Dynamic Resistance and Energy Absorption of Sandwich Beam via a Micro-Topology Optimization

The current research of sandwich structures under dynamic loading mainly focus on the response characteristic of structure.The micro-topology of core layers would sufficiently influence the property of sandwich structure.However,the micro deformation and topology mechanism of structural deformation and energy absorption are unclear.In this paper,based on the bi-directional evolutionary structural optimization method and periodic base cell(PBC)technology,a topology optimization frame work is proposed to optimize the core layer of sandwich beams.The objective of the present optimization problem is to maximize shear stiffness of PBC with a volume constraint.The effects of the volume fraction,filter radius,and initial PBC aspect ratio on the micro-topology of the core were discussed.The dynamic response process,core compression,and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method.The results demonstrated that the overpressure action stage was coupled with the core compression stage.Under the same loading and mass per unit area,the sandwich beam with a 20%volume fraction core layer had the best blast resistance.The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams.But increasing the filter radius could slightly improve the bending stiffness.Upon changing the initial PBC aspect ratio,there are three ways for PBC evolution:The first is to change the angle between the adjacent bars,the second is to further form holes in the bars,and the third is to combine the first two ways.However,not all three ways can improve the energy absorption capacity of the structure.Changing the aspect ratio of the PBC arbitrarily may lead to worse results.More studies are necessary for further detailed optimization.This research proposes a new topology sandwich beam structure by micro-topology optimization,which has sufficient shear stiffness.The micro mechanism of structural energy absorption is clarified,it is significant for structural energy absorption design.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.

Experimental and Numerical Investigation on the Aerodynamic Characteristics of High-Speed Pantographs with Supporting Beam Wind Deflectors

Aiming to mitigate the aerodynamic lift force imbalance between pantograph strips,which exacerbates wear and affects the current collection performance of the pantograph-catenary system,a study has been conducted to support the beam deflector optimization using a combination of experimental measurements and computational fluid dynamics(CFD)simulations.The results demonstrate that the size,position,and installation orientation of the wind deflectors significantly influence the amount of force compensation.They also indicate that the front strip deflectors should be installed downwards and the rear strip deflectors upwards,thereby forming a“π”shape.Moreover,the lift force compensation provided by the wind deflectors increases with the size of the deflector.Alternative wind compensation strategies,such as control circuits,are also discussed,putting emphasis on the pros and cons of various pantograph types and wind compensation approaches.

ID effects on beam dynamics in the SSRF-U storage ring

This paper introduces the proposed insertion device(ID)scheme for the Shanghai Synchrotron Radiation Facility Upgrade.Based on this scheme,the influences of the ID radiation on the intra-beam scattering emittance and energy spread were evaluated.Optical distortion caused by the IDs was comprehensively examined and compensated using both local and global corrections.Subsequently,a frequency map analysis method was used to identify potentially dangerous resonance lines.In addition,the dynamic aperture,energy acceptance,and Touschek lifetime were calculated after considering high-order magnetic field errors to ensure that the ID effect did not affect the operation of the storage ring.

Dynamic Characteristics of Long -Span Steel -Concrete CompositeBeam Bridge Based on Vehicle -Bridge Coupling Effect

In order to investigate the effect of vehicle-bridge coupling on the dynamic characteristics of the bridge,a steel-concrete composite beam suspension bridge is taken as the research object,and a three-dimensional spatial model of the bridge and a biaxial vehicle model of the vehicle are established,and then a vehicle-bridge coupling vibration system is constructed on the basis of the Nemak-βmethod,and the impact coefficients of each part of the bridge are obtained under different bridge deck unevenness and vehicle speed.The simulation results show that the bridge deck unevenness has the greatest influence on the vibration response of the bridge,and the bridge impact coefficient increases along with the increase in the level of bridge deck unevenness,and the impact coefficient of the main longitudinal girder and the secondary longitudinal girder achieves the maximum value when the level 4 unevenness is 0.328 and 0.314,respectively;when the vehicle speed is increased,the vibration response of the bridge increases and then decreases,and the impact coefficient of the bridge in the middle of the bridge at a speed of 60 km/h achieves the maximum value of 0.192.

