Beam Deflection Research Articles

Broadband all-metal reflective-mode geometric metasurfaces for visible multi‐functional wavefront manipulation

Visible light manipulation has become a well-explored subject over recent years owing to its fascinating prospect in the optical communication field. Nevertheless, the limitations imposed by materials inherent in natural hamper the progress of the optical devices. Here, a broadband reflective-mode all-metal geometric metasurface (GMS) capable of high-efficient circular polarization (CP) conversion and applicable for multi-functional wavefront manipulation was proposed and investigated numerically in visible region. The proposed all-metal GMS is comprised of the periodically arranged gold dumbbell-shaped (DBS) nanostructure with symmetrical square notch adhered on the gold substrate. Simulation results demonstrate that the cross-polarized reflection amplitude of the all-metal GMS for normal incident CP light is practically higher than 85% from 310 THz to 500 THz, and the full 2π phase shift in this frequency range can be acquired by varying oriented angle of the DBS nanostructure. As proofs of multi-functional wavefront manipulation devices, beam deflectors, reflective planar focusing metalens and vortex beam generators were constructed and demonstrated numerically with the all-metal DBS nanostructure based on geometric phase principle. Overall, the proposed GMS carries with it considerable advantages of compaction and high efficiency, thus possessing infinite potential in optical devices.

Flexural behavior of seawater sea-sand concrete short beams reinforced with bamboo sheet

Bamboo reinforced concrete beams improved beam bearing capacity, but bamboo reinforcement's cross-sectional area affected its bond strength with concrete. Plain seawater sea-sand concrete beams are prone to cracking and poor flexural resistance. In order to solve these problems, this paper proposes bamboo sheet as a reinforcement material to improve the flexural behavior of plain seawater sea-sand concrete beams. Experimental results analyzed bamboo sheet reinforced seawater sea-sand concrete beam failure and ultimate bearing capacity. This test used 6 groups of 24 short beams: 5 groups of reinforced concrete and 1 group of contrast plain concrete, this test variable was reinforcement layers. The bamboo sheet reinforcement region was the entire beam bottom, which was strongly pasted to the beam bottom by resin glue. Bamboo sheet reinforcement increased beam deflection and flexural capacity, while the number of layers affected flexural behavior. When compared to plain seawater sea-sand concrete beam, the reinforcement effect was best when the number of bamboo sheet layers was 5, with the flexural capacity improvement degree being 81.88%. Finally, a theoretical calculation model for the bamboo sheet reinforced beam predicted its ultimate flexural capacity, with errors within 10%.

Influence of geometric nonlinearity on static and dynamic response of flexible beam

The flexible beam theory is widely applied in engineering, due to that many engineering structures can be regarded as flexible beam. For the flexible beam under large rotation, researches have shown that consideration of geometric nonlinearity is necessary: beam deflection will be erroneously larger or diverge without consideration of geometric nonlinearity. The reason lies on the dynamic stiffening effect caused by geometric nonlinearity. The dynamic stiffening effect of flexible beam under large rotation is well studied already, however, most studies only focus on flexible beam with constant cross section and rarely considers flexible beam without rotation. In view of this, a flexible beam with variable and twisted cross section is adopted to analyze the influence of geometric nonlinearity, and the response of flexible beam without rotation or static response is also analyzed. The results of dynamic beam deflection with and without consideration of geometric nonlinearity is compared, the results of static beam deflection under different load is also compared. On the basis of result comparison, the influence of geometric nonlinearity on static and dynamic response of flexible beam is then explained.

