Complex Cross-section Research Articles

Development of Dispersion Calculator SAFEDC of Guided Wave with Complex Material and Waveguide

The propagation characteristics of guided waves (GW) are related to both the material, loading and geometry parameters. Correct understanding of GW is the key step towards further GW-based structural health monitoring. A dispersion calculator of GW propagating in the complex geometry with viscoelastic and anisotropic material parameter in the open waveguide is developed based on the semi-analytical finite element (SAFE) method and perfectly matched layer (PML). By assuming the simple harmonic motion along the propagation direction and adopting the mesh discretization in the cross section, SAFE features the capability of GW calculation in the complex waveguide at only a cost of limited calculation resources. Hence, besides the capabilities of the most off-the-shelf tools focusing on the analytical solution of GW in simple plate or pipeline, the developed algorithm further offers the solution of GW in open waveguide with laminates of arbitrary ply stacking sequences and in arbitrarily complex cross section. Quadratic one-dimensional and triangular elements are adopted to automatically discretize the plate structure and complex cross section, respectively. The obtained results of GW in plates are in a good agreement with the results obtained with the off-the shelf-tools that adopt analytical derivations, and show stronger robustness of mode searching and sorting by avoiding the complex root-finding procedure required in the analytical derivation. The most GW features, including phase velocity, group velocity, attenuation, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are directly calculated. All these functions are integrated and updated in the previously developed freeware SAFEDC, whose 1st version SAFEDC v1.0 was published in September 2023.

A closer look at the electromagnetic signatures of Bethe-Heitler pair production process in blazars

The “twin birth” of a positron and an electron by a photon in the presence of a nucleus, known as Bethe-Heitler pair production, is a key process in astroparticle physics. The Bethe-Heitler process offers a way of channeling energy stored in a population of relativistic protons (or nuclei) to relativistic pairs with extended distributions. Contrary to accelerated leptons, whose maximum energy is limited by radiative losses, the maximal energy of pairs is determined by the kinematics of the process and can be as high as the parent proton energy. We take a closer look at the features of the injected pair distribution, and provide a novel empirical function that describes the spectrum of pairs produced by interactions of single-energy protons with single-energy photons. The function is the kernel of the Bethe-Heitler pair production spectrum that replaces a double numerical integration involving the complex differential cross section of the process, and can be easily implemented in numerical codes. We further examine under which conditions Bethe-Heitler pairs produced in blazar jets can emit γ-ray photons via synchrotron radiation, thus providing an alternative to the inverse Compton scattering process for high-energy emission in jetted active galactic nuclei. For this purpose, we create 36 numerical models using the code ATHEνA optimized so that the Bethe-Heitler synchrotron emission dominates their γ-ray emission. After taking into consideration the broadband spectral characteristics of the source, the jet energetics, and the properties of radiation fields present in the blazar environment, we conclude that γ-rays in high-synchrotron-peaked blazars are unlikely to be produced by Bethe-Heitler pairs, because the emitting region is found to be opaque in photon-photon pair production at photon energies ≳ 10 GeV. On the contrary, γ-ray spectra of low-synchrotron-peaked blazars may arise from Bethe-Heitler pairs in regions of the jet with typical transverse size ∼ 1015 – 1016 cm and co-moving magnetic field 50 – 500 G. For such cases, an external thermal target photon field with temperatures T ∼ 4 · 102– 6 · 103 K is needed. The latter values could point to the dusty torus of the AGN. Interestingly, a Bethe-Heitler-dominated high-energy component is mostly found in models of intermediate-synchrotron peaked blazars, for a wide range of magnetic fields and source radii.

