First-order Beam Research Articles

Comparison of Higher-Order Beam Theory and First-Order Beam Theory Models on FGM Beam Element for Static Analysis

HOBT-Higher Order Beam Theory is the developing theory in the Finite Element Method (FEM), which considers the higher-order variation of transverse shear strain; therefore, the shear correction factor is not required. This paper uses beam elements and implements them to higher order beam theory developed by Vo et al., with two independent variables of bending and shear displacement, using third-order polynomial functions. This paper shows the contribution of the shear strain part as one of the independent variables. Static analyses are presented to obtain a comparative result with the First Order Beam Theory (FOBT) application on the imposition of different boundary conditions to ensure reliable results.

Generating first-order optical vortex beams by photonic crystal slabs

Optical vortices, which are beams with helical wavefronts and spiral phase mismatches, have garnered considerable attention in various fields. In this study, we theoretically proposed and experimentally implemented a simple method for generating first-order optical vortices. To generate first-order vortex beams using the polarization field in the momentum space of photonic crystal slabs, topological half charges are required. We propose a method to divide the polarization vortex in the momentum space by breaking symmetry, which results in Dirac points or circularly polarized points. This approach enables the transformation of topological integer charges into topological half-integer charges, thereby facilitating the generation of first-order vortex beams. This approach extends the application of bound states in continuum and topological photonics.

Warren truss inspired hierarchical beams for three dimensional hierarchical truss lattice materials

Networks of beams are a subject of increasing interest to create architected materials with exceptional mechanical properties and low density. This paper investigates the mechanical properties of one dimensional (1D) hierarchical beams for the development of three dimensional (3D) truss lattice materials. These 1D hierarchical beams are constructed in two configurations by placing axial and inclined struts in single and double laced Warren truss patterns in each side of a beam with polygon cross section. Analytical and numerical analyses have been used to characterize their mechanical properties, including the elastic modulus, second moment of area, and shear stiffness of hierarchical beams drawn from a broad design space. Also, the failure limits of the beams with respect to parent material failure and various buckling modes are probed. Finally, the hierarchical beams have been implemented as the constituent members of Kelvin and octet lattices, and the elastic modulus and failure boundaries of the second-order hierarchical lattices are evaluated. The investigation reveals the competition between the elastic properties in the individual hierarchical beams based on different combinations of the design variables. The stiffness of the designs under compression and bending is found to be a function of the axial member size and cross sectional shape of the hierarchical beam. On the other hand, the shear stiffness of hierarchical beam designs is a function of the inclined member size and their inclination angle. It is demonstrated that incorporating hierarchy in the Kelvin and octet truss lattices can enhance the load bearing capacity of designs at low relative densities when compared to their hollow counterparts. Also, it is shown that second-order hierarchical stretching and bending-dominated lattices incorporating first-order hierarchical beams, can not only achieve but also surpass the strength and stiffness scaling relations established for first-order lattices. This becomes particularly noteworthy when considering bending-dominated lattices, as the hierarchy can drive their stiffness toward the boundaries, enabling them to outperform their equivalent stretching-dominated rivals.

Start-to-end modeling and transmission efficiency optimization for a cyclotron-based proton therapy beamline

Utilizing first-order beam dynamics models is adequate for studying the beam properties during the conceptual design of a cyclotron-based proton therapy beamline. After finishing lattice design, particle-matter interaction simulations for passive elements (e.g., degrader, collimators, energy slit) are required. The cascade simulation is used for lattice updates in each iteration, which is complicated. In addition, when the models involve particle tracking and particle-matter interaction, their optimization process is time-consuming. Therefore, this study proposes a start-to-end modeling method using Monte Carlo Beam Delivery Simulation (BDSIM) software that considers more realistic factors, such as particle-matter interaction and the realistic vacuum chamber, to precisely evaluate working parameters, along with an efficient optimization method that utilizes multi-objective Bayesian optimization (MOBO) to improve transmission efficiency. Taking the Huazhong University of Science and Technology proton therapy facility (HUST-PTF) as an example, beam loss along the beamline is located, quantified, and subsequently reduced by tuning the quadrupole strengths based on MOBO. The results show that: (i) By considering the particle-matter interaction and the realistic vacuum chamber, the precision in the prediction of the beam properties is improved; (ii) After optimization, the transmission efficiency of the entire beamline is relatively increased by an average of 6.52 % under different energy settings, especially 11.39 % at 70 MeV.

