A semi-infinite beam theoretical model on predicting rock slope subsidence induced by underground mining

When the mining goaf is close to the cliff,rock slope subsidence induced by underground mining is significantly affected by its boundary conditions.In this study,an analytical method is proposed by considering the key strata as a semi-infinite Euler-Bernoulli beam rested on a Winkler foundation with a local subsidence area.The analytical solutions of deflection are derived by analyzing the boundary and continuity conditions of the cliff.Then,the analytical solutions are verified by the results from experimental tests,FEM and InSAR,respectively.After that,the influence of changing parameters on deflections is studied with sensitivity analysis.The results show that the distance between goaf and cliff significantly affects the deflection of semi-infinite beam.The response of semi-infinite beam is obviously determined by the length of goaf and the bending stiffness of beam.The comparisons between semi-infinite beam and infinite beam illustrate the ascendancy of the improved model in such problems.

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns

The multiple-input multiple-output(MIMO)-enabled beamforming technology offers great data rate and channel quality for next-generation communication.In this paper,we propose a beam channel model and enable it with time-varying simulation capability by adopting the stochastic geometry theory.First,clusters are generated located within transceivers'beam ranges based on the Mate?rn hardcore Poisson cluster process.The line-of-sight,singlebounce,and double-bounce components are calculated when generating the complex channel impulse response.Furthermore,we elaborate on the expressions of channel links based on the propagation-graph theory.A birth-death process consisting of the effects of beams and cluster velocities is also formulated.Numerical simulation results prove that the proposed model can capture the channel non-stationarity.Besides,the non-reciprocal beam patterns yield severe channel dispersion compared to the reciprocal patterns.

Resistance of full-scale beams against close-in explosions.Numerical modeling and field tests

This paper explores the performances of a finite element simulation including four concrete models applied to a full-scale reinforced concrete beam subjected to blast loading. Field test data has been used to compare model results for each case. The numerical modelling has been, carried out using the suitable code LS-DYNA. This code integrates blast load routine(CONWEP) for the explosive description and four different material models for the concrete including: Karagozian & Case Concrete, Winfrith, Continuous Surface Cap Model and Riedel-Hiermaier-Thoma models, with concrete meshing based on 10, 15, and 20 mm. Six full-scale beams were tested: four of them used for the initial calibration of the numerical model and two more tests at lower scaled distances. For calibration, field data obtained employing pressure and accelerometers transducers were compared with the results derived from the numerical simulation. Damage surfaces and the shape of rupture in the beams have been used as references for comparison. Influence of the meshing on accelerations has been put in evidence and for some models the shape and size of the damage in the beams produced maximum differences around 15%. In all cases, the variations between material and mesh models are shown and discussed.

Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation:an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.

The quaternion beam model for hard-magnetic flexible cantilevers

The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.

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.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Stiffness and Shear Stress Distribution of Glulam Beams in Elastic-Plastic Stage:Theory,Experiments and Numerical Modelling

Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to predict the stiffness and shear distribution of glulam beams in elastic-plastic stage,and consequently,the failure of such glulam beams cannot be predicted effectively.To address these issues,an analytical method considering material nonlinearity was proposed for glulam beams,and the calculating equations of deflection and shear stress distribution for different failure modes were established.The proposed method was verified by experiments and numerical models under the corresponding conditions.Results showed that the theoretical calculations were in good agreement with experimental and numerical results,indicating that the equations proposed in this paper were reliable and accurate for such glulam beams with wood material in the elastic-plastic stage ignoring the influence of mechanic properties in radial and tangential directions of wood.Furthermore,the experimental results reported by the previous studies indicated that the method was applicable and could be used as a theoretical reference for predicting the failure of glulam beams.

Calibration of quantitative rescattering model for simulating vortex high-order harmonic generation driven by Laguerre–Gaussian beam with nonzero orbital angular momentum

We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.

Propagation of Gaussian Schell-Model Array Beams through a Jet Engine Exhaust

Here a Gaussian Shell Model Array (GSMA) beam is used to investigate the propagation characteristics in the jet engine exhaust region. It has great significance to improve various optical systems for wide application in trapping cold atoms, creating gratings, and atmospheric optical communication. We calculate analytical formulas for the spectral density (SD) and the propagation factors Mx2 and My2 of a GSMA beam. The influence of inner scale of turbulence in the jet engine exhaust region on its power spectrum has been also analyzed. According to these results, the influence of turbulence in a jet engine exhaust on a GSMA beam has been reduced by changing the parameters of light source and turbulence. For example, it is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence to increase the source coherence length, the root-mean-squared (rms) beam width, the wavelength or reduce the outer scale of turbulence.

Possibility of reaching the predicted center of the“island of stability”via the radioactive beam-induced fusion reactions

Based on the dinuclear system model,the synthesis of the predicted double-magic nuclei^(298)Fl and 304120 was investigated via neutron-rich radioactive beam-induced fusion reactions.The reaction^(58)Ca+^(244)Pu is predicted to be favorable for producing^(298)Fl with a maximal ER cross section of 0.301 pb.Investigations of the entrance channel effect reveal that the^(244)Pu target is more promising for synthesizing^(298)Fl than the neutron-rich targets^(248)Cm and^(249)Bk,because of the influence of the Coulomb barrier.For the synthesis of 304120,the maximal ER cross section of 0.046 fb emerges in the reaction^(58)V+^(249)Bk,indicating the need for further advancements in both experimental facilities and reaction mechanisms.

