Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Experimental Study on Force Behavior of Steel Rein forced Concrete Transfer Beam Structure with Basement of Large Space

Based on comparative test of two transfer story models, in one of which the transfer beam and basement column is constructed of steel reinforced concrete, and the other is constructed of ordinary reinforced concrete, its force behavior, ductility and failure mechanism under vertical and horizontal loads are studied. The results show that loading bearing and seismic behavior of transfer story structure with steel reinforced concrete beam and basement column is good. The relative design suggestion is put forward.

Analysis of metal transfer during electron beam welding with filler wire

The metal transfer mode of electron beam welding （EBW） with filler wire was studied experimentally. The spatial position between the electron beam and the filler wire was defined. Basing on the charge coupled device （CCD） visual sensing system, the metal transfer mode of filler wire was investigated. The results showed that there were five transfer modes during EBW process due to different wire feed rates and spatial positions between beam and filler wire, such as short-circuiting mode, molten metal bridge mode, small droplet mode, big droplet mode and mixed mode. By comparing the weld appearance of different transfer modes, the molten metal bridge transfer was proved to be the best transfer mode.

Magnet lattice design of the SSRF electron-beam transfer lines

Under three-dimensional plane geometrical constraints ( X,Y,θ ), with two asymmetric achromatic sections, the combined three-section structural FODO-like magnet lattice design is adopted and finely optimized in the SSRF electron-beam transfer lines. The magnet lattice has high flexibility and robustness, and the Courant–Snyder parameters can be easily adjusted within a wide range to meet the requirements of transmission and injection for different operation modes of the linear accelerator, booster synchrotron, and storage ring. In this article, the main parameters of the linear optics design of the SSRF electron-beam transfer lines are described, involving the physical design criteria, the total geometrical layout, the magnet lattice, and the beam Courant–Snyder parameters matching. The studies of the variant beam dynamic simulation program calculations show that the design purpose of the efficient beam transmission and injection will be basically achieved.

Energy Transfer among Modes in a Non-Slender Elastic Beam Subject to Vortex-Induced Vibration

The vibration of an elastic beam experiencing vortex-induced vibration is numerically analyzed employing a wake-oscillator model. The influence of the excited mode, the initial velocity, the shedding pulsation and the mass ratio on the energy transfer among modes and the vibration amplitude is determined. Multiple frequencies are detected, and the power spectral density of the beam tip time series is used to calculate the dominant frequency.

Effective transmittance of Fabry–Perot cavity under non-parallel beam incidence

The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resonant cavity can be expressed by the Airy function. However, in reality, it is difficult to achieve perfect parallelism with collimated beams. In this article, a theoretical model is established for non-parallel light incidence, which assumes that the non-parallel incident light is a cone-shaped beam, and the cone angle is used to quantify the non-parallelism of the beam. The transmittance function of the FP resonant cavity under non-parallel light incidence is derived. The accuracy of the model is experimentally verified. Based on this model, the effects of divergence angle, tilt angle and FP cavity parameters(reflectivity, cavity length)on the ITF are studied. The reasons for the decrease in peak value, broadening and asymmetry of the interference peak under non-parallel light incidence are explained. It is suggested that a fine balance between the interference peak and the collimation effect of the incident light should be considered in the design and application of FP resonant cavities, especially for tilted applications such as angle-scanned spectroscopy. The research results of this article have certain significance for the design and application of FP resonant cavities.

FREE VIBRATION ANALYSIS AND PHYSICAL PARAMETER IDENTIFICATION OF NON-UNIFORM BEAM CARRYING SPRING-MASS SYSTEMS

To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is developed by using the transfer matrix method of multibody system（MS-TMM）, the transfer matrix of non-u- niform beam is derived, and the natural frequencies are computed. Compared with the numerical assembly method （NAM）, the results by MS-TMM have good agreement with the results by FEM, and are better than the results by NAM. When using the high precision method, the global dynamic equations of the complex multibody system are not needed and the orders of involved system matrices are decreased greatly. For the investigation on the re- verse problem of the physical parameter identification of multibody system, MS-TMM and the optimization tech- nology based on genetic algorithms（GAs） are combined and extended. The identification problem is exchanged for an optimization problem, and it is formulated as a global minimum solution of the objective function with respect to natural frequencies of multibody system. At last, the numerical example of non-uniform beam with attach- ments is discussed, and the identification results indicate the feasibility and the effectivity of the proposed aop- proach.