Comb excitation method for single guided wave modes in complex cross sections

Irregular and complex cross-sectional waveguide structures exhibit numerous guided wave modes, which become mixed at high frequencies and hinder mode identification and application in damage monitoring. To address the need for single mode excitation in nondestructive testing and structural health monitoring, this study presents a comb excitation method based on group velocity that aims to excite a single guided wave mode in irregular and complex cross-sectional waveguides. Using rails as a case study for simulation and validation of the excitation effect, array comb sensors are arranged along the rail web. By adjusting the time delay and phase compensation of the comb excitation sensors, the single excitation of the rail head, rail web, and rail base detection modes is achieved over a wide frequency range. This study also establishes the modal singularity index, employing the higher-order elements SAFE method, and proposes a target modal selection rule for a wider frequency range. In addition, an evaluation index is defined to quantify the guided wave modal excitation effect is defined. Finite element simulations are used to investigate the influence of sensor spacing and number of sensor points on the array comb excitation effect, and suggestions are made for optimising the array comb excitation. Finally, experimental verification demonstrates the high accuracy of the higher-order elements SAFE method and confirms the effectiveness of the proposed comb excitation method.

Review on Multi-pass Rolling Forming of Thin-walled Ring with Complex Section

Superalloy thin-walled ring with complex cross section plays an important role in aerospace, energy and chemical industry, and it has excellent mechanical properties and oxidation resistance in high temperature and pressure environment. However, multi-pass rolling forming of thin-walled ring with complex cross-section of superalloy is a complex forming process that needs to undergo complex uneven plastic deformation under the coupling of multiple fields and factors. The research progress of multi-pass rolling forming of superalloy thin-walled ring with complex cross section is summarized from three aspects: deformation behavior and stress analysis, defect behavior analysis, process optimization and simulation, and several directions that need further research in the future are put forward.

Imaging the magnetic nanowire cross section and magnetic ordering within a suspended 3D artificial spin-ice

Artificial spin-ice systems are patterned arrays of magnetic nanoislands arranged into frustrated geometries and provide insight into the physics of ordering and emergence. The majority of these systems have been realized in two-dimensions, mainly due to the ease of fabrication, but with recent developments in advanced nanolithography, three-dimensional artificial spin ice (ASI) structures have become possible, providing a new paradigm in their study. Such artificially engineered 3D systems provide new opportunities in realizing tunable ground states, new domain wall topologies, monopole propagation, and advanced device concepts, such as magnetic racetrack memory. Direct imaging of 3DASI structures with magnetic force microscopy has thus far been key to probing the physics of these systems but is limited in both the depth of measurement and resolution, ultimately restricting measurement to the uppermost layers of the system. In this work, a method is developed to fabricate 3DASI lattices over an aperture using two-photon lithography, thermal evaporation, and oxygen plasma exposure, allowing the probe of element-specific structural and magnetic information using soft x-ray microscopy with x-ray magnetic circular dichroism (XMCD) as magnetic contrast. The suspended polymer–permalloy lattices are found to be stable under repeated soft x-ray exposure. Analysis of the x-ray absorption signal allows the complex cross section of the magnetic nanowires to be reconstructed and demonstrates a crescent-shaped geometry. Measurement of the XMCD images after the application of an in-plane field suggests a decrease in magnetic moment on the lattice surface due to oxidation, while a measurable signal is retained on sub-lattices below the surface.

Experimental and numerical studies on unsteady galloping driving mechanism of a truss beam with solid barriers

The long-span bridges with truss beam are widely recognized as typical wind-sensitive structures, and its wind-induced divergence events may become a very predominant issue. This work evaluates the galloping performance of a typical truss beam with wind barriers, which is detected to be susceptible to the infrequent vertical instability at specific attack angles, as evidenced by experimentation and numerical analysis. Since the truss beam constitutes a complex cross section, this study employs energy analysis to distinguish the crucial parts affected by vibration and discovers that the galloping vibration is mostly caused by the surfaces of the deck. Rather than relying on conventional quasi-steady theory, this study explores the unsteady aerodynamic forces to identify the underlying galloping driving mechanism. Our findings reveal that the instigator of galloping instability is the phase rising of lift with increasing wind speed. Additionally, the nonlinear mechanical damping is not a decisive parameter. Furthermore, we have investigated the impact of an essential ancillary facility, the wind barrier, and discovered that its galloping stability can be enhanced by increasing its porousness and decreasing its height. However, the underlying mechanisms behind this improvement are distinct.