Assessing the key factors affecting the substructure of ballast-less railway track under moving load using a double-beam model and random forest method

In this paper, an approach is presented for analyzing the substructure of a slab track. The approach involves deriving a semi-analytical solution of the double-beam model, which incorporates a visco-elastic connection between two concrete beams and a spring-damping foundation. The model is then subjected to a concentrated moving load with a constant velocity. To more effectively assess the impact of various parameters, a random forest algorithm is utilized. The parameters considered include the spring-dashpot properties of the connection layer and the bedding layer, the thickness of the upper and lower beams, and the velocity of the moving load. The results of the random forest regression show that the stiffness of the intermediate and foundation layers have the greatest influence on the vertical deflection of the upper beam. However, the effect of stiffness of intermediate layer on the deflection and bending moment of the lower beam is found to be marginal. Moreover, for high-speed trains, the velocity of the concentrated moving load substantially changes the extreme responses attributed to the vertical deflection and bending moment. In this context, the damping properties of the interconnection layer and the subgrade course have a greater impact on the responses of the upper and lower beams.

Study on the Mechanical Properties of Continuous Composite Beams under Coupled Slip and Creep

Steel–concrete continuous composite beams are widely used in buildings and bridges and have many economic benefits. Slip has always existed in composite beams and will reduce the stiffness of composite beams. The effect of creep under a long-term load will also be harmful. Many scholars ignore the combined effects of slip and creep. In order to more accurately study the mechanical properties of steel–concrete continuous composite beams under long-term loads, this paper will consider the combined actions of slip and creep. By combining the elastic theory and the age-adjusted effective modulus method, the differential equation of the composite beam is derived via the energy variational method. The analytical solutions of axial force, deflection and slip under a uniform load are obtained by substituting the relevant boundary conditions. The creep equation is used to simulate the behavior of concrete with time in ANSYS. The analytical solution is verified by establishing a finite element model of continuous composite beams considering slip and creep. The results suggest the following: the analytical solution is consistent with the finite element simulation results, which verifies the correctness of the analytical solution. Considering the slip and creep effects will increase the deflection of the composite beam and the bending moment of the steel beam, reduce the bending moment of the concrete slab and have a significant impact on the structural performance of the continuous composite beam. The research results considering the coupling effect of slip and creep on continuous composite beams can provide a theoretical basis for related problems.

Two parametric SEE transformation and its applications in solving differential equations

Transformation plays a much more important role in every science. In this research article, two parametric forms of SEE transformation have been explored and the fundamental properties of two parametric SEE transformations have been shown. Furthermore, the transformed function of some fundamental functions and their time derivative rule has been shown. The application of two parametric SEE transformations in solving differential equations has been shown. The radioactive decay problem in first-order linear differential equations has been solved in this article which has large applications in nuclear energy engineering. Further, the solution to the beam deflection problem has been shown to have many applications in the engineering field. These results can be compared with other Laplace-type transformations.

Crack width, deflection, and strain limits of concrete beams with unstressed seven-wire steel strands as longitudinal reinforcement

ABSTRACT This study designed and tested six prototype beams longitudinally reinforced with either SD420 deformed steel bars, unstressed 1860-MPa seven-wire steel strands, or a combination of these. The experiment revealed that the displacement, crack width, and crack spacing increased with the increasing number of strands used to replace deformed bars as longitudinal reinforcement. Crack width was estimated using Frosch’s equation, which conservatively predicted the maximum crack width for beams with deformed bars and those with both strands and deformed bars; a modified version of the equation yielded more accurate values for the beams reinforced with strands only. A bond coefficient for strands was used in the modified equation. Strain limits for the tension- and compression-controlled sections of the beams with strands were determined to be 0.0145 and 0.0115, respectively. The deflection of the beams was well estimated using the ACI 318–19 equation.

Optical and thermal characterization of pure CuO and Zn/CuO using laser-induced breakdown spectroscopy (LIBS), x-ray fluorescence (XRF), and ultraviolet–visible (UV–Vis) spectroscopy techniques

