Fractional Fourier transform of a higher-order cosh–Gaussian beam

A higher-order cosh–Gaussian beam is an appropriate model to describe the flattened laser beam. The fractional Fourier transform (FRFT) is applied to treat the propagation of higher-order cosh–Gaussian beams. An analytical expression for a higher-order cosh–Gaussian beam passing through a FRFT system has been derived. By using the derived expression, the properties of a higher-order cosh–Gaussian beam in the FRFT plane are graphically illustrated with numerical examples.     

Uncertain dynamic response of a deterministic elastic–plastic beam

The counterintuitive phenomenon of elastic–plastic beam dynamics was demonstrated by Symonds and Yu (ASME J Appl Mech 1985;52:517). An analytical model has been developed to explain this phenomenon from a deterministic viewpoint. However, experimental evidence in (Int J Impact Eng 1991;11(3):341; Int J Impact Eng 1991;11(4):445) showed that the response of this deterministic system is uncertain, which is studied qualitatively in the present paper based on parametric sensitive characteristics of the deterministic system and parametric uncertainty of the studied system. FEM and Monte Carlo method are applied to study this phenomenon.     

Vectorial structure of Ince–Gaussian beam in the far field

By means of the vector angular spectrum representation of the electromagnetic beam and the method of stationary phase, the analytical vectorial structure of the Ince–Gaussian beam has been presented in the far field. The amplitude distributions of the Ince–Gaussian beam and its TE and TM terms are investigated in the far field. The extreme cases of the ellipticity parameter tending to infinity or zero are also considered. Although the vectorial structures of different Ince–Gaussian beams are apparently distinct, the ratios of the amplitude distributions of the TE and TM terms to the whole beam amplitude are independent of the parity and the values of the radial and angular elliptic mode numbers. This research reveals the abundant and interesting internal details of the Ince–Gaussian beam in the far field.     

Microstructure and tensile properties of laser beam welded Ti–22Al–27Nb alloys

Ti–22Al–27Nb alloys were welded using the laser beam welding process. The microstructure characterization and the tensile properties of the laser beam welded joints were investigated. The experimental results showed that a well-quality joint could be obtained using laser beam welding method. The fusion zone of the welded joint was composed of B2 phase. The tensile strength of the joints at room temperature was basically comparable to that of the base metal and the tensile ductility of the joints achieved 56% of the base metal. The average tensile strength of the welded joints at 650 °C was tested to be about 733 MPa, with the elongation of 2.93%.     

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre–Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by a diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions.     

Microstructure of copper–AISI type 304L electron beam welded alloy

Abstract

Heterogeneous butt welding of copper and AISI type 304L stainless steel was carried out using the electron beam process. Examination by scanning and transmission electron microscopy has indicated the possibility of obtaining joints free of cracks and porosity. Energy dispersive microanalysis of the weld bead cross-section has demonstrated the presence of non-equilibrium phases. The results show that the binary Cu-Fe equilibrium diagram is unable to predict the weld microstructure even at the moderate cooling and solidification rates expected under the present welding conditions. The feasibility of the Cu-304L electron beam welding process is therefore hindered by the problem of microstructural stability of the joint because of possible phase transitions during the service life of welded components.     

Seismic behavior of hybrid fiber reinforced cementitious composite beam–column joints

This paper presents the experimental results of six exterior beam–column joints with different concrete composites under cyclic loading. Engineered cementitious composite with polypropylene fiber and hybrid cementitious composites (HCC) using three different types of fiber namely hooked end steel fiber; brass coated steel fiber and polypropylene fiber are explored in this study. The hysteresis behavior, ductility response, energy dissipation with damping characteristics, crack patterns and damage index of all tested specimens are analyzed and compared with the cyclic response of conventional specimens. The test results indicate that HCC increases load carrying capacity and enhances energy dissipation with increased stiffness retention over conventional specimens. At higher rotation, joint specimens with HCC manifest better damage tolerance capacity over conventional specimens. This investigation implies that the use of HCC in the joint region may be an alternative solution to significantly increase the shear capacity, damage tolerance capacity and member ductility.     