Dynamic response analysis for bridges subjected to moving vehicle loads by using the analytical dynamic stiffness method

This paper presents a highly efficient and accurate analytical method for the dynamic analysis of subjected to moving loads. Bridges with complex cross section and considering damping are modelled as plate built-up structures by the dynamic stiffness method with few degrees of freedom. Different moving loads with time-varying amplitudes travelling at different speeds can be modelled semi-analytically: The moving vehicle loads with varying amplitude are transformed into the frequency-wavenumber domain by the analytical sine transform combined with the fast Fourier transform; then the time-spatial domain dynamic response of the bridge is computed by the associated inverse transforms from the frequency-wavenumber domain response of the dynamic stiffness model. The most commonly used box girder railway bridge is taken as an example, and the results of both free vibration and dynamic response subject to moving train wheel loads computed by the proposed method are validated well by the finite element software ANSYS. The proposed method uses about 1.2% time of that taken by the ANSYS but achieves a similar level of accuracy. The proposed method can serve as an efficient alternative tool of modal and dynamic response analysis for the design and optimization of a wide range of complex bridges.

Generalized response displacement methods for seismic analysis of underground structures with complex cross section

Generalized response displacement methods for seismic analysis of underground structures with complex cross section

Geometrical control of eddy currents in additively manufactured Fe-Si

Additive manufacturing has enabled the processing of high silicon electrical steels which have excellent soft magnetic properties. In bulk form, core losses as a result of eddy currents would be too large to allow their use in high-frequency electrical machines, therefore strategies are needed to reduce eddy currents. Additive manufacturing affords high part complexity and provides the opportunity for cross sectional patterns within the material to limit eddy current generation. This study investigates several designs, including a novel hexagonal pattern which is shown to have the lowest eddy current loss coefficient of 0.0005, less than 25% of the bulk material which has an eddy current loss coefficient of 0.0021. Heat treatment is shown to increase the eddy current losses, demonstrating that for high-frequency machines, it may be beneficial to use the material in the as-built state. Physical samples were compared to their intended geometries, showing there are defects in these complex cross sections causing increased eddy currents when compared to simulations, but that geometrical accuracy can be improved by alternative design methodology which experimentally experiences smaller losses. These novel cross sectional designs may be implemented into an electric machine that has a 3D magnetic flux pathway enabled by additive manufacturing, affording more flexibility for electrical engineers to design new motor architectures in the pursuit of higher power density machines.

Features of the Internal Force Factors Distribution in Reinforced Concrete Piles of Complex Cross Section under the Influence of a Transverse Load

Bar reinforced concrete structures, which include piles, in real working conditions perceive a whole range of internal force factors. Axial tension-compression forces, bending moments and shear forces are the most commonly perceived internal force factors. Of particular interest is the effect on the cross section of the shear force. If a complex curly shape is replaced by elementary form, then the calculation is not difficult. However, when calculating the composite cross section, there is no unambiguous solution. In accordance with the adopted regulatory documentation, it is necessary to accept only a main part, while discarding the surrounding areas. It is important to study the configuration of the shape of a complex section for the perception of a shear force. The purpose of the work was to refine the account of the entire complex section using numerical simulation by the finite element method, analytical calculations and small-scale experiments. Determination of further practical application of the obtained results on real structures was also the goal of the study. The parameters of the distribution of shear force between the main rib and flanges were obtained by numerical analysis and small-scale experiments. Numerical models of rectangular and tee cross sections beams have been developed. Analytical dependences were studied and full-scale tests of reinforced concrete beams of various sections were carried out. It has been established that when taking into account the work of the entire cross-section, the bearing capacity of concrete for the action of a shear force is 20% greater than when calculating only the main section without taking into account the shelves.