Resonance of vector vortex beams in a triangular optical cavity

We experimentally demonstrate resonance of first-order vector vortex beams (VVB) with a triangular optical cavity. We also show that, due to their symmetry properties, the VVBs commonly known as radial and azimuthal beams do not resonate at the same cavity length, which could be explored to use the triangular resonator as a mode sorter. In addition, an intracavity Pancharatnam phase shifter (PPS) is implemented in order to compensate for any birefringent phase that the cavity mirrors may introduce.

Generation of OAM beams with quasi omnidirectional pattern using simple slotted waveguide array

Theory and design aspects of the Slotted Waveguide Antenna (SWA) array for the simultaneous generation of Orbital Angular Momentum (OAM) modes are proposed in this paper. The proposed method is a novel approach to OAM generation that uses a simple feeding scheme and has better performance, especially in terms of mode purity. Due to its all-metallic structure, the high-power OAM beams with first-order modes (+1&-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ +1 \\, \\& \\,-1$$\\end{document}) can be generated simultaneously along the propagation axis but in opposite directions, which improves the coverage and makes the proposed SWA be used in applications like radar target detection by mounting it on a mechanically rotating platform. The proposed theory is verified by the electromagnetic (EM) simulations, followed by the experimental verification done on the laboratory prototype. The near-field characteristics of the proposed antenna confirm the generation of first-order OAM beams with high mode purity. The far-field characteristics show the high gain and quasi-omnidirectional radiation pattern. Transmission of high-power OAM beams with good far-field characteristics makes the proposed antenna mitigate the issues of long-range OAM communication to a certain extent. However, the proposed antenna can be served well in strategic applications where the mostly high-power microwave is involved.

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Tunable Bessel beam generator based on a 3D-printed helical axicon on a fiber tip.

We demonstrate a tunable and fully enclosed fiber-based Bessel beam generator that has the potential for applications in a tough environment. This generator consists of a few-mode fiber (FMF), a short section of graded index fiber (GIF), and a 3D-printed helical axicon. The FMF provides tunable modes that carry an orbital angular momentum (OAM). The GIF was fused to the FMF to expand and collimate the generated modes. The helical axicon was 3D-printed on the GIF tip without any holes or gaps, which reshapes the OAM modes into Bessel modes and adds an additional helical phase structure to them, resulting in the generation of zeroth-order, first-order, and second-order Bessel beams. The fully enclosed structure provides high mechanical strength and optical stability, which enable the generator to be suitable for imaging or particle manipulation in a complex liquid or air environment.

Arbitrary orthogonal polarization-dependent directional launching of Bessel-like surface plasmon polariton beams

Nondiffracting Bessel-like SPP beams, with the unique features of effectively suppressing the diffraction of the beam, have great application prospects in the fields of on-chip interconnection circuit, optical tweezers, and micromanipulation. In practical applications, active manipulation of nondiffracting Bessel-like SPP beams is essential. Here, we proposed two kinds of nondiffracting Bessel-like SPP beam unidirectional devices controlled by arbitrarily orthogonally polarized incidence light, which can generate and manipulate zeroth-order or first-order Bessel-like SPP beams, respectively. The results show that, by changing the distance between two pairs of slit couplers with different resonance responses, the nondiffracting Bessel-like SPP beams can be directionally excited at arbitrarily polarized incidence, and the excitation direction of the nondiffracting Bessel-like SPP beams will reverse under the corresponding orthogonally polarized incidence. The proposed devices provide promising opportunities for constructing polarization-based dynamic manipulation plasmonic devices of nondiffracting SPP beams and have potential applications in on-chip interconnection circuits.

Demonstration of Autonomous Emittance Characterization at the Argonne Wakefield Accelerator

Transverse beam emittance plays a key role in the performance of high-brightness accelerators. Characterizing beam emittance is often carried out using a quadrupole scan, which fits beam matrix elements to experimental measurements using first-order beam dynamics. Despite its simplicity at face value, this procedure is difficult to automate due to practical limitations. Key issues that must be addressed include maintaining beam size measurement validity by keeping beams within the radius of diagnostic screens, ensuring that measurement fitting produces physically valid results, and accurately characterizing emittance uncertainty. We describe a demonstration of the Bayesian exploration technique towards solving this problem at the Argonne Wakefield Accelerator, enabling a turn-key, autonomous quadrupole scan tool that can be used to quickly measure beam emittances at various locations in accelerators with limited operator input.