We present elemental analysis and thermal characterization of pure and two different concentrations of zinc-doped copper oxide (CuO) samples using different analytical techniques. The quantitative as well as qualitative investigations, were performed by incorporating calibration-free laser-induced breakdown spectroscopy (CF-LIBS) technique. The plasma was generated on the samples surface by focusing a first harmonic of Nd: YAG laser of 1064 nm wavelength and the time-integrated emission spectra was achieved through a set of five spectrometers equipped with a charge-coupled-device. The acquired optical emission spectra from laser-generated plasma show different concentrations of zinc and copper in different samples which are consistent with their percentage composition measured during the sample synthesis. Using LIBS emission analytical lines, the Boltzmann technique was utilized for estimating the excitation temperature, while the number density was evaluated using the well-known Stark broadening line profile method. Besides, the CF-LIBS elemental analysis was validated by the x-ray fluorescence technique. For the optical study, ultraviolet–visible spectroscopical analysis was performed to find the bandgap of pure and zinc-doped copper oxide samples and consequently, variation in bandgap was studied with the growth of zinc doping. In addition, the thermal properties of the samples were analyzed using the beam deflection spectroscopy technique. The results shows that thermal diffusivity () and thermal conductivity (), increased with an increase in zinc concentration.

Static Analysis of Isotropic Beams Resting on Elastic Foundations of the Winkler-Pasternak Type

Beams resting on elastic foundations are widely used in engineering projects, so analyzing their displacement fields is very important. The present work presents solutions for the deflection of isotropic beams resting on elastic foundations of the Winkler-Pasternak type. The proposed formulation is based on the Euler-Bernoulli beam theory, and the governing equations and the boundary conditions are derived from the principle of virtual work. The direct integration method can decouple the deflections from axial displacement and twists. The system of deflection equations decouples into two principal directions and is transformed into a first-order system. The solution of this system of equations is obtained through the method of variation of parameters. When analyzing the results of the maximal deflections, it is observed that increasing values of the foundation stiffness provide decreasing deflections and that the influence of the Pasternak parameter is more significant on the results than that of the Winkler parameter.

Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation

Due to the growing scarcity of spectrum resources in the low-frequency band, the requirement of beam-reconfigurable antennas in the millimeter wave band is urgent. In this paper, a W-band graphene-based metasurface working in a broad bandwidth is proposed with reflective amplitude coding. Here, graphene sheets play a dual role in radiating and regulating electromagnetic waves. By adjusting the Fermi levels of graphene, the reflective amplitude and phase of the metasurface can be modulated simultaneously, enabling multi-beam switching and beam deflection in far-field. The proposed metasurface achieves amplitude-phase modulation within a significantly wide bandwidth which covers 75–91.5 GHz and 99.3–115 GHz. By optimizing the coding patterns, the proposed graphene-based metasurfaces are able to not only realize 2-D beam steering, but also achieve beam switching from single beam to four beams at 87 GHz. The proposed design provides a novel solution for the flexible manipulation of millimeter waves, which can be applied to various fields such as vehicle radar, satellite communication, 6G wireless communication, and beyond.

Parabolic gratings enhance the X-ray sensitivity of Talbot interferograms

In grating-based X-ray Talbot interferometry, the wave nature of X-ray radiation is exploited to generate phase contrast images of objects that do not generate sufficient contrast in conventional X-ray imaging relying on X-ray absorption. The phase sensitivity of this interferometric technique is proportional to the interferometer length and inversely proportional to the period of gratings. However, the limited spatial coherency of X-rays limits the maximum interferometer length, and the ability to obtain smaller-period gratings is limited by the manufacturing process. Here, we propose a new optical configuration that employs a combination of a converging parabolic micro-lens array and a diverging micro-lens array, instead of a binary phase grating. Without changing the grating period or the interferometer length, the phase signal is enhanced because the beam deflection by a sample is amplified through the array of converging-diverging micro-lens pairs. We demonstrate that the differential phase signal detected by our proposed set-up is twice that of a Talbot interferometer, using the same binary absorption grating, and with the same overall inter-grating distance.

