Rigid Beam Model Research Articles

Research on Local Structure Plastic Damage of Cylindrical Shell under Near-field Underwater Explosion

The local structure of the cylindrical shell produces plastic deformation under the near-field underwater explosion load, based on the fact that the ring rib is the strong support of reinforced cylindrical shell plate, this paper simplifies the reinforced cylindrical shell model into a rigid slatted beam model at both ends, and lists the equations of slatted beams under the action of shock wave and bubble pulsation load. This equation takes the initial damage caused by shock wave into account, and compares the calculation results obtained by the theoretical method with the experimental data, which verifies the correctness of this mechanical model. At the same time, it is explained that this calculation method can better predict the plastic damage of the local structure of the cylindrical shell under the action of near-field underwater explosion.

Study on the analytical model for load distribution of multiple-ring-stiffened tube-gusset joints considering ring stiffness

Tube-gusset joints in transmission towers are usually reinforced by multiple ring stiffeners. The external loads exerted on the joints will ultimately be borne by the rings. Therefore, it is crucial to understand how the loads are distributed among the ring stiffeners during the design stage. To this end, a solution was introduced in the pertinent Japanese standard. However, this solution has been derived based on the assumption of rigid ring stiffeners. Namely, the load distribution is irrelevant to the features of each ring stiffener, e.g., height, thickness, and spacing. This has led to inaccurate results in the solution. As an advancement from it, an improved analytical model is proposed in this paper. The tube-gusset joints with multiple ring stiffeners (MS-Joints) are described by the spring-mounted rigid beam model, in which the ring stiffeners are represented by spring supports. An analytical solution is therefore derived by incorporating flexible ring stiffeners. The validity of the solution is examined by the test-validated finite element method. Comparisons with the numerical results prove that the proposed solution is significantly more accurate than the conventional one. It is then used to conduct parametric analyses on the features of the ring stiffeners. The results reveal that the load distribution is most sensitive to the height of the ring stiffeners. Also, ring stiffeners should be arranged symmetrically to the middle line of the gusset plate to exploit their bearing capacities.

Dynamic modeling and analysis of center rigid body Timoshenko beam model based on unconstrained mode

The transverse deformation of the beam will lead to the longitudinal shortening deformation, and this transverse-longitudinal deformation coupling will bring the dynamic stiffening effect term on the generalized rigidity of the beam model. For the rotating beam structure, the centrifugal force will cause axial tension, with coupling axial and transverse deformation of the beam and bring additional geometric stiffness, which is more obvious for the thick short beam. The central rigid body-Timoshenko beam model with a large-range-motion center was investigated. Firstly, the dynamic model with centrifugal forces was established by means of the Timoshenko beam theory and the Hamilton principle. Secondly, the unconstrained mode concept was introduced, and the unconstrained mode shape functions and natural frequencies were solved with the Frobenius method. Finally, numerical simulations were carried out to explore the difference of generalized stiffness between the unconstrained mode and the constrained mode at different constant speeds, and the effects of centrifugal forces on the model under unconstrained mode condition were discussed.

Coriolis Force Sliding Mode Control Method for the Rotary Motion of the Central Rigid Body-Flexible Cantilever Beam System in TBM

Beam slab structure is often encountered in a complex tunnel boring machine. Beam slab structure is subject to dynamic load, which is easy to cause fatigue damage and affect its service life. Therefore, it is necessary to control the vibration of this kind of beam slab structure. In this study, the central rigid body-flexible beam model is established for the rotating beam and plate rotating around the y-axis. Based on the Hamilton variational principle, the dynamic equation of the central rigid body-flexible beam system is established, and the dynamic model of the central rigid body-flexible beam system considering the influence of Coriolis force and centrifugal force is given. The vibration control of the central rigid body-flexible beam system is studied. The vibration mode of the rotating Euler Bernoulli beam is determined by using the elastic wave and vibration mode theory. The influence of the rotating motion on the beam vibration is analyzed, and the variable structure control law is designed to suppress the beam vibration. Numerical simulation results show that the control method can effectively suppress the first-order and second-order vibration of the beam and verify the effectiveness of the control strategy.

Modeling intense-electron-beam generated plasmas using a rigid-beam approximation

A model of an electron-beam–plasma system is introduced to model the electrical breakdown physics of low-pressure nitrogen irradiated by an intense pulsed electron beam. The rapidly rising beam current induces an electric field, which drives a return current in the plasma. The rigid-beam model is a reduction of the problem geometry to cylindrical coordinates and simplifications to Maxwell's equations that are driven by a prescribed electron beam current density. The model is convenient for comparing various reductions of the plasma dynamics and plasma chemistry while maintaining a good approximation to the overall magnitude of the beam-created electric field. The usefulness of this model is demonstrated by coupling the rigid-beam model to a fluid plasma model and a simplified nitrogen plasma chemistry. The dynamics of this coupled system are computed for a range of background gas pressures, and the results are compared with experimental measurements. At pressures 1 Torr and above, the simulated line-integrated electron densities are within a factor of two of measurements and show the same trend with pressure as observed in experiment.