Exploring the Limits of a Deflection-Based Method for the Estimation of Dynamic Stress in Beams

Estimation of the dynamic stress in structures,such as beams and plates,has previously been made using the relationship between stress and velocity spatial maxima based on far-field assumptions.This paper presents a method for the estimation of dynamic stress in a beam using Euler–Bernoulli beam theory,where deflection data from a grid of measurement points on the surface of the beam is used to estimate the dynamic bending stress in the structure.The limitations of the method are investigated via response data provided by a numerical model of a freefree beam.A nondimensional wavenumber analysis is used to determine the number of points required for an accurate estimate of stress.Beams with a range of material and geometric parameters are modeled in order to explore the limits of the estimation method,and parameters representative of several real-world materials are used to assess the suitability of the method for practical applications.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

Beam dynamics,RF measurement,and commissioning of a CW heavy ion IH-DTL

A 53.667 MHz CW(continuous-wave) heavy ion IH-DTL has been designed for the SSC-LINAC injector of HIRFL-CSR(Heavy Ions Research Facility at Lanzhou-Cooling Storage Ring). It accelerates ions with maximum mass-to-charge ratio of 7.0 from 143 to 295 ke V/u. Low-power RF measurement of the IH-DTL1 has been taken to investigate the RF performance and the quality of the electric field distribution on the beam axis.The measured Q_0 value and the shunt impedance are 10,400 and 198 MX/m, respectively. The electric field distributions on and around the beam axis were evaluated and compared with the design value. By a new approach,the dipole field component is also estimated. The beam dynamics simulation using measured field distribution was presented in this paper. Based on the dynamics analysis in both transverse and longitudinal phase space, the field distribution can meet the design requirement. Finally, the RF conditioning and very first beam commissioning on the IH-DTL1 were finished. The beam test results agree well with the simulation results; what's more, the property of the variable output beam energy about the separated functions DTL was verified.

Laser Ablation Atomic Beam Apparatus with Time-Sliced Velocity Map Imaging for Studying State-to-State Metal Reaction Dynamics

We report a newly constructed laser ablation crossed molecular beam apparatus, equipped with time-sliced velocity map imaging technique, to study state-to-state metal atom reaction dynamics. Supersonic metal atomic beam is generated by laser vaporization of metal rod, and free expansion design without gas flow channel has been employed to obtain a good quality of metal atomic beam. We have chosen the crossed-beam reaction Al＋O2 to test the performance of the new apparatus. Two-rotational-states selected AIO（X^2∑＋, v=0, N and N＋I4） products can be imaged via P（N） and R（N＋14） branches of the Av=l band at the same wavelength, during （1＋1） resonance-enhanced multi-photon ionization through the AIO（D2E＋） intermediate state. In our experiment at 244.145 nm for simultaneous transitions of P（15） and R（29） branch, two rings in slice image were clearly distinguishable, corresponding to the AiO（v=0, N=IS） and AIO（v=0, N=29） states respectively. The energy difference between the two rotational levels is 403 cm^-1. The success of two states resolved in our apparatus suggests a better collisional energy resolution compared with the recent research study [J. Chem. Phys. 140, 214304 （2014）].

Experimental and numerical investigation on the dynamic shear failure mechanism of sandstone using short beam compression specimen

In this study,a novel testing method is proposed to characterize the dynamic shear property and failure mechanism of rocks by introducing the short beam compression(SBC)specimen into the split Hopkinson pressure bar(SHPB)system.Firstly,the stress distribution of SBC specimen is comprehensively analyzed by finite element method(FEM),and the results show that the optimal notch separation ratio of SBC specimen is C/H?0.2 to achieve successful dynamic simple-shear tests.Then,dynamic shear tests are conducted on sandstone using the SBC-SHPB method.Via careful pulse shaping technique,the dynamic force balance is guaranteed for SBC specimens,and the testing results show that the dynamic shear strength of sandstone is significantly rate-dependent.Combining the results of dynamic compression and tension tests,the failure envelopes of sandstone under different loading rates are obtained in the principle stress plane.It is found that the failure envelope of sandstone constantly expands outwards with increasing loading rate.Moreover,the energy partition of SBC specimen is quantified by virtue of high-speed digital image correlation(DIC)technique.The results show that the kinetic energy portion is non-negligible,and the shear fracture energy increases with increasing loading rate.In addition,the microscopic shear cracking mechanism of SBC specimen is analyzed by the thin section observation:the intra-granular(TG)fracture of minerals dominates the dynamic shear failure of sandstone,and the portion of TG fracture increases with increasing loading rate.This study provides a convenient and reliable method to investigate the dynamic shear property and failure mechanism of rocks.

Beam Dynamics and Electromagnetic Design Studies of 3 MeV RFQ for SNS Programme

The physics design of a 3 MeV, 30 mA, 352.2 MHz Radio Frequency Quadrupole (RFQ) is done for the future Indian Spallation Neutron Source (ISNS) project at RRCAT, India. The beam dynamics design of RFQ and the error analysis of the input beam parameters are done by using standard beam dynamics code PARMTEQM. The electromagnetic stu-dies for the two-dimensional and three-dimensional cavity design are performed using computer codes SUPERFISH and CST Microwave Studio. The physics design of RFQ consisting of the beam dynamics design near the beam axis and the electromagnetic design for the RFQ resonator is described here.

Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation

Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation（ANCF）. The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.

Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

In this study,the instability and bifurcation diagrams of a functionally graded(FG)porous sandwich beam on an elastic,viscous foundation which is influenced by an axial load,are investigated with an analytical attitude.To do so,the Timoshenko beam theory is utilized to take the shear deformations into account,and the nonlinear Von-Karman approach is adopted to acquire the equations of motion.Then,to turn the partial differential equations(PDEs)into ordinary differential equations(ODEs)in the case of equations of motion,the method of Galerkin is employed,followed by the multiple time scale method to solve the resulting equations.The impact of parameters affecting the response of the beam,including the porosity distribution,porosity coefficient,temperature increments,slenderness,thickness,and damping ratios,are explicitly discussed.It is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams,some of which,including the effect of temperature and porosity distribution,are less noticeable.

Microstructural evolution and dynamic recrystallization mechanisms of additively manufactured TiAl alloy with heterogeneous microstructure during hot compression

Microstructural evolution and dynamic recrystallization(DRX)mechanisms of a Ti-48Al-2Cr-2Nb(at.%)alloy prepared by selective electron beam melting(SEBM)during hot deformation at 1150℃and 0.1 s^(-1)were investigated by hot compression tests,optical microscope(OM),scanning electron microscope(SEM),electron back-scattered diffraction(EBSD)and transmission electron microscope(TEM).The results show that the initial microstructure of the as-SEBMed alloy exhibits layers of coarseγgrains and fineγ+α_(2)+(α_(2)/γ)lamellar mixture grains alternately along the building direction.During the early stage of hot deformation,deformation twins tend to form within the coarse grains,facilitating subsequent deformation,and a small number of DRX grains appear in the fine-grained regions.With the increase of strain,extensive DRX grains are formed through different DRX mechanisms in both coarse and fine-grained regions,involving discontinuous dynamic recrystallization mechanism(DDRX)in the fine-grained regions and a coexistence of DDRX and continuous dynamic recrystallization(CDRX)in the coarsegrained regions.

Screw theoretic view on dynamics of spatially compliant beam

Beams with spatial compliance can be deformed as bending in a plane, twisting, and extending. In terms of the screw theory on rigid body motions, the concept of ＂deflection screw＂ is introduced, a spatial compliant beam theory via the deflection screw is proposed, and the spatial compliance of such a beam system is presented and analysed based on the material theory and fundamental kinematic assumptions. To study the dynamics of the spatially compliant beam, the potential energy and the kinetic energy of the beam are discussed by using the screw theory to obtain the Lagrangian. The Rayleigh-Ritz method is used to compute the vibrational frequencies based on discussions of boundary conditions and shape functions. The eigenfrequencies of the beam with spatial compliance are compared with those of individual deformation cases, pure bending, extension, or torsion. Finally, dynamics of a robot with two spatial compliant links and perpendicular joints is studied using the spatial compliant beam theory. Coupling between the joint rigid body motions and the deformations of spatial compliant links can easily be found in dynamic simulation. The study shows the effectiveness of using the screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Seismic performance evaluation of hybrid coupled shear wall system with shear and flexural fuse-type steel coupling beams

Replaceable flexural and shear fuse-type coupling beams are used in hybrid coupled shear wall(HCSW)systems,enabling concrete buildings to be promptly recovered after severe earthquakes.This study aimed to analytically evaluate the seismic behavior of flexural and shear fuse beams situated in short-,medium-and high-rise RC buildings that have HCSWs.Three building groups hypothetically located in a high seismic hazard zone were studied.A series of 2D nonlinear time history analyses was accomplished in OpenSees,using the ground motion records scaled at the design basis earthquake level.It was found that the effectiveness of fuses in HCSWs depends on various factors such as size and scale of the building,allowable rotation value,inter-story drift ratio,residual drift quantity,energy dissipation value of the fuses,etc.The results show that shear fuses better meet the requirements of rotations and drifts.In contrast,flexural fuses dissipate more energy,but their sectional stiffness should increase to meet other requirements.It was concluded that adoption of proper fuses depends on the overall scale of the building and on how associated factors are considered.

Propagation dynamics and experimental observation of quadratic vortex beam

The concept of a quadratic vortex beam is proposed, in which phase term of the beam is given by exp（i mθ2）. The phase of the quadratic vortex beam increases with azimuthal angle nonlinearly. This change in phase produces several unexpected effects. Unlike the circularly symmetric beam spot of normal vortex beams, the intensity distribution of the quadratic vortex beam is shown to be asymmetric. The phase singularities will shift in the transverse beam plane on propagation.