Planar Beam Research Articles

A refined shear deformation theory of an asymmetric sandwich beam with porous core: Linear bending problem

This paper is devoted to a sandwich beam with an asymmetric structure under uniformly distributed load. The first end of this beam is simply supported, while second end is clamped. The individual nonlinear deformation function of a plane beam cross section – the shear effect with consideration of the classical shear stress formula is analytically developed. Displacements, strains and stresses taking into account the individual nonlinear deformation function for successive layers of this beam are elaborated in detail. The system of two differential equation of equilibrium of this beam, based on the principle of stationary potential energy, is obtained. This system of equations is precisely solved analytically, according to the theory of differential equations. The individual nonlinear deformation functions, shear stresses and deflections of two cases of sample beams are determined in detail: the first with variable core porosity in the direction of the beam depth, the second with constant core porosity – standard sandwich structure. The calculations results specified in Tables and graphically presented in Figures.

Geometrically consistent nonlinear plane strain and stress constitutive models: Application to soft-material oscillations

Position-gradient constraints are used in this study to develop new geometrically consistent plane strain and stress constitutive models for the nonlinear large-displacement analysis of soft materials. The position gradients are used to define strain and stress constraints that enter into the formulation of the deformation tensor, strain-energy density function, and new constitutive models. The new approach is applied to three nonlinear hyperelastic constitutive models for incompressible materials: Neo-Hookean, Mooney Rivlin, and Yeoh Models. The underlying geometric plane-stress and plane-strain assumptions are preserved by using the finite elements (FE) of the absolute nodal coordinate formulation (ANCF). Limitations of widely used incompressibility penalty functions that produce stresses at initial stress-free configurations are discussed. Several numerical examples developed using planar ANCF shear-deformable beam and rectangular elements are used to assess the proposed formulation and verify its results using spatial solid elements implemented in commercial FE software. It is demonstrated that the ANCF plane-stress and plane-strain formulations for the incompressible materials predict accurately soft-material oscillations, demonstrating that stiffer behavior can be attributed to material-model inconsistencies and cannot always be attributed to locking.

Modeling Method for Static Large Deflection Problem of Curved Planar Beams in Compliant Mechanisms Based on a Novel Governing Equation

Abstract Slender beams serve as typical flexible components to transfer motion, force, and energy in compliant mechanisms. Therefore, the accurate and efficient kinetostatic modeling for the slender beams is highly needed in the synthesis and analysis of compliant mechanisms. Several impressive and great modeling methods have been completed by the pioneering researchers based on the governing equation of slender beams, which can solve the deflection of the beam while the beam-tip loads are known. However, parts of the beam-tip loads are unknown in some scenarios and the traditional governing equation becomes inefficient in these scenarios. The aim of this paper is to propose a novel modeling method for the compliant mechanism, which can solve the large deflection problem without iterative algorithm. In this research, a novel governing equation of slender beams has been established based on Castigliano’s principle and simplified by the differential geometry. In the proposed governing equation, the statically force equilibrium equations and geometric constraint equations between different slender beams can be established in the boundary conditions, therefore the model of compliant mechanisms can be solved directly even if parts of the beam’s tip loads and displacements are unknown. The proposed governing equation provides the deformed shapes and cross-sectional loads of the slender beams, which help the designer to check the mechanical interference and strength in the design process. The numerical examples are presented to demonstrate the feasibility of proposed method.

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Nonlinear behavior analysis of structures using finite element methods requires multiple iterative solutions. Therefore, improving computational efficiency while ensuring the accuracy of nonlinear calculations is crucial. In this paper, a new geometric nonlinear analysis method for planar beam structures is proposed, based on the co-spinning method and the substructure method, using a substructure containing two planar beam elements as an example. The co-spinning method accurately calculates small deformations by subtracting rigid body displacement from the large displacement of the structure. The substructure method condenses the degrees of freedom of internal nodes into boundary nodes, greatly reducing the order of the nonlinear equilibrium equation group of the structure. The two methods are combined, and a calculation program is developed using the arc length method, which has good performance in solving nonlinear equation groups. Two classic examples are used to verify the correctness of the proposed method by comparing the results with existing literature.