Sphere on a plane: Two-dimensional scattering from a finite curved region

Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we consider a simple case of piecewise uniform curvature: a particle moves on a plane with a spherical extrusion. Depending on the latitude at which the sphere joins the plane, the extrusion can range from an infinitesimal bump to a nearly full sphere that just touches the plane. Free classical motion on this surface of piecewise uniform curvature follows geodesics that are independent of velocity, while quantum mechanical scattering depends on energy. We compare classical, semi-classical, and fully quantum problems, which are all exactly solvable, and show how semi-classical analysis explains the complex quantum differential cross section in terms of interference between two classical trajectories: the sphere on a plane acts as a kind of double slit.

Dispersion of Guided Waves in Complex Waveguides: A Hybrid Modeling Technique Combining Gauss–Lobatto–Legendre Node Collation and Semi-Analytical Finite Element Method

Guided waves (GW) are massively used for structural health monitoring and defect evaluation in plate, pipe, and rail structures. To accurately and efficiently calculate the dispersive natures of GW in complex waveguides, this study proposes a novel Gauss–Lobatto–Legendre-based high-order semi-analytical finite element method (GLL-SAFE). Combining the GLL node collation and Lobatto quadrature into SAFE, the mass matrix in the developed GLL-SAFE is diagonal, which enables a faster solution speed and a reduced error of matrix inversion. Firstly, the GWs in the single-layer isotropic material, composite lamina, and composite laminates are calculated with both GLL-SAFE and the conventional Gauss-SAFE featuring an equidistant node collation and Gaussian quadrature. Before reaching the convergence limit, the calculated average relative errors for GLL-SAFE are smaller than those for Gauss-SAFE, and can reach an order of 10[Formula: see text] and 10[Formula: see text] for the phase and group velocity, respectively. Then a novel mesh automatic reconstruction with arbitrary element polynomial order is developed to calculate GW propagation in waveguides of complex cross section. As a hollow cylinder for validation, the calculated average relative errors reach below [Formula: see text] and [Formula: see text] for the phase and group velocity, respectively. Finally, with a complex rail track as the waveguide, the calculated dispersion characteristics with GLL-SAFE show an excellent match with those from the time-domain finite element analysis, and GLL-SAFE shows its higher calculation efficiency over Gauss–SAFE.

Strain energy form coefficients for bending of short beams having full and thin-walled arbitrary cross section with application for FEM and Airfoils

The aim of this work is to develop a new generalized formula and a numerical computation program for evaluating the energy form coefficient of a complex and arbitrary cross section for full and thin-walled cross section with respect to any central axis, for the bending of beams of small lengths in comparison with the transverse dimension of the section. This coefficient plays a very important role in the calculation of the deformation energy of beams subjected to bending under the effect of a shearing force for short beams. It also enters in the formulation of FEM bending model, in order to calculate the stresses and the strains due to the external forces. The application is made for complex sections used in various fields of construction and in particular for airfoils designed for aerospace construction. A method is developed to calculate this coefficient as a function of the rotation of the central axes. The calculation of the area, the moments, and the product of inertias with respect to the central axes is necessary. The formula for calculating this coefficient is presented as a definite integral of a non-analytical function determined point by point along the direction of the application of the shear force. This function is based on the calculation of the partial static moments. The calculation of the latter is based on the development of a technique by subdividing the upper part of the section into adjacent common triangles at one point for the full solid section or by segments on the boundary for the thin-walled section. To speed up the process of numerically calculating this integral with high precision and reduced time, Gauss Legendre quadrature of order 40 is used. The calculation of the distribution of the tangential stress as well as its maximum value is determined. A shear shape coefficient is therefore determined. In the second part of this work, an application is made for the static calculation by the FEM of a hyper static beam with a view to determining the influence of this coefficient on all the parameters of resistance and bending stiffness as a correction of the classical model of bending by the FEM. A study of the error made by the classical bending model on our shear effect model is presented. A coefficient of efficiency of a section is presented.