Longitudinal force in continuously welded rail on long-span tied arch continuous bridge carrying multiple tracks

Considering arch rib, lateral brace, suspender, girder, pier and track position, the model for the interaction between long-span tied arch continuous bridge and multiple tracks was established by using steel-concrete composite section beam element to simulate concrete-filled steel tube(CFST) arch rib, using the beam element with rigid arm to simulate the prestressed concrete girder and using nonlinear bar element to simulate longitudinal constraint between track and bridge. Taking a(77+3×156.8+77) m tied arch continuous bridge with four tracks on the Harbin-Qiqihar Passenger Dedicated Line as an example, the arrangement of continuously welded rail(CWR) was explored. The longitudinal force in CWR on the tied arch continuous bridge, the pier top horizontal force and torque due to the unbalance load case, were analyzed under the action of temperature, vertical live load, train braking and wind load.Studies show that, it can significantly reduce track displacement to set the track expansion devices at main span arch springing on both sides; the track stress due to arch temperature variation can reach 40.8 MPa; the track stress, pier top horizontal force and torque are related to the number of loaded tracks and train running direction, and the bending force applied to unloaded track is close to the loaded track, while the braking force applied to unloaded track is 1/4 to 1/2 of the loaded track; the longitudinal force of track due to the wind load is up to 12.4 MPa, which should be considered.

Applicability of small resistance fastener on long-span continuous bridges of high-speed railway

Ballastless tracks have been widely applied in high-speed railway (HSR). The adaptability research between continuous welded rails (CWR) and long-span bridges of HSR is of great practical engineering significance. Based on the HSR long-span continuous bridges, the integrative spatial finite element model of track-bridge-pier-foundation system was established with the nonlinear spring element simulating the longitudinal resistance between track and bridge. Comparative study on the various additional longitudinal forces of CWR using the common fasteners and small resistance fasteners was carried out. Analysis results indicate that the additional expansion forces and additional rail-breaking forces in long-span ballastless continuous girders can be reduced evidently by 40% 50% after adopting small resistance fasteners, but lead to greater rail broken gap. The small resistance fasteners have little influence on the additional force only caused by vertical load, but can reduce the additional force caused by vertical load combined with braking load by over 10%. Besides, transient analysis method is proved to be more accurate and safe in calculating additional longitudinal forces when the train running or braking on the bridge, compared with the traditional static method.

Seismic Behavior of Diaphragm-Through Connections of Concrete-Filled Square Steel Tubular Columns and H-Shaped Steel Beams

Based on the introductions of a type of diaphragm-through connection between concrete-filled square steel tubular columns (CFSSTCs) and H-shaped steel beams,a finite element model of the connection is developed and used to investigate the seismic behavior of the connection.The results of the finite element model are validated by a set of cyclic loading tests.The cyclic loading tests and the finite element analyses indicate that the failure mode of the suggested connections is plastic hinge at the beam with inelastic rotation angle exceeding 0.04 rad.The suggested connections have sufficient strength,plastic deformation and energy dissipation capacity to be used in composite moment frames as beam-to-column rigid connections.

Transfer function measurement for the SSRF SRF system

A digital transfer function measurement system has been embedded in the low-level radio frequency (LLRF) system of the storage ring of the Shanghai Synchrotron Radiation Facility. The measurement results indicate that the decreased control accuracy at high current is primarily owing to ripples from the high-voltage power supply, the transient beam loading effect, and the digital aliasing effect. The current LLRF algorithm is not able to suppress these disturbances.

Numerical analysis of thermal fluid transport behavior during electron beam welding of 2219 aluminum alloy plate

A two-dimensional mathematical model based on volume-of-fluid method is proposed to investigate the heat transfer,fluidflow and keyhole dynamics during electron beam welding(EBW)on20mm-thick2219aluminum alloy plate.In the model,anadaptive heat source model tracking keyhole depth is employed to simulate the heating process of electron beam.Heat and masstransport of different vortexes induced by surface tension,thermo-capillary force,recoil pressure,hydrostatic pressure and thermalbuoyancy is coupled with keyhole evolution.A series of physical phenomena involving keyhole drilling,collapse,reopening,quasi-stability,backfilling and the coupled thermal field are analyzed systematically.The results indicate that the decreased heat fluxof beam in depth can decelerate the keyholing velocity of recoil pressure and promote the quasi-steady state.Before and close to thisstate,the keyhole collapses and complicates the fluid transport of vortexes.Finally,all simulation results are validated againstexperiments.