Flexural property and design method evaluation of BFRP and steel bars hybrid reinforced concrete beams

AbstractFiber reinforced polymer (FRP) bars have been widely used as a replacement for steel bars in civil engineering due to their high strength and superior durability. However, compared to steel reinforced concrete (RC) beams, FRP RC beams have insufficient ductility and are more expensive. Therefore, a hybrid beam reinforced with steel and FRP bars has been proposed recently. In this study, the flexural properties of steel bar RC beam, basalt FRP (BFRP) bar RC beam, and BFRP steel bars hybrid RC beams were studied based on numerical simulation. The effect of As/Af on the stress of longitudinal reinforcements, load–midspan curves, ductility, and overall performance of the hybrid RC beams is analyzed. Results indicated that the hybrid RC beams exhibited a second‐order stiffness after the steel bars yielded owing to the contribution of the BFRP bars. As As/Af increases, the ductility of the hybrid RC beam and the strength utilization of BFRP bars increase, and a preferable ductility and overall performance can be achieved when As/Af was close to 1.0. The theoretical calculation results of hybrid RC beams based on ACI, CSA, and GB codes are compared with the simulation results, and the accuracy of the ultimate flexural strength of the prediction results is verified. In addition, equations for predicting the deflection of hybrid RC beams are proposed, and they exhibit higher prediction accuracy compared to the prediction models based on the ACI code.

Active Probe Atomic Force Microscopy with Quattro-Parallel Cantilever Arrays for High-Throughput Large-Scale Sample Inspection.

An Atomic Force Microscope(AFM) isa powerful and versatile tool for nanoscale surface studies to capture 3D topography images of samples. However, due to their limited imaging throughput, AFMs have not been widely adopted for large-scale inspection purposes. Researchers have developed high-speed AFM systems to record dynamic process videos in chemical and biological reactions at tens of frames per second, at the cost of a small imaging area of up to several square micrometers. In contrast, inspecting large-scale nanofabricated structures, such as semiconductor wafers, requires nanoscale spatial resolution imaging of a static sample over hundreds of square centimeters with high productivity. Conventional AFMs use a single passive cantilever probe with an optical beam deflection system, which can only collect one pixel at a time during AFM imaging, resulting in low imaging throughput. This work utilizes an array of active cantilevers with embedded piezoresistive sensors and thermomechanical actuators, which allows simultaneous multi-cantilever operation in parallel operation for increased imaging throughput. When combined with large-range nano-positioners and proper control algorithms, each cantilever can be individually controlled to capture multiple AFM images. With data-driven post-processing algorithms, the images can be stitched together, and defect detection can be performed by comparing them to the desired geometry. This paper introduces principles of the custom AFM using the active cantilever arrays, followed by a discussion on practical experiment considerations for inspection applications. Selected example images of silicon calibration grating, highly-oriented pyrolytic graphite, and extreme ultraviolet lithography masks are captured using an array of four active cantilevers ("Quattro") with a 125 µm tip separation distance. With more engineering integration, this high-throughput, large-scale imaging tool can provide 3D metrological data for extreme ultraviolet (EUV) masks, chemical mechanical planarization (CMP) inspection, failure analysis, displays, thin-film step measurements, roughness measurement dies, and laser-engraved dry gas seal grooves.

Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Prismatic fixed-end beams with circular cross-section are often used in engineering. Therefore, there is a need for a solution of an elastoplastic deflection of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam, which is suitable for practical use. The elastoplastic deflection beam theory does not provide a solution in a closed form for such a problem. Hence, a semi-analytical solution is proposed in this paper. Homogenous and isotropic beams with the bilinear elastoplastic strain hardening behaviour are covered in the proposed solution. The elastic deflection of a beam is determined by the Bernoulli–Euler formula. However, differential equation of beam bending in the plastic domain of material behaviour does not have a solution in a closed form. Therefore, an incremental procedure for determining the curvature of the plasticised region of the beam is suggested. The proposed semi-analytical solution is validated by comparing to the finite element analysis results of 16 different fixed-end beam models with varying geometric and material characteristics. Also, validation is done with experimental results of the bar damper device, available in the literature, which has been selected as a sample of a real engineering system where the proposed solution can be applied. A satisfying agreement between the proposed semi-analytical results and the subsequent numerical and experimental results is herein achieved, confirming the solution’s reliability. Finally, a parametric study is conducted using the proposed semi-analytical solution in order to determine the influence of geometrical parameters and material characteristics on the mechanical properties of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam.

