Beam Deflection Research Articles

Fractional calculus in beam deflection: Analyzing nonlinear systems with Caputo and conformable derivatives

<p>In this paper, our study is divided into two parts. The first part involves analyzing a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo derivatives. The also system incorporates the Caputo derivatives in the initial conditions, which adds a layer of complexity and realism to the problem. We focus on proving the existence of a unique solution for this system, and highlighting the robustness and applicability of fractional derivatives in modeling complex physical phenomena. In the second part of the paper, we employ conformable fractional derivatives, as defined by Khalil, to examine another system consisting of two coupled evolution equations. By the Tanh method, we derive new progressive waves. The connection between these two parts lies in the use of fractional calculus to extend and enhance classical problems.</p>

Beam test of a harmonic kicker cavity

A harmonically resonant kicker cavity designed for beam exchange in a circulator cooler was built and successfully tested at the Upgraded Injector Test Facility (UITF) at Jefferson Lab. This type of cavity is being considered for the injection scheme of the Rapid Cycling Synchrotron at the Electron-Ion Collider, where the spacing of neighboring bunches demands very short kicks. Operating with five transversely deflecting modes simultaneously that resonate at 86.6 MHz and consecutive odd harmonics thereof, the prototype cavity selectively deflects 1 of 11 electron bunches while leaving the others unperturbed. An RF driver was developed to synthesize phase- and amplitude-controlled harmonic signals and combine them to drive the cavity while also separating the modes from a field-probe antenna for RF feedback and dynamic tuning. Beam deflection was measured by sweeping the cavity phase; the deflection waveform agrees with expectations, having sub-nanosecond rise and fall times. No emittance increase is observed. Harmonically resonant cavities like the one described provide a new capability for injection and extraction at circulators and rings.

РАСЧЁТ НА ПРОЧНОСТЬ И ПРОВЕРКА ЖЁСТКОСТИ СТАТИЧЕСКИ ОПРЕДЕЛИМОЙ БАЛКИ ДВУТАВРОВОГО СЕЧЕНИЯ

This paper presents a strength calculation for a statically determinate I-beam. Diagrams of internal force factors (transverse forces and bending moments) are constructed and the number of the I-beam is selected according to the given external load and the values of the material strength characteristics. The given material characteristics are permissible normal stress, elastic modulus and permissible shear stress. The strength of a beam with a selected cross-section for shear stresses was tested. To construct the I-beam elastic line, the deflections of cross-sections with a unit interval along the length are calculated. The beam deflections were calculated using the universal elastic line equation. The obtained value of the maximum beam deflection made it possible to draw a conclusion about the beam sufficient hardness and operability under given external loads.

Broadband polarization conversion metasurface for beam deflection with switchable characteristics

A broadband polarization conversion metasurface (PCM) for anomalous reflection and beam deflection with switchable characteristics.

ЭЛЕМЕНТЫ ОЦЕНКИ РЕСУРСА СТАЛЬНЫХ БАЛОК, ПРЕДВАРИТЕЛЬНО НАПРЯЖЕННЫХ ВЫТЯЖКОЙ СТЕНКИ

The article presents possible ways to determine service life of steel single-span beams with prestressed web. The authors implement the method for searching coefficients of optimal distribution of material over the cross section of a symmetrical, monometallic steel I-beam. Basing on structures theory the study determines the maximum permissible moments of external loads for ordinary and prestressed beams. It formulates analytical expressions characterizing the first and second limit states of prestressed beams and establishes the resource of their bearing capacity. As a result of performed analysis, analytical dependences of prestressed beams stiffness are determined and structures resource is established according to this criterion. The study determines height of beams and its change with span variations and actual uniformly distributed load. Resource height of prestressed beams is established in comparison with height of conventional bending structures. Load-bearing capacity of beams with prestressed web is 1,8 times higher than the corresponding capacity of conventional beam and their resource is 180 %. Deflections of prestressed beams are 77,3 % less than deflections of traditional beams and stiffness resource is 1,29. Height of conventional beam is 1,847 times higher than height of prestressed structure. Service life of prestressed beam is 187%. Key words: prestressing, optimal design, load-bearing capacity, rigidity, service life.