Manipulating self-focusing beams induced by high-dimensional parabolic umbilic beams

The excellent property that the intensity of autofocusing beams in the focal plane increases exponentially, makes them especially beneficial for biomedical treatment. We experimentally generate tunable (2+1)-dimensional circular parabolic umbilic beams (CPUBs) for the first time based on the high-dimensional diffraction catastrophe integral, which is determined by the potential function. Such CPUBs have circular and symmetrical intensity distributions in space through radial symmetry transformation. Due to the flexibility of high dimensionality, these light beams have rich light field structures and self-focusing property. Where, the maximum intensity suddenly increases by orders of magnitude in the focal plane. Unlike the classical circular Airy beams, CPUBs exhibit multiple self-focusing points along the optical axis and a needle-like structure during propagation, which can be affected by manipulating the control parameters. The rich properties provide a new perspective for exploring the novel physical mechanisms and phenomena in autofocusing beams. The experimental results verify the correctness of the numerical simulations. CPUBs greatly enrich the autofocusing beam family and will be advantageous for medical treatments, optical micromanipulation, and microscopic imaging.

Seismic behaviour of a wall-type concrete-filled steel tubular column with an end plate steel beam reinforced joint

To solve the problem of square concrete-filled steel tubular columns (CFSTCs) protruding from the walls and occupying indoor spaces, this study proposed a wall-type concrete-filled steel tubular column (WCFSTC) with end-plate steel beam in-plane and out-of-plane joints. The construction details, assembly process, and performance parameters of the WCFSTC with end-plate steel-beam-reinforced joints are presented. The seismic performance of four full-scale specimens under a low-cycle horizontal load, influence of side-plate height on the seismic performance of the specimenswere studied based on the test. According to the test results, the ductility, hysteresis curve, skeleton curve, and energy-dissipation capacity of the specimens were studied. A finite element model was developed and verified experimentally. The effect of the end-plate and column thickness on the seismic performance of the joints was investigated using the finite element model with variable reference analysis of the end-plate and column thickness. The results showed that the specimens exhibited good seismic performance whilst meeting the requirements of ‘strong joints and weak members’, and the thickness of the end plate had an important influence on the seismic performance of the specimens.

Nonlinear Stress-Free-State Forward Analysis Method of Long-Span Cable-Stayed Bridges Constructed in Stages

Structural analysis and construction control of staged-construction processes are major subjects in the context of modern long-span bridges. Although the forward and backward analysis methods are able to simulate situations, their main disadvantage is that they usually apply the stage superposition principle. In the actual construction process, due to changes made to the plan, the construction process needs to be adjusted at any time, and it is difficult to implement the construction process in complete accordance with the established plan. As a result, the existing simulation method based on the incremental structural analysis of each construction stage has poor adaptability to such adjustments. In this study, considering the strong geometric nonlinear behavior of the long-span cable-stayed bridge construction process, the geometrically nonlinear mechanical equations of the staged-construction bar system structure were derived. The minimum potential energy theorem was used by introducing the concept of the stress-free-state variable of the structural elements. The equation reflects the influence of the change in the stress-free-state variables of structural elements on the completion state of the structure. From the analysis of the geometrical condition that the equilibrium equation holds, the stress-free installation condition of the closing section of the planar beam element structure was obtained. A new simulation method for long-span cable-stayed bridge construction has been proposed, which is called the stress-free-state forward analysis. This method can directly obtain the intermediate process state of cable-stayed bridge construction without performing stage-by-stage demolition calculations, and causing the internal force and deformation of the completion state to reach the design target state. This method can realize the simulation of multi-process parallel operation in construction, and solves the problem of automatic filtering of temporary loads. To illustrate the application of the method, a long-span cable-stayed bridge was analyzed.

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.

Многолучевая антенна с полным азимутальным углом обзора на основе многослойной геодезической линзы с осевой симметрией

A multibeam antenna with a full azimuthal survey based on a cylindrical lens with axial symmetry in the form of a set of layers, each of which is a metal-dielectric geodesic lens with a shell, is proposed and investigated. A cylindrical lens converts the fields of feeds located on a circle centered on the axis of symmetry in the plane of its base into directed beams in the same plane. The analysis of a multibeam lens antenna with metal horn and metal-dielectric feeds was carried out by numerical simulation using the finite element method.

Ultrasound Speckle Decorrelation-Based Blood Flow Measurements.

