Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal

We have observed and simulated the dynamic evolution of a beam launched into a biased transversely shifting photorefractive crystal. Propagating in this scheme, the beam can trap into spatial solitons and then deflect to the beam shifting side. The deflected amplitude of solitons relates to the shifting velocity of the sample (beam). At a higher shifting velocity, the bending amplitude of the beam will be decreased. We attribute this bending to the nonlinear relaxation effect present in the samples. The experiment and the simulation show fairly good agreement.     

Semi-Inverse Solution of a Pure Beam Bending Problem in Gradient Elasticity Theory: The Absence of Scale Effects

The semi-inverse solutions of pure beam bending problems within the three-dimensional formulation of gradient elasticity theory as exact tests for the problem of estimating the efficient bending stiffness of so-called scale-dependent thin beams and plates due to the necessity of modeling sensing devices are presented. It is shown that the solutions within the gradient elasticity theory give classic beam bending stiffnesses and demonstrate the invalidity of the widespread results and estimates obtained in the past 15 years during study of scale effects within the gradient beam theories, according to which the relative bending stiffness grows by a hyperbolic law with decreasing thickness.     

Self-bending of photorefractive solitons

Self-bending of photorefractive solitons is caused by diffusion in photorefractive crystals and becomes an important effect when the beam size is in the range of the charge carriers diffusion length. In this paper we present an experimental and numerical examination of the beam bending dependence on relevant parameters such as the applied electric field and the beam intensity. We demonstrate that the bending dependence on the electric field in the low saturation regime has the form of a square function at low values of the field and becomes linear for higher values. For stronger saturation the curve gets the form of a square root function. The bending dependence on the beam intensity has a maximum at defined intensity. The experimental data are compared with numerical simulations, giving a good qualitative agreement.     

An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam

An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.     

Transmission of structure-borne sound from a beam into an infinite plate

An analytical study of transmission of structure-borne sound from a semi-infinite beam into an infinite, isotropic plate is presented. The beam is assumed to carry a torsional, a quasi-longitudinal and bending wave and the transmission is obtained with the help of the admittances of the beam and the plate. The analysis is restricted to the case of low frequencies but is otherwise general; thus due regard is given not only to the bending wave of the plate but also to the other propagating waves and to the local reactions. An interesting result from the study is that a bending wave on the beam will transfer a substantial part of its power into quasi-longitudinal and transverse waves in the plate, especially if the plate is thin compared with the beam. This is thought to be a factor that is important and not so easily quantifiable in the analysis of a complex structure. The local reactions on the other hand are of small importance for the power transmission from a torsional and quasi-longitudinal wave on the beam but may be important for the transmission of a bending wave, especially if the Young's modulus of the beam is larger than that of the plate.     

Simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating embedded on a flexible cantilever beam

We propose and experimentally demonstrate a simple and practical scheme for simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating with multiple resonant peaks, which is embedded on a flexible cantilever beam. The wavelength spacing of the grating can be changed by adjusting the bending curvature change, since the compressive strain gradient induced by the bending of the cantilever beam changes the chirp ratio of the fiber grating. However, the wavelength spacing of the fiber grating is not changed by the temperature variation; the multiple resonant wavelengths are only shifted into the longer wavelength because of the positive thermal-expansion and thermo-optic coefficients of the fiber grating. Consequently, the proposed scheme allows for discrimination between two effects of bending and temperature.     

Finite element simulation of laser tube bending: Effect of scanning schemes on bending angle, distortions and stress distribution

Laser forming has received considerable attention in recent years. Within laser forming, tube bending is an important industrial activity, with applications in critical engineering systems like micro-machines, heat exchangers, hydraulic systems, boilers, etc. Laser tube bending utilizes the thermal stresses generated during laser scanning to achieve the desired bends. The parameters to control the process are usually laser power, beam diameter, scanning velocity and number of scans. Recently axial scanning has been used for tube bending instead of commonly used circumferential scans. However the comparison between the scanning schemes has involved dissimilar laser beam geometries with circular beam used for circumferential scanning and a rectangular beam for the axial scan. Thermal stresses generated during laser scanning are strongly dependent upon laser beam geometry and scanning direction and hence it is difficult to isolate the contribution made by these two variables. It has recently been established at the Corrosion and Protection Centre, University of Manchester, that corrosion properties of material during laser forming are affected by the number of laser passes. Depending on the material, the corrosion behaviour is either adversely or favourably affected by number of passes. Thus it is of great importance to know how different scanning schemes would affect laser tube bending. Moreover, any scanning scheme which results in greater bending angle would eliminate the need for higher number of passes, making the process faster. However, it is not only the bending angle which is critical, distortions in other planes are also extremely important. Depending on the use of the final product, unwanted distortions may be the final selection criteria. This paper investigates the effect of scanning direction on laser tube bending. Finite-element modelling has been used for the study of the process with some results also validated by experiments.     