Free vibration analysis of thin to thick straight or curved beams by a solid-3D beam finite element method

A solid-3D beam finite element method is presented for the vibration analysis of thin to thick beam-like structures. This method is efficient for a spatial beam and considers all mechanical effects: membrane, bending and torsion. The structure is discretized with solid elements and contains several elements throughout the cross-section. Displacement fields of first-order or higher-order beam theories are met by directly applying kinematic relations on the solid finite element model, throughout the cross-section. This leads to a set of linear equations applied at slave nodes. Only the master nodes are kept in the final model, resulting in a model size reduction. The effectiveness of this method is demonstrated through two numerical examples, including a straight and a curved beam. The modal shapes and natural frequencies obtained by the proposed method are compared with the complete solid model and classical beam model. The size of these solid-beam models is slightly larger than that of an approach with classical beam element.

Time-efficient soft computational approach on vibration response of carbon-enriched drive shafts of super-fast race cars

Carbon-enriched nanocomposite drive shafts have received considerable attention in super-fast race cars because of their superb material and mechanical properties. thus, for the first time, vibration behavior of drive shafts enriched by three conventional distribution patterns of carbon nanotubes (CNT) in the polymer matrix are explored and reported. A new form in the framework of First-order Timoshenko beam theory is employed. The elasticity moduli of the CNT enriched nanocomposite material are approximated through a refined model of rule of mixtures. Hamilton’s variational principle serves as a way to determine the beam’s equations of motion. Differential quadrature approach (DQA) is employed to predict the system’s frequency for some conditions labeled as the training information. A new soft computation approach based on deep-learning methods employs the training information to adjust a predictor mechanism for obtaining the system’s vibration for any other conditions. This novel methodology provides this opportunity to considerably reduce the computational effort. Validity of the mentioned solution is verified through a comparative scrutinization by low discrepancy between its results and those of the published studies. Importance of these agility in computations would be discerned in cataloging process of the manufactured drive shafts in car industry.

Terahertz Bessel beam generator.

The Bessel beam has broad application prospects in wireless energy transmission and high-speed communications. The traditional Bessel beam generation method has the problems of large volume, low efficiency, and complex manufacturing. To solve the above problems, we present a terahertz Bessel beam generator based on the reflective metasurface, which is composed of a metal pattern, dielectric layer, and bottom metal plate. Under the incidence of right circularly polarized (RCP) wave, the zero-order Bessel beam and zero-order symmetric double Bessel beam are generated. It can be found that the bottom angle of the axicon of the first-order Bessel beam is inversely proportional to the propagation distance of the Bessel beam. Comparing the electric field intensity distribution, phase distribution, and mode purity of the second-order Bessel beam and the second-order vortex beam in different observation planes, it can be seen that the energy of the higher-order Bessel beam is more concentrated and the field distribution is more stable than those of the ordinary vortex beam. The reflective terahertz Bessel beam generator has potential application value in terahertz wireless communications, measurement, radar detection, and imaging.

Buckling analysis of laminated composite thin-walled I-beam under mechanical and thermal loads

Despite the extensive use of thin-walled structures, the studies on their behaviours when exposed to extreme thermal environment are relatively scarce. Therefore, this paper aims to present the buckling analysis of thin-walled composite I-beams under thermo-mechanical loads. The thermal effects are investigated for the case of studied beams undergoing a uniform temperature rise through their thickness. The theory is based on the first-order shear deformation thin-walled beam theory with linear variation of displacements in the wall thickness. The governing equations of motion are derived from Hamilton's principle and are solved by series-type solutions with hybrid shape functions. Numerical results are presented to investigate the effects of fibre angle, material distribution, span-to-height's ratio and shear deformation on the critical buckling load and temperature rise. These results for several cases are verified with available references to demonstrate the present beam model’s accuracy.

Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model

Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.

Study of coil configuration and local optics effects for the GaToroid ion gantry design

GaToroid, a novel gantry configuration for hadron therapy, is based on superconducting coils that generate a toroidal magnetic field to deliver the beam to the tumour location. Designing the complex GaToroid coils requires careful consideration of the local beam optical effects. We present a Python-based tool for charged particle transport in complex electromagnetic fields. The code implements fast tracking in arbitrary three-dimensional field maps, and it does not require a definition of specific or regular reference trajectories, as is generally the case for accelerator physics codes. The tool was used to characterise the beam behaviour inside the GaToroid system: to automatically determine the reference trajectories in the symmetry plane and analyse three-dimensional beam dynamics around these trajectories. Beam optical parameters in the field region were compared for various magnetic configurations of GaToroid. This paper introduces the new tracker and shows the benchmarking results. Furthermore, first-order beam optics studies for different arrangements demonstrate the main code features and serve for the design optimisation.