Static Behavioral Studies of a 2D Taper Beam using Finite Elements Comprised of Functionally Graded Materials

The study examines the thermal and structural properties of beams made of functionally graded materials (FGMs) using the Finite Element Analysis (FEA) method and Reddy’s beam theory. The distribution of material qualities in thickness and length directions is influenced by mechanical and thermal loads. We calculate the stress and deflection of FG beams with a uniform load distribution. Quantitative results demonstrating the effects of multiple factors are provided by the Fusion 360 software. These include the change from alumina (ceramic) to aluminum (metal), boundary conditions, volume fraction distribution, and geometric features.

Methane gas spectral imaging method based on dual wedge scanning mirrors

With the increase in the number of oil and gas pipelines laid in China, more attention needs to be paid to pipeline maintenance work. At present, the main methods of detecting natural gas leaks in oil and gas transmission stations include manual inspections, opposing natural gas detection equipment, and cloud desktop natural gas detection equipment. Hand held natural gas detection equipment is used for manual inspection, which requires regular manual inspection. However, the response speed is poor and gas leaks cannot be detected in a timely manner. The opposed laser gas detection method can only detect the presence of gas on the beam path. If a larger area of leakage detection is desired, more equipment needs to be installed, resulting in a greatly increase in hardware costs. The existing cloud desktop laser gas detection method controls the deflection of the laser beam through the cloud platform to achieve leak detection at various points in the area to be tested. However, the rotation speed of the cloud platform is slow, and a complete detection cycle takes dozens of minutes, and only the presence of gas can be detected. For accurate leak location, manual on-site survey is also required to further determine the leak location. In order to meet the needs of the real-time monitoring and rapid positioning of oil and gas pipeline leaks, in this work, a fast and accurately controlled dual wedge scanning mirror system is designed, which combines tunable semiconductor laser absorption spectroscopy technology to convert the gas measurement laser beam from point measurement to surface measurement, thereby obtaining the two-dimensional distribution of gas, which is conducive to subsequent analysis and positioning of gas leakage sources. By using the inverse solution iterative optimization algorithm, the angle of the wedge mirror is controlled to obtain an efficient and uniform beam scanning trajectory. The deflection direction and detection position of the laser beam are fused with the corresponding methane concentration information, and a methane concentration data containing position information is constructed. In order to quantitatively verify the measurement accuracy and spatial resolution in the experiment, a standard air bag is used to simulate the methane leakage distribution. The results show that the minimum detection limit of the system can be lower than 5×10<sup>–4</sup> m, and the spatial resolution can be less than 6 cm. At the same time, this method can adjust the scanning step node based on the measurement distance of the oil from gas station, thereby achieving adjustable imaging resolution. This imaging method provides a new idea for accurately positioning and detecting the methane leakage location and amount.

Magnetism of single-doped paramagnetic tin clusters studied using temperature-dependent Stern-Gerlach experiments with enhanced sensitivity: impact of the diamagnetic ligand field and paramagnetic dopant.