Bioeffects of Low Energy Ion Beam Implantation:DNA Damage,Mutation and Gene Transter

Low-energy ion beam implantation （10 - 200 keV） has been proved to have a wide range of biological effects and is broadly used in the breeding of crops and micro-organisms.To understand its mechanisms better and facilitate its applications, the developments in the bioeffects of low energy ion beam implantation in the past twenty years are summarized in this paper.

Numerical analysis of thermal fluid transportation during electron beam welding of 2219 aluminum alloy plate and experimental validation

A three-dimensional mathematical model using volume-of-fluid method is developed to investigate the heat transfer, fluid flow and keyhole dynamics during electron beam welding of 2219 aluminum alloy plate. In the model, an adaptive heat source is employed to simulate the heating process of electron beam. Fluid flow is mainly driven by surface tension, thermo-capillary force, recoil pressure, hydrostatic pressure and thermal buoyancy. The thermal-fluid transport behaviors of welding pool during the drilling and backfilling stages of keyhole and the formation reason of the nail-shaped weld with an arc crater are systematically analyzed. Finally, all calculation results are validated by experiments and show good agreements.

Analytical solution of temperature in laminated beams subjected to general thermal boundary conditions

The temperature distribution in laminated beams underging thermal boundary conditions has been investigated.The thermal boundary conditions are general and include various combinations of prescribed heat fluxes and temperatures at the edges.An analytical solution of temperature for the laminated beam is present on the basis of the heat conduction theory in this paper.The proposed method is applicable to the beams with arbitrary thickness and layer numbers.Due to the complexity of the boundary conditions,the temperature field to be determined was considered from two sources.The first part was the temperature field from the complex temperature conditions at two edges of the laminated beam.The solution for the temperature of the first part was constructed to satisfy temperature boundary conditions at two edges.The second part was the temperature field from the upper and lower surface temperatures without taking account of the thermal conditions at two edges.In this part,the exact solution for the temperature was obtained based on the heat conduction theory.The convergence of the solution was examined by analyzing terms of Fourier series.The validity and feasibility of the proposed method was verified by comparing theoretical results with numerical results due to the equivalent single layer approach and the finite element method(FEM).The influences of surface temperatures,beam thicknesses,layer numbers and material properties with respects to the solution of the temperature field of the beam were investigated via a series of parametric studies.

Elastic-plastic study on high building with SRC transferring story

A new type of transferring structure for steel reinforced concrete (SRC) beams is used in high building. The pushover analysis method was used to study the failure mechanism and ductility of SRC transferring structure through consulting pseudo-static test results for the structure. And, the occurrence order and position of the plastic hinge, the weak story and seismic capacity of high building with SRC transferring story were also studied through consulting shaking table test results for the high building, showing that the seismic behavior of high building with SRC transferring story is good.

Coupled flexural-torsional vibration band gap in periodic beam including warping effect

The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.

Gaussian wave formalism model for propagation of charged-particle beam through a first-order optical systems

An elliptical Gaussian wave formalism model of a charged-particle beam is proposed by analogy with an elliptical Gaussian light beam. In the paraxial approximation, the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains. Therefore, the propagation and transform of charged-particle beam passing through a first-order optical system is represented by the ABCD-like law. As an example of the application of this model, the relation between the beam waist and the minimum beam spot at a fixed target is discussed. The result, well matches that from conventional phase space model, and proves that the Gaussian wave formalism model is highly effective and reasonable.

Biological Dose Estimation Model for Proton Beam Therapy

Purpose: The recommended value for the relative biological effectiveness (RBE) of proton beams is currently assumed to be 1.1. However, there is increasing evidence that RBE increases towards the end of proton beam range that may increase the biological effect of proton beam in the distal regions of the dose deposition. Methods: A computational approach is presented for estimating the biological effect of the proton beam. It includes a method for calculating the dose averaged linear energy transfer (LET) along the measured Bragg peak and published LET to RBE conversion routine. To validate the proposed method, we have performed Monte Carlo simulations of the pristine Bragg peak at various beam energies and compared the analysis with the simulated results. A good agreement within 5% is observed between the LET analysis of the modeled Bragg peaks and Monte Carlo simulations. Results: Applying the method to the set of Bragg peaks measured at a proton therapy facility we have estimated LET and RBE values along each Bragg peak. Combining the individual RBE-weighted Bragg peaks with known energy modulation weights we have calculated the RBE-weighted dose in the modulated proton beam. The proposed computational method provides a tool for calculating dose averaged LET along the measured Bragg peak. Conclusions: Combined with a model to convert LET into RBE, this method enables calculation of RBE-weighted dose both in pristine Bragg peak and in modulated beam in proton therapy.

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.