Order Beam Research Articles

An isogeometric frictionless beam‐to‐beam contact formulation for hyperelastic Cosserat rods with unconstrained directors

AbstractWe present an isogeometric finite element formulation of frictionless beam‐to‐beam contact, using a Cosserat beam formulation with unconstrained directors. The beam's cross‐sectional deformation can be efficiently represented by director vectors. For the first order beam kinematics, Poisson locking due to the inability to represent linear in‐plane strain field in the cross‐section is alleviated by an enhanced assumed strain (EAS) method [1]. We employ a Gauss point‐to‐surface contact formulation combined with an active set iteration and a penalty method. The beam's cross‐sectional boundary as well as the axis is parameterized by a NURBS (non‐uniform rational B‐spline) curve, so that the lateral boundary surface has at least C2‐continuity, which yields a continuous surface metric and curvature in the closest point projection [2]. Since we do not employ zero stress conditions, a three‐dimensional nonlinear constitutive law can be straightforwardly utilized. We present several numerical examples, where a compressible Neo‐Hookean material is particularly considered.

Nonlocal state-space strain gradient wave propagation of magneto thermo piezoelectric functionally graded nanobeam

Abstract In this work, the state -space nonlocal strain gradient theory is used for the vibration analysis of magneto thermo piezoelectric functionally graded material (FGM) nanobeam. An analysis of FGM constituent properties is stated by using the power law relations. The refined higher order beam theory and Hamilton’s principle have been used to obtain the motion equations. Besides, the governing equations of the magneto thermo piezoelectric nanobeam are extracted by developed nonlocal state-space theory. And to solve the wave propagation problems, the analytical wave dispersion method is used. The effect of magnetic potential, temperature gradient, and electric voltage in variant parameters are presented in graph.

First-order statistics of intensity and phase in Laguerre-Gauss speckles.

Laguerre-Gaussian (LG) beams are characterized by an azimuthal index or topological charge (m), associated with the orbital angular momentum, and by a radial index (p), which represents the number of the rings in the intensity distribution. We present a detailed, systematic study of the first-order phase statistics of the speckle fields created when LG beams of different order interact with random phase screens with different optical roughness. The phase properties of the LG speckle fields are studied in both the Fresnel and the Fraunhofer regimes using the equiprobability density ellipse formalism such that analytical expressions can be derived for the phase statistics.

Spin-Orbit Coupling in Quasi-Monochromatic Beams

We investigate the concept that the value of the spin-orbit coupling is the energy efficiency of energy transfer between orthogonal components. The energy efficiency changes as the beam propagates through the crystal. For a fundamental Gaussian beam, its value cannot exceed 50%, while the energy efficiency for Hermite–Gaussian and Laguerre–Gaussian beams of higher orders of the complex argument can reach a value close to 100%. For Hermite–Gauss and Laguerre–Gauss beams of higher orders of real argument, the maximum energy efficiency can only slightly exceed 50%. It is shown that zero-order Bessel–Gauss beams are able to achieve an energy efficiency close to 100% when generating an axial vortex in the orthogonal component in both monochromatic and polychromatic light, while for a polychromatic Laguerre–Gauss or Hermite–Gauss beam of a complex argument, the energy efficiency reduced to a value not exceeding 50%. The spin angular momentum is compensated by changing the orbital angular momentum of the entire beam, which occurs as a result of the difference in the topological charge of the orthogonally polarized component by 2 units.

An analysis of vibration and buckling behaviors of nano-composite beams reinforced with agglomerated carbon nanotubes via differential quadrature finite element method

This article aims to investigate the buckling and free vibration behaviors of nanocomposite beams reinforced with functionally graded (FG) agglomerated carbon nanotubes (CNTs) in polymeric beams matrix. In order to estimate the material properties of the FG CNTs reinforced beam, the Eshelby–Mori–Tanaka rule on the basis of equivalent fiber is employed. Moreover, the Lagrange’s principle is used to achieve the governing equations under supposition of the refined higher order beam theory without need of any shear correction factor. The differential quadrature finite element method (DQFEM) as a robust and precise numerical procedure is utilized to achieve the natural frequencies and buckling loads with various boundary supports. Then, the assessment of the effects of different factors such as of CNTs agglomeration parameters, different patterns of CNTs distribution, length to thickness quotients, and mixed boundary conditions on the vibrational and buckling responses of agglomerated CNTs reinforced beam are explored. It is concluded that the current numerical solution based DQFEM is efficient and accurate for predicting the mechanical behavior of the nanocomposite structures. Moreover, the stability and vibration responses of the NC beams can be significantly affected by tailoring the agglomeration parameters.