In this work, the magnetic properties of tetrel clusters SnNTM, which are singly doped with transition metals (TM), are investigated. On the one hand, the number of tetrel atoms (N = 11, 12, 14 and 17 with TM = Mn) is varied; on the other hand, different transition metals (N = 14, TM = Cr, Mn, Fe) are studied. Magnetic deflection experiments under cryogenic conditions show that the variation of the number of tetrel atoms strongly changes the magnetic properties of the Mn-doped clusters. It is observed that Sn12Mn, Sn11Mn and Sn14Mn partially show super-atomic behaviour, while spin relaxation occurs in Sn17Mn. Magnetic deflection experiments at higher nozzle temperatures were carried out for the first time enhanced by a second parallel-aligned Stern-Gerlach magnet to achieve larger deflections. The resulting temperature-dependent one-sided deflections are quantitatively analysed using Curie's law and show that Sn17Mn possesses the highest magnetic moment of these clusters, followed by Sn12Mn and Sn11Mn. Sn14Mn shows the lowest magnetic moment. The replacement of Mn by Cr in Sn14Mn leads to a diamagnetic singlet, i.e., the magnetic moment of Cr in Sn14Cr is completely quenched. The replacement of Mn by Fe in turn leads to a paramagnetic species, whereby Sn14Fe is most likely present as a triplet. On this basis, the geometrical and electronic structures are analysed using quantum chemical calculations, indicating an arachno-type structure for Sn14Cr, Sn14Mn and Sn14Fe, which has already been predicted in the literature for Si14Cr. This is experimentally confirmed by deflection of molecular beams with an electric field under cryogenic conditions, suggesting that the arachno-type geometry is crucial for the overall stability of the transition-metal-doped tetrel clusters Sn14TM with TM = Cr, Mn, Fe.

Study of a consistent assembly system for AFM probes based on beam deflection method

Study of a consistent assembly system for AFM probes based on beam deflection method

Isothermal and non-isothermal transport properties of diluted fullerene binary and ternary aromatic solvent mixtures.

We present mass transport properties of C60 fullerene in five aromatic solvents, methylnaphthalene, toluene and three xylene isomers. Optical beam deflection and thermogravitational column techniques were used to determine molecular diffusion, thermodiffusion and Soret coefficients. All thermo-optical properties necessary to determine the abovementioned coefficients are also given at a mean working temperature of 298.15 K and an atmospheric pressure of 0.101 MPa. The magnitude of all transport properties is governed by the molecular weight ratio. In the particular case of the isomers, experiments revealed that movement under isothermal conditions (described by molecular diffusion) is dominated by density, while under non-isothermal conditions viscous forces affect the displacement (thermodiffusion depends on the dynamic viscosity). In the case of the Soret coefficients, as a combination of both, density is the dominant parameter and also the moment of inertia.

A transmission-type terahertz beam reconfigurable metasurface based on a multilayer annular structure.

To achieve flexible control over terahertz beams, vanadium dioxide (VO2) with phase transition temperatures of 60 °C and 72 °C is selected. The effects of VO2 in its two states-insulator (before phase transition) and metallic (after phase transition)-on the amplitude and phase of the unit structure are analyzed. A terahertz beam reconfigurable phase gradient metasurface based on VO2 with different phase transition temperatures is designed. By adjusting the surrounding temperature, the metasurface demonstrated the capability to produce distinct beam deflection angles corresponding to different thermal conditions. Specifically, at a frequency of 1.35 THz, the beam deflection angle was measured at 0° for temperatures below 60 °C, 67.6° for temperatures ranging from 60 °C to 72 °C, and 27.5° for temperatures exceeding 72 °C. This VO2-based terahertz phase gradient metasurface with different phase transition temperatures provides a novel approach for the flexible control of terahertz beams, showing significant potential applications in terahertz transmission, imaging, and wireless communication.

Study of spatially confined copper plasma by probe beam deflection technique

In the last decade, laser induced plasma (LIP) has emerged as one of the most promising techniques for various applications. It is now commonly investigated using various expensive techniques. Probe beam deflection (PBD) is an inexpensive technique generally utilized to characterize the shock wave. In this work, the copper laser-induced plasma plume and shock wave are both investigated using PBD technique. The plasma is generated at atmospheric pressure using Nd:YAG laser at a low laser power density (0.8 GW/cm2). The contribution of the plasma plume components to the PBD signal is clarified in space and time. The spatial confinement effect by a metallic disk is also investigated. It approves the physical mechanisms responsible for the deflection signal. As well, the spatial distribution of the weak shock wave velocity is considered.