Photo-Excited Metasurface for Tunable Terahertz Reflective Circular Polarization Conversion and Anomalous Beam Deflection at Two Frequencies Independently.

In this paper, a photo-excited metasurface (MS) based on hybrid patterned photoconductive silicon (Si) structures was proposed in the terahertz (THz) region, which can realize the tunable reflective circular polarization (CP) conversion and beam deflection effect at two frequencies independently. The unit cell of the proposed MS consists of a metal circular-ring (CR), Si ellipse-shaped-patch (ESP) and circular-double-split-ring (CDSR) structure, a middle dielectric substrate, and a bottom metal ground plane. By altering the external infrared-beam pumping power, it is possible to modify the electric conductivity of both the Si ESP and CDSR components. By varying the conductivity of the Si array in this manner, the proposed MS can achieve a reflective CP conversion efficiency that ranges from 0% to 96.6% at a lower frequency of 0.65 THz, and from 0% to 89.3% at a higher frequency of 1.37 THz. Furthermore, the corresponding modulation depth of this MS is as high as 96.6% and 89.3% at two distinct and independent frequencies, respectively. Moreover, at the lower and higher frequencies, the 2π phase shift can also be achieved by respectively rotating the oriented angle (αi) of the Si ESP and CDSR structures. Finally, an MS supercell is constructed for the reflective CP beam deflection, and the efficiency is dynamically tuned from 0% to 99% at the two independent frequencies. Due to its excellent photo-excited response, the proposed MS may find potential applications in active functional THz wavefront devices, such as modulators, switches, and deflectors.

Nanoelectromechanical Tuning of High-Q Slot Metasurfaces.

Nanoelectromechanical devices have been used widely in many applications across photonics, electronics, and acoustics. Their incorporation into metasurface systems could be beneficial in designing new types of active photonic devices. Here, we propose a design of active metasurfaces using a nanoelectromechanical system (NEMS) composed of silicon bars which operates under CMOS-level voltage and achieves phase modulation with wavelength-scale pixel pitch. By introducing a perturbation to the slot mode propagating between the silicon bars, the device operates in a high-Q regime, making the optical mode highly sensitive to mechanical movement. An over 12 dB reflection modulation is observed by full-wave simulation, and over 10% is achieved in the proof-of-concept experiment under CMOS-level voltage. We also simulate a device with 1.8π phase response using a bottom gold mirror. Based on this device, a 3-pixel optical beam deflector is shown to have 75% diffraction efficiency.

Achieving Photonic Spin Hall Effect, Spin-Selective Absorption, and Beam Deflection with a Vanadium Dioxide Metasurface.

Metasurface-based research with phase-change materials has been a prominent and rapidly developing research field that has drawn considerable attention in recent years. In this paper, we proposed a kind of tunable metasurface based on the simplest metal-insulator-metal structure, which can be realized by the mutual transformation of insulating and metallic states of vanadium dioxide (VO2) and can realize the functional switching of photonic spin Hall effect (PSHE), absorption and beam deflection at the same terahertz frequency. When VO2 is insulating, combined with the geometric phase, the metasurface can realize PSHE. A normal incident linear polarized wave will be split into two spin-polarized reflection beams traveling in two off-normal directions. When VO2 is in the metal state, the designed metasurface can be used as a wave absorber and a deflector, which will completely absorb LCP waves, while the reflected amplitude of RCP waves is 0.828 and deflects. Our design only consists of one layer of artificial structure with two materials and is easy to realize in the experiment compared with the metasurface of a multi-layer structure, which can provide new ideas for the research of tunable multifunctional metasurface.