Toward a diffraction limited light source

This paper introduces a storage ring lattice design for synchrotron radiation sources which fulfills all the required features for the realization of a diffraction limited light source. Insertion devices half gaps of 2.5 mm are assumed and enabled by the design of dedicated straight sections. The use of long straight sections is possible for such a lattice and led to the definition of a set of transparency conditions used to minimize the effect of such insertions for on- and off- energy beam dynamics. The design proposed enables an extremely long Touschek lifetime and beam accumulation. A real case study will be shown for large circumference storage ring upgrade lattices.17 MoreReceived 17 October 2022Accepted 17 January 2023DOI:https://doi.org/10.1103/PhysRevAccelBeams.26.021601Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeam dynamicsBeam trackingCollimationHigher order beam dynamicsLattices in beam opticsSingle-particle dynamicsAccelerators & Beams

The collimation of the Bessel Gauss beams using a composite optical system consisting of multiple pairs of Cassegrain antennas

Collimation of Bessel Gauss beams has always been a problem and has hindered its application in free space optical communication. In this work, the Bessel Gauss beam can have a diffraction-free distance of 10,000 km with the aid of a new composite optical system. The optical system consists of several pairs of Cassegrain antennas, each pair of which allows the divergence angle of the beam to be compressed to one-tenth of its original size. Bessel Gauss beams with a topological charge of one to five can achieve an efficiency of 81.05%, 88.68%, 88.68%, 85.75%, 80.12% when the wavelength of beams is 860 nm, after 10,000 km propagation in the composite optical system. At this time, the corresponding divergence angles of the first to fifth order beams are 0.118 μrad, 0.141 μrad, 0.169 μrad, 0.184 μrad, 0.192 μrad, respectively. We give a relationship between the ability to compress the angle of divergence of the system and the number of primary and secondary mirror pairs contained in the antenna and the focal length ratio of primary and secondary mirrors, which is verified by calculations that guide the design of the new system. It is possible to design an antenna suitable for different application scenarios by changing the number of primary and secondary mirror pairs and the focal length ratio of the primary and secondary mirrors.

ABCD transfer matrix model of Gaussian beam propagation in Fabry-Perot etalons.

A numerical model of Gaussian beam propagation in planar Fabry-Perot (FP) etalons is presented. The model is based on the ABCD transfer matrix method. This method is easy to use and interpret, and readily connects models of lenses, mirrors, fibres and other optics to aid simulating complex multi-component etalon systems. To validate the etalon model, its predictions were verified using a previously validated model based on Fourier optics. To demonstrate its utility, three different etalon systems were simulated. The results suggest the model is valid and versatile and could aid in designing and understanding a range of systems containing planar FP etalons. The method could be extended to model higher order beams, other FP type devices such as plano-concave resonators, and more complex etalon systems such as those involving tilted components.

FLEXURAL ANALYSIS OF THERMALLY LOADED SYMMETRIC SANDWICH BEAM

In the present paper, an attempt has been made to study the effect of temperature gradient on simply supported symmetric sandwich beam. A Navier’s solution technique is used. The temperature profile is assumed to be linear across the thickness of a sandwich beam. A higher order beam theory (HBT) is used to include the effect of shear deformation on thermal flexural response of the sandwich beam. The theory satisfies the shear stress free boundary condition at the top and bottom surfaces of the sandwich beam. No shear correction factor is required. The principle of virtual work is used to obtain the governing equations and boundary conditions. A program has been developed in FORTRAN-77 to obtain thermal stresses and displacements in the sandwich beam for various aspect ratios. The numerical results are presented for moderately thick and thin sandwich beams to assess the performance of the theory. The validity of the present theory is verified by comparing the results with the results available in the literature. The present results are in good agreement with the results of other theories.

Effect of two-dimensional material distribution on dynamic and buckling responses of graded ceramic-metal higher order beams with stretch effect

The contribution provided in this article is to examine free vibration and stability response of bidirectional graded material beams (BDFB) considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence are integrated for accurate results. The beam materials features are expected to depend on gradation pattern over the length and transverse directions via power law form. Lagrange’s principle is employed in order to extract the governing equations of motion. A novel approach namely differential quadrature-based Galerkin method (DQGM) is used as an effective and accurate semi-analytical tool to compute the critical stability loads and natural frequencies of (BD-FG) beam for the first time. The approach takes features from simplicity and reduced computational cost of the DQ in combination with the efficacy of the Galerkin method for its analytical aspect and easy dealing with mixed boundary conditions resulting in more accurate results. The correctness of the results obtained from the present approach for two-directional functionally graded materials (FGMs) beams have been verified. Finally, the impacts of design parameters such as material grading exponent distributions, length to thickness ratios, porosity amount, and end support types on the natural frequencies and maximum of stability loads related to the present 2D-FGM beams are examined.