Modulated Beam Deflection by Liquid Crystal Optical Wedge Arrays

Modulated Beam Deflection by Liquid Crystal Optical Wedge Arrays

Effect of chlorine salt erosion on flexural performance of GFRP and steel bars hybrid reinforced beams

Hybrid reinforced beams subjected to chloride salt erosion are susceptible to chloride ion infiltration, leading to corrosion of longitudinal reinforcement within the beams and thus impacting their flexural capacity. This study aims to assess the impact of varying reinforcement material area ratio and chloride salt erosion environments on the flexural behavior of hybrid GFRP-steel reinforced concrete beams. This is achieved through bending tests conducted on one reinforced concrete beam and seven concrete beams incorporating hybrid GFRP-steel reinforcement, coupled with finite element analysis. The results demonstrate that the better reinforcement material area ratio (RMAR) for hybrid reinforced beams is 1.36. When compared to the non-eroded beam, beams exposed to chloride salt erosion consistently exhibited a failure mode characterized by steel yield-concrete crushing failure, and the development of cross-sectional strain of the erosion beams aligning with the assumption of a plane section. The more severe erosion conditions lead to increased beam deflection, reduced maximum crack width, and reduced load-bearing capacity. Based on these findings, formula for accurately predicting the upper limits of load-induced crack widths at all levels and the formula for the load carrying capacity are deduced. Moreover, the feasibility of the nonlinear spring finite element method is validated. The results of this study offer significant reference value for the design and practical application of hybrid reinforcement beams.

Digital simulation of load-bearing structures with movable cargo carts

The process of digital simulation of the design parameters of load-bearing structures when moving a cargo cart on them is developed on the example of a load-bearing beam of a crane (bridge. gantry, ...). This process includes three main stages. The first stage is the creation of appropriate mathematical multiparametric equations for automated simulation of: the values of reactions in the supports of the crane load-bearing beam; bending moments; transverse forces; displacements; beam deflection angles and maximum stresses at different positions of the cargo cart on the crane beam. The second stage is the creation of appropriate computer models in the Mathcad system using an effective functional programming language built into the system with a graphical representation of the simulation results depending on the location of the cargo cart on the load–bearing beam of the crane. The third stage is the animation simulation of the studied parameters, both for each parameter individually and all together.

ПОСТРОЕНИЕ УПРУГОЙ ЛИНИИ БАЛКИ И ОПРЕДЕЛЕНИЕ ВЕЛИЧИНЫ И НАПРАВЛЕНИЯ ГЛАВНЫХ НАПРЯЖЕНИЙ В СЕЧЕНИИ БАЛКИ

The paper uses the data from diagrams of I-beam transverse forces and bending moments to calculate the values and directions of primary stresses at three points of the beam cross-section – on the neutral axis, above and below it. To calculate the values of primary stresses, the graphic analytical method with the construction of Mohr's circles is used. Further, the article presents an algorithm for constructing a beam deflection line and calculating cross-section deflections. To determine deflections, the universal beam deflection line equation is used. After determining the largest deflection value, conclusion is made that the hardness condition of a steel I-beam is met.

Experimental Analysis of Mechanical Behavior of Timber-Concrete Composite Beams with Different Connecting Systems

Timber-concrete composite structures are innovative structural systems which have become the subject of extensive research and practical usage, primarily due to their attractive mechanical properties. This article deals with the experimental procedure and the analysis of the mechanical behavior of two different series of timber-concrete composite beams with the same span and geometry of cross-sections. In the first BF-series, the screws were used as a connecting system between the timber and concrete parts, whereas in the BN-series the combination of notches and screws, as a more complex system, was used for the same purpose. Both series were exposed to loading up to a failure by means of the standard four-point bending test. The mechanical behavior of the BF and BN-series beams was analyzed by a comparative analysis referring to: the correlation of the failure loading and the deflection, mechanisms of failure, the strain development across the height of mid-span’s and support’s cross-sections, the horizontal displacement in the timber-concrete interlayer at the support zones, the value of shear stresses and the calculated values of the effective bending stiffness of the beams. The differences in bearing capacity between both series of beams were negligible (about 5%), the effective bending stiffness of BF beams is lower for 32.86% compared to the BN-series and the average value of deflections in BF-series beams is twice as high than in the BN-series. The BN-series beams showed better mechanical behavior in aspects of development of shear stresses in support zones, exhibiting lower shear stress values with an average of 40%.