Load-Bearing Performance of Non-Prismatic RC Beams Wrapped with Carbon FRP Composites

This study investigated the influence of CFRP composite wrapping techniques on the load–deflection and strain relationships of non-prismatic RC beams. A total of twelve non-prismatic beams with and without openings were tested in the present study. The length of the non-prismatic section was also varied to assess the effect on the behavior and load capacity of non-prismatic beams. The strengthening of beams was performed by using carbon fiber-reinforced polymer (CFRP) composites in the form of individual strips or full wraps. The linear variable differential transducers and strain gauges were installed at the steel bars to observe the load–deflection and strain responses of non-prismatic RC beams, respectively. The cracking behavior of unstrengthened beams was accompanied by excessive flexural and shear cracks. The influence of CFRP strips and full wraps was primarily observed in solid section beams without shear cracks, resulting in enhanced performance. In contrast, hollow section strengthened beams exhibited minor shear cracks alongside the primary flexural cracks within the constant moment region. The absence of shear cracks was reflected in the load–deflection curves of strengthened beams, which demonstrated a ductile behavior. The strengthened beams demonstrated 40% to 70% higher peak loads than control beams, whereas the ultimate deflection was increased up to 524.87% compared to that of the control beams. The improvement in the peak load was more prominent as the length of the non-prismatic section increased. A better improvement in ductility was achieved for the case of CFRP strips in the case of short non-prismatic lengths, whereas the efficiency of CFRP strips was reduced as the length of the non-prismatic section increased. Moreover, the load–strain capacity of CFRP-strengthened non-prismatic RC beams was higher than the control beams.

Flexural behavior and serviceability performance of SSC beams reinforced with hybrid GFRP-stainless steel bars

Using fiber-reinforced polymer (FRP) bars instead of steel bars to reinforce concrete structures has become an important method to solve the corrosion problems. FRP bars reinforced concrete (FRP-RC) beams suffer sudden failure owing to the brittleness of FRP bars. Therefore, it is suggested to add steel reinforcements in FRP-RC beams to improve the ductility. This study analyzes the flexural performance of seawater and sea sand concrete (SSC) beams reinforced with hybrid GFRP and stainless steel (SS) bars, in which GFRP bars are used as tension bars while SS bars are used as compression bars. The flexural performances of GFRP bars reinforced SSC beams and SS bars reinforced SSC beams were also studied for comparison. Based on the test results, the cracking moment, load-carrying capacity, deflection, and ductility of the SSC beams are discussed and compared with the guidance in current design codes. Results show that ACI 440.1R-15 and CSA S806-12 reasonably predict the cracking moment and bearing capacity, but both underestimate the deflection at the service load. Furthermore, the moment capacity calculation equation is proposed with good accuracy. The ratio between the reinforcement ratios of GFRP bars and SS bars is suggested to meet the ductility requirement.

Stiffness degradation analysis of reinforced concrete beams under corrosion-fatigue coupling action based on experimental research

In order to study the effect of corrosion-fatigue coupling action on the stiffness degradation of reinforced concrete beams, a novel corrosion-fatigue coupling experimental device is designed, eleven reinforced concrete T-shaped test beams are made, in which a set of static load test, then seven sets of simple fatigue tests under different stress amplitudes and three sets of corrosion-fatigue coupling tests under different stress amplitudes are conducted respectively. The test phenomenon, load-deflection relationship, and fatigue life of the simple fatigue test beams and the corrosion-fatigue coupling test beams are compared. The test results show that the deflection development of the corrosion-fatigue coupling test beams includes three stages of sudden increase-stable-sudden increase, as the same as the simple fatigue beams. The deflection growth rate of the corrosion-fatigue coupling beams in the second stage is greater than that of the simple fatigue beams. Fatigue cyclic loading significantly increases the residual deflection of the test beams compared to the static load test beam. Then a new calculation method of the midspan deflection of the simple fatigue beam and the corrosion-fatigue coupling beam is developed according to the measured deflection data and the fatigue life test results. In this method the influence factors such as fatigue loading times, fatigue stress amplitude, concrete elastic modulus degradation, steel corrosion and other factors are systematically considered, and this method is verified by experimental data.