On uncertainty modeling of thermoelastic vibration for porous nanosandwich beams with gradient core based on nonlocal higher order beam model

In the present paper, the size-dependent random thermoelastic vibration analysis of porous nanosandwich beams with gradient core are demonstrated based on the nonlocal higher order beam model. The nonlocal elasticity theory incorporation with the higher order shear deformation theory is used to describe the kinematic and constitutive relations. The governing equations are obtained from minimum potential energy principle. The finite element method is used to solve the governing equations. Three types of the FG sandwich nanobeams with three types of porous cores are taken into account, and the influences of these structures and porosity types on the deterministic and stochastic behavior of sandwich beams are thoroughly discussed. Initially convergence and validation study is preformed to validate the present theoretical model by comparing the present results with the several previous works and Monte Carlo Simulation (MCS). Further, a comprehensive parametric study is performed to demonstrate the influence of the length to thickness ratio, degree of uncertainty in the material properties, nonlocal parameter, porosity distribution type, porosity volume fraction, temperature change, and gradation of material on the deterministic and stochastic behaviors of the FG nanosandwich beams. The developed model and computed results may be useful in the precise and reliable design of the components of nanodevices and systems.

Performance improvement of focused acoustic-vortex tweezers constructed by a hyperboloidal acoustic lens and a circular array

Although the traditional focused acoustic-vortex (FAV) beams can be realized by a spherical acoustic lens, the manipulation performance still suffers from the incomplete focusing at a preassigned point. In the current study, by applying the Fermat’s principle to the phase-coded circular array of planar sectorial sources, a hyperboloidal concave acoustic lens determined by the refractive index and the focal length is designed to construct hyperboloidal-focused acoustic-vortex (H-FAV) tweezers to improve the manipulation capability in a minimized focal region. Compared with the FAV beam, the peak-pressure of the H-FAV tweezer is obviously enhanced in a smaller-sized focal region, and the trapping capability of the tweezer can be greatly improved by the strengthened acoustic gradient force due to the smaller vortex radius. With the established 16-channel system, H-FAV beams of different orders are built using a hyperboloidal lens manufactured by 3-D printing. The experimental acoustic fields of pressure and phase show good agreements with numerical results and attest to the improved performance of H-FAV tweezers. Moreover, benefiting from the flexible and controllable focusing, the H-FAV tweezers exhibits prosperous perspectives in high-precision application fields of acoustic focusing, ultrasonic therapy, acoustic levitation and particle manipulation.

Scattering properties of acoustic beams off spinning objects: Induced radiation force and torque

Understanding the acoustic scattering and radiation force and torque of an object is important in various fields, such as underwater communication, acoustic imaging, and noninvasive characterization, as well as biomedical ultrasound. Generally, acoustic scattering is considered for static (non-moving) objects and the impinging signal is typically a plane wave. Here, we consider scattering off cylindrical objects in spinning motion around the axis of rotational symmetry. We investigate the radiation force and torque induced by various incident signals, e.g., cylindrical diverging and converging beams as well as quasi-Gaussian beams of different orders. It is assumed in this study (unless otherwise stated) that the acoustic parameters of the objects (density and compressibility) are identical to those of the surrounding medium, in order to isolate the effects purely attributed to rotation. The scenario of a spinning inhomogeneous object is also shown to play a prominent role for generating torque with single plane waves. Our findings may add to the current interest in time-varying and moving metamaterials and open vistas in manipulation of movement and position of ultra-small objects via acoustic beams.

Polarization-sensitive direct laser patterning of azopolymer thin films with vortex beams.

Laser patterning of thin films of materials is widely used for the fabrication of one-, two- and three-dimensional functional nanomaterials. Using structured laser beams with a complex structure of amplitude, phase, and polarization distributions allows one to significantly simplify and speed up the procedure of manufacturing nano- and microstructures with a complex shape, such as a spiral structure. Here, we demonstrate the use of vortex laser beams with a helical wavefront for the realization of spiral mass transfer in azopolymer films. The polarization sensitivity of this material allows us to demonstrate the formation of different three-dimensional structures in the case of linearly or circularly polarized vortex beams of different orders. The presented theoretical analysis shows that the profile of the fabricated structures is defined by the structure of the longitudinal component of the incident radiation, and thus can be easily controlled with the polarization state of the radiation without the need to change the amplitude-phase structure of the beam.

Vibration analysis of cracked beam based on Reddy beam theory by finite element method

The lateral vibration of cracked isotropic thick beams is investigated. Generally, the analysis of thick beam based on line elements can be undertaken using either Timoshenko beam theory or a third order beam theory (TSDT) such as Reddy beam theory. TSDT is superior to Timoshenko beam theory, as it eliminates the need for a shear correction coefficient. However, there is no available solution for a cracked beam based on Reddy beam theory which is the main focus of this paper. The investigated beam is divided into several elements where their stiffness and mass matrices are derived using Reddy beam theory. Each element has two nodes with 3 degrees of freedom (1 lateral and 2 rotational) at each node. The crack was modeled using two rotating springs with stiffnesses that varied with crack depth. These elements are used to connect the adjacent beam elements. The impact of boundary conditions, slenderness ratio, crack location, and crack depth are investigated. In addition, experimental and finite element analyses of cracked steel beams is undertaken to validate the results of the present model. The results show that the maximum deviation between the analytical and the experimental results is less than 3% up to the third mode shape.