Ohmic heating curing of carbon fiber concrete beam in realistic cold weather: The influence of electrically insulated steel rebars

This work attempted to investigate the on-site application of ohmic heating curing method on the structural concrete with steel reinforcement. The steel reinforced carbon fiber concrete beams were cured by ohmic heating method in the realistic severely cold weather. It was found that steel rebars disturbed the electrically conductive network formed by carbon fibers, resulting in a reduced curing duration of 48 h and an abnormal temperature distribution with high corner temperature and low core temperature. Electrical insulation treatments (epoxy resin coating and heat-shrink tubing) were taken and evaluated based on the ohmic heating features and mechanical properties. The results showed that the epoxy resin coating had a limited insulation effect, with an electrical resistance of 3.9 Ω, which displayed a similar temperature distribution with the uninsulated beam. On the contrary, the heat-shrink tubing had a significant insulation effect with an electrical resistance of 36.5 Ω, leading to an average core temperature of 23.6 ℃ during 7 days of curing period. The average rebound strength of beams with epoxy resin coating and heat-shrink tubing was 34.0 MPa and 41.6 MPa, respectively, and the ultimate deflection of beams was 34.37 mm and 49.18 mm, respectively, which was in correspondence with the temperature distribution. Besides, the heat-shrink tubing increased crack spacing width of beam, while the epoxy resin had little influence on crack pattern. This work emphasized the importance of electrically conductive path of concrete for ohmic heating curing method and gained practical experience of this method on the structural concrete.

Laser In Situ Joining as a Novel Approach for Joining Large‐Scale Thermoplastic Carbon Fiber‐Reinforced Polymer Aircraft Structures

Thermoplastic matrix composites are a viable option to reduce the carbon footprint during the life of an aircraft due to their ability to be molten and resolidified again. Tape‐based layup processes, such as automated tape placement, are well‐examined but have not seen extensive use in large‐scale joining applications, since they have to be processed layer‐by‐layer. In contrast, the advanced laser in situ joining method (CONTIjoin) utilizes fully consolidated and cut‐to‐size multilayered laminates, enabling the continuous layup of tailored laminates aligned with the mechanical application requirements. Herein, sample joints are manufactured using CONTIjoin technology, describing the general process principle, and are compared with samples produced using a standard heat press process. The base material, carbon fiber‐reinforced LMPAEK (low‐melt polyaryletherketone) is characterized using infrared spectroscopy. Using a 3.5 kW carbon dioxide (CO2) laser (10.6 μm wavelength) coupled with highly dynamic beam deflection, multidirectional reinforced laminates with up to six plies are processed to produce 24‐ply plates. The influence of joining temperatures up to 400 °C on the joint quality is investigated. Cross‐cuts are examined and interlaminar shear strength tests are conducted. With CONTIjoin, maximum strengths of 48.5 MPa are observed, reaching over 90% of the heat press reference.

High quality factor metasurfaces for two-dimensional wavefront manipulation

The strong interaction of light with micro- and nanostructures plays a critical role in optical sensing, nonlinear optics, active optical devices, and quantum optics. However, for wavefront shaping, the required local control over light at a subwavelength scale limits this interaction, typically leading to low-quality-factor optical devices. Here, we demonstrate an avenue towards high-quality-factor wavefront shaping in two spatial dimensions based on all-dielectric higher-order Mie-resonant metasurfaces. We design and experimentally realize transmissive band stop filters, beam deflectors and high numerical aperture radial lenses with measured quality factors in the range of 202–1475 at near-infrared wavelengths. The excited optical mode and resulting wavefront control are both local, allowing versatile operation with finite apertures and oblique illumination. Our results represent an improvement in quality factor by nearly two orders of magnitude over previous localized mode designs, and provide a design approach for a new class of compact optical devices.