Ultrasound imaging is the preferred noninvasive technique to measure blood flow to diagnose cardiovascular disease such as heart failure, carotid stenosis, and renal failure. Conventional ultrasound techniques such as Doppler ultrasound, ultrasound imaging velocimetry, vector Doppler and transverse oscillation beamforming have been used for blood flow velocity profile measurement. However, these techniques were limited to measuring blood flow velocities within the 2-D lateral (across the ultrasound beam) plane of a vessel, and the blood flow velocity profile was derived by assuming that blood vessels have a circular cross-section with axis symmetry. This assumption is incorrect because most vessels have complex geometries, such as tortuosity and branches, and an asymmetric flow profile in the presence of vascular plaque. Consequently, ultrasound speckle decorrelation has been proposed to measure blood flow from transverse views of blood vessels wherein the ultrasound beam is perpendicular to the vessel axis. In this review, we present a summary of recent progress in ultrasound speckle decorrelation-based blood flow measurement techniques.

Comparison of Aerosol Emissions during Specific Speech Tasks

Recent investigations into the behavior of aerosolized emissions from the oral cavity have shown that particulate emissions do indeed occur during speech. To date, there is little information about the relative contribution of different speech sounds in producing particle emissions in a free field. This study compares airborne aerosol generation in participants producing isolated speech sounds: fricative consonants, plosive consonants, and vowel sounds. Prospective, reversal experimental design, where each participant served as their own control and all participants were exposed to all stimuli. While participants produced isolated speech tasks, a planar beam of laser light, a high-speed camera, and image software calculated the number of particulates detected over time. This study compared airborne aerosols emitted by human participants at a distance of 2.54cm between the laser sheet and the mouth. Statistically significant increases in particulate count over ambient dust distribution for all speech sounds. When collapsed across loudness levels, emitted particles in vowel sounds were statistically greater than consonants, suggesting that mouth opening, as opposed to the place of vocal tract constriction or manner of sound production, might also be influential in the degree to which particulates become aerosolized during speech. The results of this research will inform boundary conditions for computational models of aerosolized particulates during speech.

An S‐band wide beam miniaturized omnidirectional circularly polarized antenna

AbstractA wide beam miniaturized broadband omnidirectional circularly polarized antenna operating at S‐band is proposed. It is composed of a hub‐shaped circular horizontally polarized radiator, a vertically polarized radiator consisting of a monopole and eight shorting‐circuited pins, and a coupling feed device. The measured results indicate that the impedance matching band of |S11| < −10 dB is from 2.15 to 2.75 GHz (24.4%), and the band of the axial ratio <3 dB is from 2.2 to 2.7 GHz (20.4%). The gain of the antenna is about 1 dB, and the noncircularity in the azimuth plane is <1.2 dB. In addition, the antenna has the characteristics of wide axis ratio beam in the pitch plane with sizes of 0.68 λ0 × 0.68 λ0 × 0.14 λ0. The antenna is very suitable for satellite receiving system and short‐range wireless communication system.

Optimization of 12Х18Н9Т-Steel Processing by Ring Laser Beams

Using the MOGA genetic algorithm built into the DesignXplorer module of the ANSYS Workbench program, optimization of laser processing of 12Х18Н9Т-steel by annular beams has been performed. The calculation of temperature fields has been carried out taking into account the dependence of the thermophysical properties of the material on temperature by the finite element method in the ANSYS Workbench program. A regression model has been obtained for processing 12Х18Н9Т-steel by annular laser beams using a face-centered variant of the central compositional plan of the experiment. The power density and duration of laser radiation pulses, the outer and inner diameters of the laser beam in the processing plane were used as variable factors. The penetration depths of the material and the maximum temperatures in the laser processing zone were used as responses. The influence of processing parameters on the penetration depths of the material in the laser impact zone and the maximum temperature values has been evaluated. It has been established that the depth of penetration of the material and the maximum temperatures are most affected by the power density of laser radiation. Optimization of laser processing of 12Х18Н9Т-steel by annular beams was carried out by setting the limiting values of the maximum tempe-rature in the processing zone for three variants of the minimum penetration depth. The parameters obtained as a result of optimization using the MOGA algorithm and the parameters obtained as a result of finite element modeling are compared. The maximum relative error of the results when determining the maximum temperatures did not exceed 1 % and when determining the maximum penetration depths did not exceed 6 %.