The M 2 factor matrix of a paraxial Laguerre–Gaussian beam

The M ² factor matrix of a paraxial Laguerre–Gaussian beam has been derived based on the combination of the M ² factor definition and introduced quantities such as the coupled beam’s half width square, the coupled M ² factor and 2×2 rotational matrix, when the beam is rotated around the propagation z-axis by an arbitrary azimuth angle α. The beam’s half widths at different distances from the beam waist along the z-axis, the M ² factors of the beam with different orders, and the track of M ² factor matrix elements versus α have been obtained by numerical simulation and analytical derivation. Results illustrate that by using the invariability of the M ² factor matrix, the beam quality of the mode with an arbitrary rotational angle can be easily evaluated. Like the M ² factor matrix of the Hermite–Gaussian mode, this M ² factor matrix is meaningful in the evaluation of the beam quality of a two-dimensional astigmatic or asymmetric laser beam.     

Experimental study of RC beam–column joints strengthened using CFRP composites

This paper presents an experimental study to strengthen the shear capacity of non-seismic joints using Carbon Fiber Reinforced Plastic (CFRP) materials. Eight exterior RC beam–column joint specimens including a non-seismic specimen, a seismic specimen and six retrofitted specimens with different configurations of CFRP sheets were developed and tested to find out an effective way to improve the seismic performance of the joints in terms of the lateral strength and ductility. The different configurations of CFRP sheets considered were the T-shape, L-shape, X-shape and strip combinations. The research focused on the effect of using CFRP sheets for enhancing strength and increasing ductility of the non-seismic beam–column joints. The test results showed that appropriately adding CFRP composites to the non-seismic specimen significantly improved the lateral strength as well ductility of the test specimens. Especially, the X-shaped configuration of wrapping, the strips on the column and two layers of the CFRP sheets resulted in a better performance in terms of ductility and strength.     

Reinforced concrete beam–column joint strengthened with carbon fiber reinforced polymer

An effective rehabilitation strategy is proposed to enhance the strength and stiffness of the beam–column joint in this study. An analytical model is proposed to predict the column shear of the joints strengthened with carbon fiber reinforced polymer (CFRP). Three full scale interior beam–column joints, including two specimens strengthened with CFRP and one prototype specimen, are tested in this study. The specimens are designed to represent the pre-seismic code design construction in which there is no transverse reinforcement. A new optical non-contact technique, digital image correlation (DIC), which can measure the full strain field of specimen, is used to measure and observe the full strain field of the joint. The experimental results show that the beam–column joints strengthened with CFRP can increase their structural stiffness, strength, and energy dissipation capacity. The rehabilitation strategy is effective to increase the ductility of the joint and transform the failure mode to beam or delay the shear failure mode. By observing the measured results, it is found that the mechanical anchorages can prevent the debonding of CFRP. Comparing the analytical and experimental results, the proposed model can accurately predict the column shear and shear strength of the joints strengthened with CFRP.     

Microstructure and mechanical properties of a new Al–Zn–Mg–Cu alloy joints welded by laser beam

A new type of Al–Zn–Mg–Cu alloy sheets with T6 temper were welded by laser beam welding (LBW). Microstructure characteristics and mechanical properties of the joints were evaluated. Results show that grains in the heat affected zone (HAZ) exhibit an elongated shape which is almost same as the base metal (BM). A non-dendritic equiaxed grain zone (EQZ) appears along the fusion line in the fusion zone (FZ), and grains here do not appear to nucleate epitaxially from the HAZ substrate. The FZ is mainly made up of dendritic equiaxed grains whose boundaries are decorated with continuous particles, identified as the T (AlZnMgCu) phase. Obvious softening occurs in FZ and HAZ, which mainly due to the changes of nanometric precipitates. The precipitates in BM are mainly η′, while plenty of GPI zones exist in FZ and HAZ adjacent to FZ, in the HAZ farther away from FZ, η phase appears. The minimum microhardness of the joint is always obtained in FZ at different times after welding. The ultimate tensile strength of the joint is 471.1 MPa which is 69.7% of that of the BM. Samples of the tensile tests always fracture at the FZ.     

Mo surface enrichment on a Fe–Cr alloy by electron beam irradiation

Mo alloying has been carried out on a Fe–Cr alloy by electron beam irradiation. It is shown that a Mo surface enrichment can be obtained in the range 2–8 at %. Scanning and transmission electron microscopy, X ray microanalysis and electron energy loss spectroscopy have been used to investigate the microstructures obtained after irradiation. Mo–Cr carbide and intermetallic X phase have been identified after alloying. The intermetallic phase is preferentially formed when the Mo content increases. It is concluded from electrochemical studies and potentiostatic attacks that the active and transpassive dissolution rates are closely related to the Cr content in the ferritic phase. This work must be also regarded as a first step towards the surface preparation of 316 S. S. by Mo incorporation to 304 S. S.     

