme to find out the critical surface wavelength, L, at which Class I Bragg resonance will be excited. In comparison with existing experimental, numerical, and analytical results of Bragg resonance excited by the five types of bar fields, it is shown that the modified Bragg's law is much more accurate than the Bragg's law, and the phenomenon of phase downshift can be well explained. In the linear long-wave limit, owing to the simple dispersion relation, the modified Bragg's law becomes an explicit expression and coincides with Liu's approximate law very well, although the former is a straight line segment while the latter is a curved line segment. Finally, it is shown that the phase downshift of Bragg resonance becomes more significant as the cross-sectional area of bars increases.

An approximate law of Class I Bragg resonance of linear shallow-water waves excited by five types of artificial bars

Based on the band theory of Bloch waves, an approximate law is established for locating the phase of Class I Bragg resonance when linear shallow-water waves are reflected by a finite periodic array of widely spaced artificial bars, including rectangular, parabolic, rectified cosinoidal, isosceles trapezoidal, and isosceles triangular bars. The approximate law is described by a function of several parameters such as the bar shape, dimensionless bar height with respect to the global water depth, and dimensionless bar width with respect to the incident wavelength. It is found that Bragg’s law that accurately describes Bragg resonances in X-ray crystallography cannot be simply applied to Bragg resonances of linear shallow-water waves excited by any finite periodic array of widely spaced bars, because the height and width of any bar is nonzero. Based on the approximate law, the phenomenon of phase downshifting can be well explained and accurately predicted. It is revealed that the phase downshifting becomes more significant with increasing the cross-sectional area of artificial bars.

Near-Net Forging of Titanium and Titanium Alloys by the Plasma Carburized SKD11 Dies

The carbon supersaturated SKD11 punch and core-die were prepared by the plasma carburizing at 673 K for 14.4 ks. The upsetting experiment was performed by using this punch to describe the plastic flow of pure titanium and β-titanium works in higher reduction of thickness than 50%. The measured load – stroke relationship was utilized to describe the frictional behavior on the contact interface of punch to work materials and their work hardening process. The contact interface of carbon supersaturated punch to work was analyzed to investigate the formation of isolated carbon tribofilms from punch material and to describe the in situ solid lubrication on the contact interface. The micro-hardness mapping technique was also utilized to investigate how to suppress the work-hardening behavior by this in-situ solid lubrication. Free near-net forging experiments were performed to shape the circular β-titanium alloy wires to triangular bars.

Additive Manufacturing of Interdigital Filters With Arbitrary Line Cross Section

This article investigates the novel use of additive manufacturing (AM) in the production of interdigital cavity filters. It is found that AM enables the production of interdigitated pins of complex cross-sectional geometry, leading to the development of a suitable synthesis method using a commonly available 2-D eigenmode port impedance solver. The method is validated by manufacturing an L-band interdigital filter of 70% fractional bandwidth with triangular bars through selective laser melting, as well as a classical design using rectangular bars. It is found that triangular bars obtain similar coupling to rectangular bars over the average of 35% wider spacing gaps, reducing its sensitivity to manufacturing error. In addition, neither filter requires postproduction tuning, although the bars do warp slightly during printing. These results illustrate the advantages of using AM for the synthesis of wideband interdigital filters.

Identifying the dominant physical processes for mixing in full-scale raceway tanks

Abstract Open racetrack flumes represent the most common reactor for algae cultivation in the biodiesel industry, however, despite numerous experimental and numerical studies into reactor modifications, conditions remain suboptimal for algal growth. In response, a full-scale racetrack flume was constructed at the Ecohydraulics and Ecomorphodynamics Laboratory at the University of Illinois. Experiments on the racetrack flume were conducted for various depth and velocity conditions, using acoustic doppler velocimetry and surface particle velocimetry to characterize mean and turbulent velocity statistics, and dissolved oxygen measurements to investigate the effect of turbulent structures on gas transfer at the water-air interface. Longitudinal bed modifications were introduced to induce secondary flows in the straight portions of the flume. Semicircular and triangular bars of two different sizes were tested in an effort to increase the transfer velocity at the free surface. A range of flow structures were observed including secondary currents of Prandtl's first and second kinds, vortex shedding off of bend vanes, and periodic oscillations in surface lateral currents. Findings indicate that bend dynamics introduce the strongest and most resilient flow structures, and any attempt to induce vertical mixing or accelerate transfer velocities at the free surface will need to utilize or overwhelm these existing structures.