Analysis on Polarization Responses of Resonators for Frequency-Coded Chipless RFID Tags

This article presents a method to analyze co- and cross-polarized responses of the resonators exploited in the development of frequency-coded chipless radio frequency identification (RFID) tags. The method uses the complex radar cross Section (RCS) matrix to characterize the polarization of the scattered response of resonators. Four different symmetry states are introduced, and all resonators are classified under each category based on their structures. Then, the complex RCS matrix is obtained for each group. Then, four different resonators, each representing the respective symmetry state, are simulated and measured to validate the theory. To highlight the advantages of the presented method, two significant applications of the method are investigated. The presented theory is used in the first application to determine resonator structures for designing orientation independent cross-polarized tags. The proposed technique not only accelerates the design of frequency-coded chipless RFID tags but also helps figure out proper geometry for resonators with cross-polarized responses with minimum amplitude deviation at different azimuth plane orientation angles. In the latter application, we predict co- and cross-polarized responses of a tag at arbitrary orientation angles, using one initial measurement. This prediction provides a thorough insight into the co- and cross-polarized responses of tags at different orientation angles.

Broadband achromatic metalens for linearly polarized light from 450 to 800 nm.

Metalens is a planar optical component that uses nanostructures with a thickness on the order of the wavelength to manipulate the wavefront of the incident light. A key problem, especially in color imaging and display applications, is the correction of chromatic aberration, which is an inherent effect caused by the dispersion of periodic lattices and resonance modes. However, the current achromatic metalenses either use the PB phase method that is only valid for circularly polarized light or nanostructures with complex cross sections that are difficult to manufacture. Here, we designed a broadband achromatic metalens for linearly polarized light from 450 to 800 nm. Rectangular titanium dioxide nanofins of various lengths and widths were applied to modulate the phase and dispersion of the incident light. The metalens can fulfill three target phases simultaneously by using an optimization method. The designed metalens has a stable focus from 450 to 800 nm with an average focusing efficiency of 64%. It can be potentially applied in microscopes, lithography machines, sensors, and displays.

Viscoplastic flow in a pipe of complex cross section with stick–slip at the wall

The Poiseuille flow of a Bingham fluid with the yield slip condition at the wall is examined. The governing equations are solved employing the accelerated augmented Lagrangian method for both the viscoplastic model and the yield slip equation. We solve numerically the flow in pipes with different cross sections: equilateral and isosceles triangles, L-shape, and hourglass-shape. The combined effects of viscoplasticity and slip on the flow have been investigated. The evolution of the unyielded regions has been studied. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are identified in ducts of various cross sections.

Dynamical spin susceptibility in La2CuO4 studied by resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) is a powerful probe of elementary excitations in solids. It is now widely applied to study magnetic excitations. However, its complex cross section means that RIXS has been more difficult to interpret than inelastic neutron scattering (INS). Here we report $\ensuremath{\sim}37$ meV resolution RIXS measurements of the magnetic excitations in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$, the antiferromagnetic parent of one system of high-temperature superconductors. At high energies ($\ensuremath{\sim}2$ eV), the RIXS spectra show angular-dependent $dd$ orbital excitations in agreement with previous RIXS studies but show new structure. They are interpreted with single-site multiplet calculations. At low energies ($\ensuremath{\lesssim}0.3$ eV), we model the wave-vector-dependent single magnon RIXS intensity as the product of the calculated single-ion spin-flip RIXS cross section and the dynamical structure factor $S(\mathbf{Q},\ensuremath{\omega})$ of the spin-wave excitations. When $S(\mathbf{Q},\ensuremath{\omega})$ is extracted from our data, the wave-vector-dependence of the single-magnon pole intensity shows a similar variation to that observed by INS. Our results confirm that suitably corrected RIXS data can yield the genuine wave-vector and energy dependence of $S(\mathbf{Q},\ensuremath{\omega})$ for a cuprate antiferromagnet. In addition to spin waves, our data show structured multimagnon excitations with dispersing peaks in the intensity at energies higher than the single-magnon excitations.