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.

Double-layer model updating for steel-concrete composite beam cable-stayed bridge based on GPS

In order to establish the relationship between the measured dynamic response and the health status of long-span bridges, a double-layer model updating method for steel-concrete composite beam cable-stayed bridges is proposed. Measured frequencies are selected as the first-layer reference data, and the mass of the bridge deck, the grid density, the modulus of concrete and the ballast on the side span are modified by using a manual tuning technique. Measured global positioning system （GPS） data is selected as the second-layer reference data, and the degradation of the integral structure stiffness EI of the whole bridge is taken into account for the second-layer model updating by using the finite element iteration algorithm. The Nanpu Bridge in Shanghai is taken as a case to verify the applicability of the proposed model updating method. After the first-layer model updating, the standard deviation of modal frequencies is smaller than 7%. After the second-layer model updating, the error of the deflection of the mid-span is smaller than 10%. The integral structure stiffness of the whole bridge decreases about 20%. The research results show a good agreement between the calculated response and the measured response.

Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model

Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35℃ according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0. 85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality.

Dynamic response of clamped sandwich beams: analytical modeling

An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF)system,and the core is idealized using the rigid-perfectly-plastic-locking(RPPL)model.Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core.The model is validated with existing analytical predictions and FE simulation results,with good agreement achieved.Compared with existing analytical models,the proposed model exhibits superiority in two aspects:the deformation resistance of front face sheet during shock wave reflection is taken into account;the effect of pulse shape is considered.The practical application range of the proposed model is therefore wider.

Verification of Beam Models for Ionic Polymer-Metal Composite Actuator

Ionic Polymer-Metal Composite (IPMC) can work as an actuator by applying a few voltages.A thick IPMC actuator,where Nafion-117 membrane was synthesized with polypyrrole/alumina composite filler,was analyzed to verify the equivalent beam and equivalent bimorph beam models.The blocking force and tip displacement of the IPMC actuator were measured with a DC power supply and Young's modulus of the IPMC strip was measured by bending and tensile tests respectively.The calculated maximum tip displacement and the Young's modulus by the equivalent beam model were almost identical to the corresponding measured data.Finite element analysis with thermal analogy technique was utilized in the equivalent bimorph beam model to numerically reproduce the force-displacement relationship of the IPMC actuator.The results by the equivalent bimorph beam model agreed well with the force-displacement relationship acquired by the measured data.It is confirmed that the equivalent beam and equivalent bimorph beam models are practically and effectively suitable for predicting the tip displacement,blocking force and Young's modulus of IPMC actuators with different thickness and different composite of ionic polymer membrane.

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.

Modeling and Experimental Validation of the Electron Beam Selective Melting Process

Electron beam selective melting （EBSM） is a promising additive manufacturing （AM） technology. The EBSM process consists of three major procedures：（1） spreading a powder layer, （2） preheating to slightly sinter the powder, and （3） selectively melting the powder bed. The highly transient multi-physics phenomena involved in these procedures pose a significant challenge for in situ experimental observation and measurement. To advance the understanding of the physical mechanisms in each procedure, we leverage high- fidelity modeling and post-process experiments. The models resemble the actual fabrication procedures, including （1） a powder-spreading model using the discrete element method （DEM）, （2） a phase field （PF） model of powder sintering （solid-state sintering）, and （3） a powder-melting （liquid-state sintering） model using the finite volume method （FVM）. Comprehensive insights into all the major procedures are provided, which have rarely been reported. Preliminary simulation results （including powder particle packing within the powder bed, sintering neck formation between particles, and single-track defects） agree qualitatively with experiments, demonstrating the ability to understand the mechanisms and to guide the design and optimization of the experimental setup and manufacturing process.

Natural frequencies analysis of a composite beam consisting of Euler-Bernoulli and Timoshenko beam segments alternately

Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections.For the special geometry characteristic,the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately.By using continuity conditions,the hybrid beam unit(ETE-B) consisting of Euler-Bernoulli beam,Timoshenko beam and Euler-Bernoulli beam in sequence was developed.Classical boundary conditions of pinned-pinned,clamped-clamped and clamped-free were considered to obtain the natural frequencies.Numerical examples of the equal-length composite beam with 1,2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam,respectively.The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam,which in practice,is the interpretation that the inner-welded plate can strengthen a hollow beam.In this work,comparisons with the finite element calculation were presented to validate the ETE-B model.

Timoshenko beam model for chiral materials

Natural and artificial chiral materials such as deoxyribonucleic acid （DNA）, chromatin fibers, flagellar filaments, chiral nanotubes, and chiral lattice materials widely exist. Due to the chirality of intricately helical or twisted microstructures, such materials hold great promise for use in diverse applications in smart sensors and actuators, force probes in biomedical engineering, structural elements for absorption of microwaves and elastic waves, etc. In this paper, a Timoshenko beam model for chiral materials is developed based on noncentrosymmetric micropolar elasticity theory. The governing equations and boundary conditions for a chiral beam problem are derived using the variational method and Hamilton＇s principle. The static bending and free vibration problem of a chiral beam are investigated using the proposed model. It is found that chirality can significantly affect the mechanical behavior of beams, making materials more flexible compared with nonchiral counterparts, inducing coupled twisting deformation, relatively larger deflection, and lower natural frequency. This study is helpful not only for understanding the mechanical behavior of chiral materials such as DNA and chromatin fibers and characterizing their mechanical properties, but also for the design of hierarchically structured chiral materials.