Production of a positron beam in the energy range 1–10 MeV

The setup and characteristics of a low energy positron beam at the Giessen linac are desribed. The beam energy can be varied between 1.1 and some MeV. The measured mean positron currents are in the order of some pA within a momentum bin of 0.5%.     

Aluminum–GFRP hybrid square tube beam reinforced by a thin composite skin layer

Ultimate bending moments and energy-absorption capability of aluminum–glass fiber reinforced plastic (GFRP) hybrid tube beams were experimentally analyzed with particular focuses on effects of thin GFRP skin layer in relation to bending deformation behavior and fracture characteristics. Various hybrid tube beams were fabricated by inserting adhesive film between prepreg and metal layers and by aligning various composite ply angles. Under 3-point bending loads, aluminum–GFRP hybrid tube beams showed characteristic fracture processes according to the lay-up kinds of the skin layer in comparison to the virgin aluminum tube beams. In particular, the hybrid tube beams having a 0.5 mm thick [0°/90°]_s skin layer showed the largest improvement in specific maximum moment (about 67%) and in specific energy-absorption (29%). Consequently, there was an optimal thickness and lay-up of the composite skin layer in creating the best performance of the hybrid tubes.     

An elastic–plastic and residual stress analysis steel reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. Although it starts first at the upper surface for 15°, 30° and 45°, it starts first at the lower surface for 60° and 75° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the х-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 15°, 30°, 45°, 60°, 75° and 90° orientation angles.     

Effect of beam interaction time on laser alloying with pulsed Nd–YAG laser

Abstract

Surface alloying of aluminium with nickel was carried out using a pulsed Nd–YAG laser. The effect of beam interaction time on laser alloying of aluminium with pulsed Nd–YAG laser has been studied. It was found that the beam interaction time of a pulsed laser has a significant effect on microstructure and properties of alloyed layers. The results indicated that with changes in the beam diameter, higher thickness of alloyed layer and higher microhardness are both obtained at a lower effective interaction time. When travel speed changes, the same conditions are obtained at a higher effective interaction time.     

A note on the integrability of a remarkable static Euler–Bernoulli beam equation

It has recently been shown that the fourth-order static Euler–Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, in the maximal case has three symmetries. This corresponds to the negative fractional power law y ^?5/3, and the equation has the nonsolvable algebra ${sl(2, \mathbb{R})}$ . We obtain new two- and three-parameter families of exact solutions when the equation has this symmetry algebra. This is studied via the symmetry classification of the three-parameter family of second-order ordinary differential equations that arises from the relationship among the Noether integrals. In addition, we present a complete symmetry classification of the second-order family of equations. Hence the admittance of ${sl(2, \mathbb{R})}$ remarkably allows for a three-parameter family of exact solutions for the static beam equation with load a fractional power law y ^?5/3.     

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Kármán “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.     

The kurtosis parametric characterization of the passage of a standard Hermite–Gaussian beam and an elegant Hermite–Gaussian beam through a fractional Fourier transformation system with a spherically aberrated lens

The propagation characteristics of the kurtosis parameters of a standard Hermite–Gaussian (SHG) beam and of an elegant Hermite–Gaussian (EHG) beam, each passing through a fractional Fourier transformation (FRFT) system with a spherically aberrated lens, are studied in detail. Some numerical calculations are made by introducing an efficient algorithm, based on the Collins diffraction integral formula. The resulting graphs illustrate the striking difference between ideal FRFT systems and those with a spherically aberrated lens. The kurtosis parameters of both SHG and EHG beams passing through a type I Lohmann system with a spherically aberrated lens are seen to change with the fractional order periodically and the fundamental period is 4, but for type II the fundamental period is 2. Different values of spherical aberration coefficients affect the kurtosis parameters in greatly different ways. The values of the kurtosis parameters of a SHG beam passing through either type of Lohmann system with a spherically aberrated lens are no longer equal to those of an EHG beam, even when they have the same fractional orders and the same spherical aberration coefficients.