Moisture Sorption and Desorption in Epoxy Composites Reinforced with Triangular and V-Shaped Bars: Determination of Diffusion Coefficient and Effect of Varied Factors

Sorption and desorption of moisture in epoxy composites reinforced with triangular and V-shaped bar fillers were studied. Epoxy was reinforced with vinyl ester bar assemblies fabricated according to 4 varied factors: bar orientation relative to diffusion direction (pointed or base side), bar alignment (parallel or staggered), spacing between bars (1 or 5 mm), and bar cross-sectional shape (triangular or V-shaped). Unlike previous studies, the bar fillers were initially coated with small amount of epoxy resin to improve wetting during fabrication of composites. Moisture uptake and loss of composites during one-side exposure to water vapor (50% relative humidity at 60°C) and hot air (60°C), respectively, were monitored with time. Experimental results show weight change of composites during moisture sorption and desorption varies linearly with square root of exposure time. Diffusion coefficients of composites were determined by assuming the material to be semi-infinite and fitting a mathematical solution to Fick’s second law of diffusion to weight change data. Results show diffusion coefficient of composites during moisture sorption is increased when bars are oriented pointed relative to diffusion direction, aligned parallel, spaced at 1 mm, and has triangular cross-sectional shape. However, during desorption, the diffusion coefficient is increased when base side of bars are exposed and when the bars are aligned staggered. The observed effects of factors on moisture diffusion coefficients of epoxy composites during sorption and desorption are discussed in relation to path length, available diffusion area, and status of epoxy/vinyl ester interphase before and after moisture sorption in composites.

Desorption Behavior of Epoxy/Amine-Coated Polyester Triangular Bar Composites Pre-Exposed to Acid Environment

Epoxy/amine-coated polyester triangular bar composites were fabricated and exposed to 5 wt% hydrochloric acid (HCl) solution at 40 °C. The weight loss characteristics of pre-exposed composites in heated air at 40 °C under forced convection were studied as function of size, spacing, alignment, and orientation of triangular bars. The diffusion coefficient of composites during desorption increases when the bars are oriented flat and are aligned in parallel. The same result is observed when the size of triangular bars is increased, and when spacing between bars is decreased. These results are attributed to the presence of epoxy/polyester interphase regions, which are more accessible when the triangular bars are oriented flat and aligned parallel, have larger size, and have smaller spacing. These interphase regions are preferred conduits of water during desorption of composites. The diffusion coefficients of composites being higher than the values of epoxy and polyester resins further confirm the effect of interphase regions. Among the factors, orientation of triangular bars has the highest influence on the desorption behavior of epoxy composites.

Band gaps for Bloch waves over an infinite array of trapezoidal bars and triangular bars in shallow water

The problem of shallow-water wave propagation over an infinite array of periodic trapezoidal bars and triangular bars is studied. By employing the linear shallow-water wave theory and the well-known Bloch theorem, the eigenvalue problem in terms of the wave number for given wave frequency, water depth, and geometric properties of the bars is formed. A closed-form solution of the eigenvalue problem is derived which breaks the restriction of piecewise constant water depth required in almost all of the previous analytic solutions. The solution is verified against the existing solution for the special case of rectangular bars. Based on the present solution, gap maps in various cases are plotted which exactly show the distribution of band gaps for wave propagation over both trapezoidal bars and triangular bars, and the influence of the given wave frequency and the geometric parameters of bars such as height and width on the occurrence of band gaps is analyzed. By using the gap maps presented in the paper, the condition under which the waves can be completely blocked by an infinite array of trapezoidal bars and triangular bars can be easily and exactly determined.

Deformation in and Efficiency of Rolling in Two- and Multi-Roll Passes

For experimental evaluation of the efficiency of two-, three-, and four-directional rolling, round, square, and triangular bars made of AK6 aluminum alloy were used. It is established that the most efficient process is the four-directional rolling of square bars, which allow obtaining higher reduction without lateral flow of metal and with minimum roll force and minimum energy consumption.