A Rotationally Symmetric Multifocal Pearcey Beam with a Polygonal Profile

AbstractThe polygonal multifocal propagation properties and particle trapping experiments of a new kind of power‐exponential‐phase vortex chirped circular Pearcey Gaussian beam are investigated. Theoretical and experimental results show that it is possible to adjust the position and transverse spatial distribution of the beam in focal plane, as well as to make the transverse intensity distribution emerge an arbitrary polygonal profile by changing the distribution factor and vortex topological charge. Stable trapping of multiple particles is achieved in the experiment with transverse intensity fields in the polygon plane with different topological charges.

Multibeam Antenna with a Full Azimuth Field Angle Based on a Layered Metal-Dielectric Cylindrical Lens

A multibeam antenna based on a layered lens with axial symmetry in the form of a set of dielectric disks with a refractive index gradient along the radius, which are located between metal disks, is proposed and investigated. A layered lens converts the fields of feeds located on a circle centered on the axis of the lens in the plane of its base into highly directed beams in the same plane. A synthesis of a layered lens is carried out, the layers of which are made in the form of a set of dielectric rings of variable thickness. The analysis of a multibeam lens antenna with metal-dielectric feeds was carried out by numerical simulation using the finite element method.

3D structured Bessel beam polarization and its application to imprint chiral optical properties in silica

Polarization plays a crucial role in light–matter interactions; hence its overall manipulation is an essential key to unlock the versatility of light manufacturing, especially in femtosecond laser direct writing. Existing polarization-shaping techniques, however, only focus on their manipulation in the transverse plane of light beams, i.e., two-dimensional control. In this paper, we propose a novel passive strategy that exploits a class of femtosecond laser written space varying birefringent elements to shape the polarization state along the optical path. As a demonstration, we generate a three-dimensional structured Bessel beam whose linear polarization state slowly evolves along the focus (typ. 90° within 60λ). Such a “helically polarized” Bessel beam allows imprinting “twisted nanogratings” in SiO2 glass which result in an extrinsic optical chirality at a micrometric scale and own a high optical rotation. Our work provides new perspectives for three-dimensional polarization manipulation and insights into applications in structured light, light–matter interaction, and chiral device fabrication.

Impacts of Aerosol Scattering Attenuation on Free-Space Optical Communication in Owerri, Nigeria

In spite of the several benefits of using free-space optical (FSO) communication systems as complementary platforms for next-generation networks, the existence of atmospheric disturbances such fog and scintillations are key sources of signal impairment that affect system performance. Thus, it is crucial to learn about the specific weather patterns of the areas where FSO lines will be installed. The purpose of this work is to estimate the availability performance of FSO lines broadcasting at both 850 nm and 1550 nm by performing a statistical analysis of meteorological visibility data gathered for Owerri in Nigeria over a 21-year period (2000-2021). The results shows that the visibility during the most common fog events in Owerri is 100 meters. The probabilities of encountering and exceeding the scattering attenuations associated with Owerri’s most common fog event are 0.0002 and 0.0229, respectively. This research could be expanded in the future by exploring the effects of varying localized climatic conditions on the many forms of optical signals, such as plane, spherical, and Gaussian beam waves.

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.

Multi-focusing surface-emitting lasers.

Complete control of a beam pattern requires not only projecting a two-dimensional (2D) pattern but also focusing on a three-dimensional (3D) point cloud, which is typically achieved utilizing holography under the framework of diffraction. We previously reported direct focusing from on-chip size surface-emitting lasers that utilize a holographically modulated photonic crystal cavity based on 3D holography. However, this demonstration was of the simplest 3D hologram with a single point and single focal length, and the more typical 3D hologram with multiple points and multiple focal lengths has not yet been examined. Toward direct generation of a 3D hologram from the on-chip size surface-emitting laser, we here examined a simple 3D hologram featuring two different focal lengths with a single off-axis point in each to reveal the fundamental physics. Two types of holography, one based on superimposition and the other on random tiling, successfully demonstrated the desired focusing profiles. However, both types caused a spot noise beam in the far field plane due to interference between focusing beams with different focal lengths, especially in the case of the superimposing method. We also found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. Secondly, we demonstrated a typical 3D hologram with multiple points and focal lengths and successfully showed the desired focusing profiles by both methods. We believe our findings will bring innovation to mobile optical systems and pave the way to developing compact optical systems in areas such as material processing, micro fluidics, optical tweezers, and endoscopy.

The Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

AbstractThe Numerical Assembly Technique (NAT) is extended to investigate arbitrary planar frame structures with a focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and coupling conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this improvement by investigating the condition number of the system matrix and also by the use of variable precision arithmetic.