A Novel Finite Element Model for Simulating Residual Stress in Laser Melting Deposition

The geometry of the cladding pass cross section cannot be easily predicted in laser melting deposition. Due to the huge difference between the actual and the predicted cross section, it is difficult to conduct numerical simulations. In this paper, the finite element method (FEM) with thermal–mechanical coupling is performed. A novel cladding pass cross section model, isosceles trapezoid model, is proposed. The comparisons between the isosceles trapezoid model and the traditional model (disk model and rectangle model) are performed in terms of geometrical deviation, heat dissipation, temperature field, and stress field. The results show that the geometrical deviation and heat dissipation between trapezoid model and disk model is small, and that between trapezoid model and rectangle model is large. The trapezoid model has an additional degree of freedom for modeling, i.e., contact angle, which helps to conform complex cross section geometry more flexibility. The results of temperature field and stress field show that the deviation between the isosceles trapezoid model and the traditional models is small on the upper surface of the sample, and rectangle model has worse prediction results than the other two models at the interface between cladding pass and substrate. Finally, the validation experiment is carried out and the stress is measured by laser ultrasound technique. The experimental result matches the FEM result based on isosceles trapezoid model.

Method of assessment of stress-strain state of timber-reinforced concrete structure with complex cross section

Problem statement. The application of timber structures is often limited by the size of the lumber, insufficient load-bearing capacity and rigidity of the elements. To overcome these limitations hybrid designs which rationally use materials with different characteristics are used in modern construction. The existing techniques do not take into account the peculiarities of the diagrams of deformation of structural materials (wood and reinforced concrete). The purpose of the article is to improve of methods for calculating wood-reinforced concrete structures, taking into account the stress-strain relationships of materials and the degree of joint work. Conclusion.A numerical-analytical method is proposed for the assessment of the stress-strain state of a timber-reinforced concrete structure with complex section, taking into account the deformation diagrams of materials and joints, as well as the degree of joint work. A considered structure consists of two components (reinforced concrete slab and timber beam) connected by shear elements (pins, bolts, screws, nails). It is supposed that the Bernoulli hypothesis is valid for the considered element; the deformations are linearly distributed along the height of the cross section, while a gap arises along the line between the components of the structure due to mutual displacement; structural components under load have equal deflections and curvatures of the longitudinal axes, and the connecting elements are uniformly spaced along of the structure. Determination of the internal deformations and stresses in a section of a structure is based on the condition of equilibrium of the external and internal forces in the section. The solution of the equations for "absolutely" joint work is performed, and the coefficient of joint work is introduced to take into account the redistribution of forces in the section due to the ductility of the joints. The obtained values of longitudinal deformations and curvatures are used to calculate the deformations of concrete and timber elements. Normal stresses are determined using the deformation diagrams of materials, then the strength checks are performed in accordance with the current regulatory documents.

Frequency shifts of the magnetic resonance of Rb and K atoms in the K-Rb tandem magnetometer

Collisions of alkali atoms in the ground state are accompanied by the exchange of electron polarization between the colliding atoms, which lead to the polarization transfer between particles. As a result of this process, the electronic orientation is transferred from the spin oriented atoms to unpolarized atoms, along with the polarization transfer, the magnetic resonance frequency shifts of polarized atoms occur too. In this work the magnetic resonance frequency shifts of arising from spin exchange collisions in a mixture of alkali potassium and rubidium atoms at the optical orientation of atoms are calculated. The situation when optical pumping by resonant polarized radiation is carried out only for atoms of the one kind is considered. The spin exchange process between alkali atoms was described in the formalism of the complex cross section for spin exchange process. The real and imaginary parts of the complex cross section were calculated using the interaction potentials of alkali atom dimers. The calculation of the frequency shifts is carried out on the basis of data on the interaction potentials for the following pairs of alkali atoms K-K, K-Rb and Rb-Rb. Maxwell averaging of the cross sections over the velocities was done and the temperature dependences of the magnetic resonance frequency shifts for K and Rb atoms were plotted.