Sorption and Degradation Behaviour of Epoxy Composites Reinforced with Amine-Coated Polyester Triangular Bars in Acid Environment

Sorption and degradation characteristics of epoxy composites reinforced with amine-coated polyester triangular bars in acid environment were studied. The following aspects of amine-coated triangular bars were varied during preparation of epoxy composites: orientation (flat or pointed), alignment (parallel or staggered), spacing (1 or 5 mm), and size (5 or 7 mm). Composites were tested using a one-side acid exposure test in 5 wt% hydrochloric (HCl) acid solution at 40°C for 308 h. Weight change curves of composites with pointed orientation show continuous sorption of acid solution with square root of time, while composites with flat orientation display an initial increase in weight followed by continuous weight loss. This can be attributed to the large interfacial area of triangular bars exposed to diffusing acid in flat orientation. Since the bars are amine-coated, the acid preferentially diffuses in the interfacial region, resulting to early degradation of composite. The following parameters were measured from the weight curves for data analysis: initial sorption rate (% - h-0.5), maximum weight change during sorption (%), and weight loss due to degradation (%). Analysis of variance (ANOVA) shows maximum weight change and weight loss due to degradation of epoxy composites are significantly affected by orientation and spacing.

Analysis and comparison between rough channel and pipe flows

Direct numerical simulations of turbulent channel and pipe flows are presented to highlight the effect of roughness at low Reynolds number (Reτ = 180 − 360). Several surfaces are reproduced with the immersed boundaries method, allowing a one-to-one comparison of the two canonical flows. In general, all rough surfaces produce the same effect on the flow in pipes and channels, with small differences in the roughness function, RMS velocities and spectral energy density of pipes and channels. The only exception is for the rough surfaces made of longitudinal bars. In particular, the triangular bars (riblets) show drag reduction in the channel and drag increase in the pipe. This behaviour is linked to the development of spanwise rollers and wide u-structures near the plane of the crest of the pipe.

Moisture Sorption of Epoxy Composites Reinforced with Aligned and Notched Triangular Bars

Moisture diffusion in acid anhydride-cured epoxy matrices reinforced with aligned and notched triangular bars has been investigated. The reinforcing bars were first treated with molded and cured vinyl ester resin before their manual assembling. Gravimetric experiments were performed on epoxy composites fully immersed in water at 80°C for 1200 h. Weight uptake curves showed that the composites had suffered limited material degradation after an initial stage of moisture sorption; another sorption stage was observed after this degradation phase. Based on the initial sorption stage, the moisture diffusion behavior in composites is found to be independent of the orientation and alignment of reinforcing bars. This result is confirmed by transient 3D finite-element simulations. The numerical results are in close agreement with experimental data for the initial sorption stage.

Flow and Heat Transfer Phenomena Across Two Confined Tandem Heated Triangular Bluff Bodies

Confined flow and heat transfer phenomena across two long triangular bars in tandem arrangement in a horizontal channel have been studied for the range of Reynolds number (Re) = 1–40, Prandtl number (Pr) = 0.71–50 and gap ratio (S/B) = 1–4 for a fixed blockage ratio of 25%. The average Nusselt number of the first triangular cylinder is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Heat transfer correlations in terms of the Colburn jh factor have been established in the steady regime.

Modelling anisotropic water transport in polymer composite reinforced with aligned triangular bars

This work reports anisotropic water transport in a polymer composite consisting of an epoxy matrix reinforced with aligned triangular bars made of vinyl ester. By gravimetric experiments, water diffusion in resin and polymer composites were characterized. Parameters for Fickian diffusion and polymer relaxation models were determined by least-square curve fitting to the experimental data. Diffusion parameters of epoxy and vinyl ester resin were used as input during development of finite element (FE) model of polymer composite. Through transient FE diffusion analysis, anisotropic water transport in thickness direction of the polymer composite was numerically predicted and validated against experimental results. The case of using impermeable triangular bars was also numerically simulated. The diffusivity of reinforced aligned triangular bars was confirmed to affect anisotropic water transport in the composite. The results of this work suggest possible use of polymer composite for barrier and fluid removal applications.

Investigation of Water Diffusion in Triangular Bar-Reinforced Composites

This work investigated water diffusion in composites consisting of a permeable matrix reinforced with aligned, impermeable, triangular elements. The triangular elements are expected to induce single axis-, filler orientation-dependent transport behaviour in the composite. Such property is suggested to be useful in slow barrier applications and fast drying processes. To test this idea experimentally, triangular bar-reinforced composite specimens are prepared using thermosetting plastics as representative components. Using water as model diffusant, specimens undergo absorption-desorption-reabsorption gravimetric experiments at 80°C. It is observed that diffusivity decreases when the base side of the reinforced triangular bars is exposed to diffusion and increases when it is the sloped side. Diffusion is also reduced when the triangular bars are in staggered alignment.