Wavelength-spacing-tunable multichannel filter incorporating a sampled chirped fiber Bragg grating based on a symmetrical chirp-tuning technique without center wavelength shift

We propose and experimentally demonstrate a simple and flexible scheme for a wavelength-spacing-tunable multichannel filter exploiting a sampled chirped fiber Bragg grating based on a symmetrical modification of the chirp ratio. Symmetrical bending along a sampled chirped fiber Bragg grating attached to a flexible cantilever beam induces a variation of the chirp ratio and a reflection chirp bandwidth of the grating without a center wavelength shift. Accordingly, the wavelength spacing of a sampled chirped fiber Bragg grating is continuously controlled by the reflection chirp bandwidth variation of the grating corresponding to the bending direction, which allows for realization of an effective wavelength-spacing-tunable multichannel filter. Based on the proposed technique, we achieve the continuous tunability of the wavelength spacing in a range from 1.51 to 6.11 nm, depending on the bending direction of the cantilever beam.     

Vibration analysis of a new curved beam element

The common practice in developing a locking-free curved beam element is to ensure that its interpolation functions of displacement explicitly satisfy the inextensible bending mode condition for the membrane locking-free instead of the rigid body modes. In this paper, we study the impact of this practice on the dynamic characteristics of a finite element by conducting vibration analysis using our newly developed three-node locking-free curved beam element. In this case, the inextensible bending mode condition is satisfied explicitly, while the rigid body modes are satisfied implicitly to 4th-order accuracy. Numerical and experimental examples show that with the newly developed curved beam element, developed by using the implicit representation of a rigid body mode condition, it is possible to recover the rigid body modes of curved beams with low and medium slenderness ratios. This is even true for cases involving a half-circular element and the vibration of the curved beam is predicted with high accuracy.     

Dynamics of plastic bending of whiskers, induced by bombardment by a dense electron beam

We report new results from experimental investigations of the strong plastic bending induced in whiskers by nanosecond pulsed bombardment by a dense electron beam. The bending dynamics has been traced for the first time by means of a VFU-1 high-speed movie camera synchronized with a powerful small GIN-600 electronic accelerator. The measured duration of the plastic bending process for whiskers 40–100 μm in diameter was 1–2 msec. This is of the same order of magnitude as the characteristic relaxation time of the quasistatic mechanical stresses that are formed under uneven bombardment because of temperature gradients and disappear when the temperature is evened out by heat conduction. The measured bending dynamics was found to be nonmonotonic and rather complicated. After a nanosecond pulse of bombardment by a strong electron beam the bending of the whisker at first increases, then decreases, increases once again, and finally is saturated at some final value during flexural damping vibrations. The experimental data are discussed on the basis of the dislocation theory of plastic bending. Tomsk Polytechnic University. Institute of Strong-Current Electronics, Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 93–103, November, 1997.     

Horizontal phase-space distortions arising from magnetic pulse compression of an intense,relativistic electron beam

We report detailed measurements of the transverse phase space distortions induced by magnetic chicane compression of a high brightness, relativistic electron beam to subpicosecond length. A strong bifurcation in the phase space is observed when the beam is strongly compressed. This effect is analyzed using several computational models and is correlated to the folding of longitudinal phase space. The impact of these results on current research in collective beam effects in bending systems and implications for future short wavelength free-electron lasers and linear colliders are discussed.     

Experimental study on negative laser bending process of steel foils

In this paper, laser bending experiments were carried out on the stainless foil for producing negative bending angles. BM-dominated laser parameters, such as larger ratio of beam diameter to specimen thickness and lower scanning speed, help to produce negative bending angles. However, the bending direction in BM-dominated process will be uncertain due to the influence of the specimen's initial stress state and surface conditions. For this reason, experiments on stainless foil loaded with controlled pre-stresses were carried out for producing certain negative bending angles. The effect of the pre-stress and laser parameters are investigated experimentally. The experimental results show that negative bending angles could be produced conveniently when the pre-stresses were induced by elastic pre-bending which direction away from the laser beam, and the angles increase remarkably with the pre-stresses increasing. A set of reasonable laser parameters (laser power, scanning speed and beam diameter) for good quality negative bending angles forming were gotten by analyzing the effect of each parameter respectively in the experiments.     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility (SSRF)booster ring, a full energy injector for the storage ring, is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping. Closed orbit distortion (COD) caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting. Considering the affections of random errors in measurement, both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5 is given as the final installation sequence of the booster bending magnets in this paper.     