Ring focus reflector design for topological charge multiplexing based on a perfect vortex beam.

A ring focus reflector is proposed for transmitting a perfect vortex (PV) beam, and the transmission characteristics of the PV beam with different topological charges in free space after passing through the reflector are studied. The reflector parameters can be determined by fitting the structural formula, and PV beams of different orders transmit with small spot sizes at the same time. The transmission trajectory calculated by the diffraction formula is consistent with the ray tracing results. The research results show that the reflector can achieve a high level of transmission efficiency of beams with different topological charges, which is conducive to the multiplexing of PV beams.

Flattop Beam Shaping Using Hybrid Gratings

A new method of laser beam shaping with hybrid gratings is presented. The hybrid gratings consist of a blazed grating and a gradient binary grating. The blazed grating is used to separate the incident Gaussian beam into zero order and nonzero diffraction orders. A filter is used to block the nonzero order beams and obtain the zero orders with the desired shape. The gradient binary grating is used to improve the energy distribution of the inside area of the geometric shape. A phase hologram designed with the desired shape and hybrid gratings, is loaded on a phase-only spatial light modulation to achieve arbitrary geometric flattop shapes with high uniformity. Squared and hexagonal shaping experiments demonstrated that the presented method can convert a Gaussian beam into a flattop beam with steepness edge and high uniformity. Experimental results show that the beam non-uniformity is less than 0.037.

Novel bi-layer beam elements for elastic fracture analysis of delaminated composite beams

A general finite element method is proposed for linear elastic fracture analysis of delaminated bilayer composite beams. An interface deformable bilayer beam model is adopted in modeling the virgin portions of bilayer beams, and it is capable of guaranteeing the continuity condition of internal forces at the tip of delamination because the bilayers are modeled as two separate shear deformable sub-beams and both the interface normal and shear compliances are introduced to account for interface deformation. The stiffness matrices of bilayer beams using the linear and quadratic interpolation polynomials are both derived using the principle of minimum potential energy. Then, a finite element program is developed by assembling the element stiffness matrices of virgin and delaminated portions of bilayer beams and applying the corresponding equivalent nodal forces. Two typical fracture specimens (i.e., single leg bending and end-notched flexure bilayer beams) are analyzed using the proposed bilayer beam elements. The computed displacement and energy release rate are compared well with those of analytical solutions, and the mode components of energy release rate for single leg bending specimen are also obtained using the virtual crack closure technique. It demonstrates that the proposed novel bilayer beam elements are capable of effectively and efficiently predicting the displacement and energy release rate (including its mode components) of delaminated bilayer beams. The developed bilayer beam element is general in nature and accurate and efficient in particular, because it can achieve the same accuracy as the high order beam theory and be easily implemented in the existing commercial finite element software.

Symplectic analysis of thin-walled curved box girders with torsion, distortion and shear lag warping effects

Shear lag effect and torsional and distortional warping can significantly affect the performance of thin-walled curved box girders used in modern bridge engineering. The structural behaviour of these bridges exhibits complexity due to coupled bending and torsion together with warping effects of non-uniform torsion, distortion and shear lag. A practical method of analysis, based on the symplectic approach, with the same perspective as the Higher Order Beam Theories, is presented for overcoming the difficulties of numerical approaches via the Finite Element Method. In this paper, the Hamiltonian Structural Analysis method implements the analysis of the shear lag effect together with non-uniform torsion and distortion, for curved box girder bridges. The examples given can allow engineers to evaluate the effects of the negative shear lag phenomenon and the distribution of axial stresses in box slabs and webs, due to different warping effects, which strongly influence thin-walled box sections subjected to point loads and restrained areas.

Vibration analysis of laminated composite higher order beams under varying axial loads

The article develops a computational mathematical model to predict the dynamic response of composite laminated beam under variable axial load using a third higher order shear deformation beam theory, for the first time. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equations of composite beam are used on the basis of plane stress problem. The variable axial load is distributed along the axial direction by: constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived using Hamilton's principle. Then, the variable coefficients-differential equations of motion are discretized in spatial direction by using numerical differential quadrature method (DQM). The proposed model is verified with previous works available in literature. Parametric analyses are developed to present the influence of axial load type, orthotropy ratio, slenderness ratio, fiber orientations, and boundary conditions on the natural frequencies of composite beams. The present enhanced model can be used specially in designing of spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.