Mitigation of shock waves within a liquid filled tank

An experimental study was implemented in order to understand the pressure generated by a hydrodynamic ram event. This event was created by firing spherical projectiles into a large 1000 gallon water tank that was used to simulate an aircraft fuel tank. Standard high-speed video and a large-scale shadowgraph technique were used to visualize pressure waves produced from the projectile impact and to relate the images to pressure transducer measurements. Four different geometries of triangular bars were installed within the simulator to provide shock wave mitigation of the internal pressures. Pressure transducers recorded the initial pressure wave and the cavity collapsing pressure and related these to the back wall pressure. These pressure differences were compared to those generated by projectiles in the absence of the shock mitigating members and it was determined that the hydrodynamic ram effect can be reduced with the appropriate design of such an assembly.

Degenerate scale problem when solving Laplace's equation by BEM and its treatment

AbstractIn this paper, Laplace problems are solved by using the dual boundary element method (BEM). It is found that a degenerate scale problem occurs if the conventional BEM is used. In this case, the influence matrix is rank deficient and numerical results become unstable. Both the circular and elliptical bars are studied analytically in the continuous system. In the discrete system, the Fredholm alternative theorem in conjunction with the SVD (Singular Value Decomposition) updating documents is employed to sort out the spurious mode which causes the numerical instability. Three regularization techniques, method of adding a rigid body mode, hypersingular formulation and CHEEF (Combined Helmholtz Exterior integral Equation Formulation) concept, are employed to deal with the rank‐deficiency problem. The addition of a rigid body term, c, in the fundamental solution is proved to shift the original degenerate scale to a new degenerate scale by a factor e−c. The torsion rigidities are obtained and compared with analytical solutions. Numerical examples including elliptical, square and triangular bars were demonstrated to show the failure of conventional BEM in case of the degenerate scale. After employing the three regularization techniques, the accuracy of the proposed approaches is achieved. Copyright © 2004 John Wiley & Sons, Ltd.

Near‐bottom flow and flow resistance for currents obliquely incident to two‐dimensional roughness elements

Measurements of the three components of the velocity when a steady current is flowing over a rippled bottom are presented. The bottom consisted of equally spaced triangular bars placed at angles of 0°, 30°, 45°, and 60° to the incident flow. The experiments show that close to the bottom, there is a transverse component of the velocity, which, for the larger angles of incidence, can be of the same order of magnitude as the main flow. The spatial average velocity profiles obtained from the measurements performed between two ripple crests show that close to the bottom, there is a well‐defined logarithmic region. The bottom roughness obtained by fitting a logarithmic law in the near‐bottom region to the longitudinal component of the flow depends strongly on the angle of incidence. In contrast, the analysis of the near‐bottom velocity component in the direction perpendicular to the ripple axis shows that the bottom roughness is independent of the angle of incidence. These experimental observations support the concept of a direction‐dependent equivalent bottom roughness when currents are obliquely incident to two‐dimensional bottom roughness elements, such as wave‐generated ripples.

The regular prismatic bar under torsion: A new approach based on caustics

A new approach to the general torsion problem of the regular prismatic bar was introduced, based on extensive and meticulous experimental evidence, indicating that the twisted prismatic bars, except the cylindrical ones, present, a longitudinal warping, following a sinusoidal type of curves for the warping displacements with their extrema displaced towards the corners. As a guide for the establishment of the method the solutions of the elliptical and the equiangular triangular bars were used. It was found that the regions inside the inscribed circles tangent to the sides of their undeformed cross-sections constituted regions whose warped surfaces constitute undulated forms following sinusoidal surfaces. This property was proved exact for the exact solutions for the elliptic and triangular cross-sections and it is assumed by induction valid for any regular cross-section. Comparing the warping displacements along the inscribed circle to a square or regular polygon cross section with the classical Timoshenko solution for the square bar it was found an exact coincidence in these displacements. It was further shown that these circles and all concentric full circles constitute the initial curves of the caustics formed from reflections of the warped cross-sections of the twisted bars. The differences between the stresses and displacements between the existing approximate solutions and the new approach appear in the partly curved triangles lying outside the inscribed circles. For the square cross-section it was shown that thew-displacements between Timoshenko's solution and the present one were less than 5 percent. Experimental evidence with the Moire method and comparison with the exact solution for the equiangular triangular cross section proved that the present approach is closer to reality and therefore presents higher accuracy than any approximate method. Furthermore, it presents the advantage that the full circles inscribed inside the cross-section constitute the initial curves forming caustics in space when a parallel light beam is reflected on the warped cross-section of the twisted bars. interesting properties of caustics, proved in this paper, help down-rightly for a thorough study of the form and properties of the twisted bars.