Statistical analysis of parameter effects on bending angle in laser forming process by pulsed Nd:YAG laser

In recent years, laser application has been introduced for bending and forming as new processes in manufacturing. The capability of laser bending demands more studies to recognize parameters influencing bending angle of sheet metals. In this study the effects of parameters such as material, laser power, beam diameter, scan velocity, sheet thickness, pass number and pulse duration on bending angle were studied by FEM initially and then followed by experiments. Furthermore, the Taguchi experimental design method was employed to pin point parameters, which significantly affect the bending process of laser bending of St12 and 304 alloy steels, which have a wide range of applications in products manufacturing. A regression analysis was conducted and a closed form equation was derived. The closed form equation can be used in industry to determine which process parameters (factors) enhance the bending angle in laser bending process.     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

Bending dual-core photonic crystal fiber coupler

In this paper, we systematically study a designed structure of a bending dual-core photonic crystal fiber (PCF). We propose the controllable wavelength-selective coupling PCF. This coupler allows highly accurate control of the filtering wavelength. The different wavelengths can be selected by controlling the bending radius of the fiber. Coupling characteristics of novel bending wavelength-selective coupling PCF are evaluated by using a vector finite element method and their application to a multiplexer demultiplexer (MUX–DEMUX) based on the novel coupler is investigated. When the fiber length is 4168 μm, the bending radius of PCF couplers for 1.48/1.55 μm, 1.3/1.55 μm, 0.98/1.55 μm, and 0.85/1.55 μm is calculated, respectively, and the beam propagation analysis is performed. Different from the traditional wavelength-selective coupling PCF, the dual-core PCF is bent and it can realize the separation of multiple wavelengths.     

Research and development of an electron beam focusing system for a high-brightness X-ray generator

A new type of rotating anticathode X-ray generator, where an electron beam of up to 60 keV irradiates the inner surface of a U-shaped Cu anticathode, has achieved a beam brilliance of 130 kW mm(-2) (at 2.3 kW). A higher-flux electron beam is expected from simulation by optimizing the geometry of a combined-function-type magnet instead of the fringing field of the bending magnet. In order to minimize the size of the X-ray source the electron beam has been focused over a short distance by a new combined-function bending magnet, whose geometrical shape was determined by simulation using the Opera-3D, General Particle Tracer and CST-STUDIO codes. The result of the simulation clearly shows that the role of combined functions in both the bending and the steering magnets is important for focusing the beam to a small size. FWHM sizes of the beam are predicted by simulation to be 0.45 mm (horizontal) and 0.05 mm (vertical) for a 120 keV/75 mA beam, of which the effective brilliance is about 500 kW mm(-2) on the supposition of a two-dimensional Gaussian distribution. High-power tests have begun using a high-voltage 120 kV/75 mA power supply for the X-ray generator instead of 60 kV/100 mA. The beam focus size on the target will be verified in the experiments.     

Improved beam theory for multilayer graphene nanoribbons with interlayer shear effect

The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed in this Letter. An improved beam theory is adopted and extended in which the in-plane extension of each layer is also taken into account. The governing equations for bilayer and trilayer graphene nanoribbons subjected to bending are presented as illustrative examples. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Compared with the molecular dynamics (MD) simulations, the present beam model predicts much better results than the previous beam model in which the in-plane extension is ignored. The current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures.     

On prandtl's cantilever beam subjected to a bending moment

The stability behaviour of a cantilever beam subjected to the bending moment is investigated. It is found that the beam has divergence and flutter instability loads depending on the type of the loading. Moreover, it is shown that a beam subjected to a follower moment and a beam subjected to a bending moment which keeps its direction in the course of the motion behave in exactly the same way, according to the numerical calculations.     

Branching optical signals by fractional vortex dipoles

We study the evolution and interaction of semi-infinite dark beams carrying phase dislocations, where step- and screw-like phase profiles are combined. Similar to dark beams with a finite length, semi-infinite dark beams tend to move in transversal direction with respect to their background beam. In addition, they develop a snake-like instability and optical vortices detach from their bending ends. We are looking for appropriate conditions to control the process of concatenating and crossing the ends of several such semi-infinite dark beams in a way suitable for probe-beam branching and routing in self-defocusing Kerr nonlinear media. Colinear and perpendicular probe beam propagations in the optically-induced guiding structures are modeled and analyzed with respect to the branching efficiency to respective virtual output channels.