Phase matched scanning optical parametric chirped pulse amplification based on pump beam deflection

Combined with the optical beam deflection,a novel approach of phase matched broadband scanning optical parametric chirped pulse amplification(OPCPA)was proposed.For this scheme,there was no superfluous operations to the chirped signal pulse which propagated in a changeless direction straightforward,but the pump beam were deflected in space with time by passing through a KTN crystal,which was applied with varied driving voltage.The theories of phase matching of each chirped signal frequency based on pump beam deflection was analyzed detailedly.And the type-I amplification of chirped signal with 800 nm central wavelength and 20 nm bandwidth pumped by 532 nm in BBO crystal was simulated as a case in point.The simulation results showed that the spectral distribution of chirped signal pulse was almost the same as the initial form,i.e.,there was nearly no narrowing on the amplified spectrum by using of the scanning OPCPA based on pump beam deflection.In addition,the simulations demonstrated that it was worth minimizing the voltage deviation applied to KTN crystal as much as possible for the sake of better waveform,larger bandwidth and higher conversion efficiency of amplified signal pulse in the proposed scanning OPCPA.

Determination of Kinetic Parameters and Metal Ions in Urea-Urease System Based on the Biochemical Reaction Heat Induced Laser Beam Deflection

A new analytical method for the determination of urea-urease system based on biochemical reaction heat induced laser beam deflection is presented in this paper. With the method, the Michaelis constant (K-m) of urease and apparent inhibition constant (K-i) of some metal ion inhibitors were measured respectively. This method was also used for the quantitative determination of metal ions with satisfactory result.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

Analytic Static Deflection Solutions of Uniform Cantilever Beams Resting on Nonlinear Elastic Rotational Boundary

In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam,Bernoulli numbers and Euler numbers

Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.

Growth and collapse of laser-induced bubbles in glycerol-water mixtures

Comprehensive numerical and experimental analyses of the effect of viscosity on cavitation oscillations are performed. This numerical approach is based on the Rayleigh-Plesset equation. The model predictions are compared with experimental results obtained by using a fibre-optic diagnostic technique based on optical beam deflection （OBD）. The maximum and minimum bubble radii as well as the oscillation times for each oscillation cycle are determined according to the characteristic signals. It is observed that the increasing of viscosity decreases the maximum bubble radii but increases the minimum bubble radii and the oscillation time. These experimental results are consistent with numerical results.

Mechanism of laser-induced plasma shock wave evolution in air

A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.

Deflection analysis of reinforced concrete beams strengthened with carbon fibre reinforced polymer under long-term load action

This paper presents the results of an experimental research on reinforced concrete beams strengthened with an external carbon fibre reinforced polymer(CFRP) layer under long-term load action that lasted for 330 d.We describe the characteristics of deflection development of the beams strengthened with different additional anchorages of the external carbon fibre composite layer during the period of interest.The conducted experiments showed that the additional anchorage influences the slip of the external layer with respect to the strengthened element.Thus,concrete and carbon fibre composite interface stiffness decreases with a long-term load action.Therefore,the proposed method of analysis based on the built-up-bars theory can be used to estimate concrete and carbon fibre composite interface stiffness in the case of long-term load.

THE ANGULAR SPREAD OF THE DEFLECTED SAW BEAM DIFFRACTED BY BRAGG GRATING

In this paper , the angular spread of the SAW beam diffracted by Bragg grating , denoted by δθ1 ,is analysed based on the equations of the deflection angle and the deflection effciency . A parameter δθB is defined to refer to ' Bragg angular spectrum width ' of the grating . The importance of this parameter in distinguishing the angular spread range of the deflected beam for different regimes is discussed as well. It is show from the analysis that if the spread angle of the incident beam labelled with δθinc is larger than the ' Bragg witdth of the angular spectrum ' of the grating , the spread angle δθ1 of the deflected beam will equal to δθB ; but if the angular divergence of the incident beam is less than δθB , then δθ1 =δθinc.Experimentally , four kinds of samples with different configurations are investigated by optical method , two of which operate in the regime of δθinc<<δθB and the others correspond to the case in the regime of δθinc >>δθB . The widths of the angular spread of the incident beam and the deflected beam are estimated by measuring the widths of their own acousto - optical diffraction points . It is demonstrated that the experimental results agree with the theoretical results approximately .

Critical transitions in the shape morphing of kirigami metallic glass

Kirigami, the ancient Japanese paper cutting technique, has been applied to achieve high stretchability and low energy loss of designed metallic glass. Despite the exploration of the underlying deformation mechanism of kirigami-inspired structures from the energy point of view, the morphable responses of the kirigami patterns and the origin of the kirigami response are yet to be fully understood. This study reveals the mechanical driven-forms of the kirigami structure with the corresponding deformation stages. Based on the beam deflection theory, the elastic buckling behavior of kirigami metallic glass is manifested and a critical force prediction model is developed. Moreover, a force concentration parameter is introduced in the rigid-plastic deformation stage, predicting the nominal ultimate force. The kirigami-inspired facture force is firstly proposed. The findings of these models are in good agreement with the experimental sizedependent kirigami responses, and expected to provide significant insights into the understanding of the deformation behavior and the design of kirigami metallic glasses.

EXPERIMENTAL AND THEORETICAL STUDY OF CAVITATION-INDUCED MECHANICAL EFFECT ON A SOLID BOUNDARY

The mechanical effect induced by the cavitati- on bubble collapse in the neighborhood of a solid boundary was investigated by focusing a Q-switched laser pulse on a metal target in water. By means of a fiber-coupling optical beam deflection technique, the displacement generated by liquid jet impact at the final stage of the bubble collapse was detected at the epicenter of the rear metal surface. Furthermore, by combining a widely used laser ablation model with the detection principles of this detector, the transient impact force exerting on the target material could be easily estimated. Besides, according to experimental results and the modified Ray leigh theory, the maximum bubble radius and the liquid-jet pressure were also obtained, which are in good agreement with previous results,

Using portable falling weight deflectometer to determine treatment depth of subgrades in highway reconstruction of Southern China

Based on a highway reconstruction project in southern China,this study aims to put forward a method to determine the proper treatment depth of the existing subgrade.First,some field tests including the Beckman beam deflection test and portable falling weight deflectometer(PFWD)test were carried out.The results showed that there was a good correlation between the Beckman beam deflection(L)and PFWD modulus(Ep).Subsequently,a subgrade section was excavated and backfilled with cement-stabilized soil in layers.Compaction test,dynamic cone penetrometer rate test,plate load test and Beckman beam deflection test were performed to evaluate the treatment effect.To make sure,the subgrade was treated deeply enough,the Beckman beam deflection(L)was used as the controlled indicator among all the measured indexes for it was the hardest metric to meet.According to the design deflection and decreasing law of the measured deflections with the different number of the stabilized layers,the treatment depth was finally determined.As the PFWD test is superior to the deflection test in the detection efficiency,and the deflection value can be calculated from PFWD modulus by correlation formulas,thus the latter index can be used as a more suitable parameter for estimating the treatment depth instead of the former.Consequently,based on the measured PFWD moduli of the existing subgrade,six treatment schemes considering different treatment depths were proposed.It was confirmed that the method developed from this study is feasible and worth being extensively applied.