Coherent Transfer of Transverse Optical Momentum to the Motion of a Single Trapped Ion.

Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).

On the Static Flexural Response of Shear Deformable Isotropic Rectangular Nanobeams under the Parabolic Loading

It is well known that size-dependent effects, which are insignificant for macroscopic structures, become significant for small-scale structures like nanobeams. In addition, effects of the beam transverse shear deformation, which are insignificant for slender beams, become significant for shear deformable beams. Hence the need arises for a beam theory which is simple-to-use as well as which accounts for just-mentioned features of shear deformable nanobeams. Recently, the authors have developed a single variable new first-order shear deformation nonlocal beam theory (NFSDNBT, doi: 10.1007/s40430-019-2128-6). The NFSDNBT is applicable for the flexure of linear isotropic nanobeams undergoing small deformations. Displacement functions of the NFSDNBT give rise to the constant transverse shear strain through the beam thickness. Hence similar to the nonlocal Timoshenko beam theory (NTBT), the NFSDNBT also requires a shear correction factor. In the NFSDNBT, nonlocal differential stress-strain constitutive relations of Eringen are utilized, through which size-dependent effects have been taken into account. These relations relate not only the beam axial stress with the beam axial strain but also the beam transverse shear stress with the beam transverse shear strain. The governing equation of the NFSDNBT is obtained by utilizing beam gross equilibrium equations and it has a strong resemblance with the governing equation of the nonlocal Bernoulli-Euler beam theory (NBEBT). In this paper, the NFSDNBT is utilized for finding the static flexural response of shear deformable isotropic rectangular nanobeams under the action of parabolically distributed transverse loading. For the simply-supported, clamped-clamped and cantilever nanobeams, effects of variations in values of the nonlocal parameter of Eringen and beam thickness-to-length ratio on the maximum non-dimensional beam transverse displacement are presented. Obtained results are compared with corresponding results obtained by utilizing the NTBT and NBEBT so as to demonstrate the efficacy of the NFSDNBT. Along-the-length profiles of the non-dimensional beam transverse displacement for the just-mentioned cases of nanobeams, for various values of the nonlocal parameter and beam thickness-to-length ratio are also presented.

Vibration fatigue properties of laminated and 2.5D woven composites: A comparative study

Laminated and 2.5D woven composites are the two main configurations for CFRP used in turbofan engine blades. However, vibration fatigue behaviors of both structures and their differences are still lacking investigation. In this study, resonance fatigue tests based on the first-order cantilever beam bending are performed under eight strain levels on the laminated and 2.5D woven T800/epoxy composites with special angle-interlock architecture. Parameters related to the vibration fatigue behaviors, such as the variations of the normalized resonance frequency with the number of fatigue cycles, the retention rate of the load capacity, and the stiffness of the laminated and 2.5D woven composites are obtained and compared. The mathematical expressions of the ε-N curves for the two materials under the first-order resonant bending fatigue tests are obtained, and the strain limit values of the laminated and 2.5D woven composites that can withstand 107 cycles are estimated to be about 5000 με and 2400 με respectively, which can be used for guiding the design of aeroengine blades. Besides, the damage mechanisms of both materials are revealed by X-ray Micro CT. The main damage mode of the laminated structures is delamination, which is prone to unstable crack propagation. However, the damage propagation within the 2.5D woven structures exhibits multiple paths as a result of the warp yarns interlocked in the thickness direction. By comparing the vibration fatigue behavior and test data of these two materials, it can be concluded that the design limit for the vibration fatigue strain level of the laminated structures is higher than that of woven structures, but the damage resistance of the woven structures is better than laminated structures.

Nonlinear finite element analysis of electromechanical behaviors in a piezoelectric semiconductor beam

In this paper, a one-dimensional beam model with extensional, flexure and shearing deformations for a piezoelectric semiconductor fiber is established based on the first-order beam theory and nonlinear electric current constitutive relation. To solve such a nonlinear beam model under transverse and axial forces, a finite element method is proposed together with an iterative process. Throughout numerical case studies, effects of the external forces and initial electron concentration are investigated on electromechanical fields. It is shown that the applied forces have a great influence on the distribution of electron concentration, which can freely regulate the electron transport in piezoelectric semiconductors.