A Rigid-Beam-Model for studying the dynamic behaviour of cantilever masonry walls

In this work, a simple and effective Rigid Beam Model recently introduced for studying the dynamic behaviour of ancient freestanding stone columns is extended to the case of cantilever unreinforced masonry walls, considered along their thickness and subjected to out-of-plane loading. Both monolithic and multi-block walls were investigated. The proposed model assumes each block of the wall as a rigid beam element and each interface as a node. By assuming no sliding along the interfaces and small displacements of blocks, rocking can be simulated by a bi or tri-linear moment rotation non-linear constitutive law. Different in geometry monolithic and multi-block masonry walls were developed in the numerical model and subjected to different in magnitude and frequency harmonic loading. Their response was compared against those from the literature and good agreement was found. From the analysis results, it was found that monolithic walls can overturn with acceleration magnitudes larger than their corresponding static load multipliers, if input frequency values increase. However, overturning accelerations of multi-block walls increase less rapidly for increasing input frequency with respect to the corresponding equivalent monolithic walls. Collapse mechanisms involving wall portions above the base were found in addition to traditional overturning ones with respect to the base. To ensure reproducibility of results, input and output files will be made publicly available.

The effect of roof systems on seismic performance of reinforced concrete frame-bent main building of large-scale thermal power plant

The roof systems of turbine hall in large-scale thermal power plant are often simulated by approximate rigid beam model. Wenchuan earthquake again revealed the frequent destruction of these roof systems. In this study, three kinds of general roof systems as space grid, trapezoid steel roof truss and reinforced concrete (RC) mansard roof truss were considered. Also, the numerical model of RC frame-bent main building in large-scale thermal power plant was established. Seismic performance of main building was compared with approximate rigid beam model, and the damage mechanism of roof systems was also investigated. The results indicate that the response calculation of frame part by rigid beam model is feasible, and roof systems give most contribution to the response of bent part. After considering roof systems, overall collaborative performance is enhanced, but bent part is still unable to become a second defence part after shear walls fail. The torsional irregularity of roof systems is very serious, and more attentions should be paid to the bearing shear failure of space grid and components strength failure of RC roof systems. Copyright © 2014 John Wiley & Sons, Ltd.

Transverse instabilities of coasting beams with space charge

Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.

Electron beam hollowing in laser–solid interactions

Electron beam hollowing in a plasma is investigated using an analytical, rigid beam model and two different hybrid codes in an attempt to explain observations of hollow plasma formations on the back of plastic targets in experiments carried out on the Vulcan terawatt laser. The relevance of the results to electron transport in fast ignition inertial confinement fusion is considered using dimensionless scaling parameters.

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions with large beam-beam parameter

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA, where the lepton beam has such a large beam-beam parameter (up to xi(y) = 0.272 ) that the single-particle motion is locally unstable at the origin (closed orbit). Unlike the symmetrical case of beam-beam interactions, the ratio of the coherent beam-beam tune shift and the beam-beam parameter in this unsymmetrical case of beam-beam interactions was found to decrease monotonically with an increase of the beam-beam parameter. The results of self-consistent beam-beam simulation, the linearized Vlasov equation, and the rigid-beam model were compared with the experimental measurement. It was found that the coherent beam-beam tune shifts measured in the experiment and calculated in the simulation agree remarkably well but they are much smaller than those calculated by the linearized Vlasov equation with the single-mode approximation or the rigid-beam model. The study indicated that the single-mode approximation in the linearization of the Vlasov equation is not valid in the case of unsymmetrical beam-beam interactions. The rigid-beam model is valid only with a small beam-beam parameter in the case of unsymmetrical beam-beam interactions.

425 弾性支持部を通過する柔軟梁に生じる不安定

The stability of translating flexible beam that passes through the elastic support is investigated. The instability of the beam is observed as the axial moving velocity increases from numerical simulation results. It is clarified from the consideration with the rigid beam model that the increasing of mass and damping coefficient ratio of the support yields negative damping effect of the system and the increasing of damping coefficient and stiffness ratio of the support yields negative stiffness effect of the system as the axial moving velocity increases.

Effects of a solenoidal focusing field on the electron–ion two-stream instability in high-intensity ion beams

A rigid-beam model is used to investigate the influence of a solenoidal focusing field B 0 e ̂ z on the electron–ion two-stream instability that can occur in high-intensity ion beams when an (unwanted) component of background electrons is present. A relatively weak solenoidal magnetic field strongly constrains the transverse electron motion and can lead to a significant reduction in instability growth rate whenever ω 2 ce ⪢2( n b e b / n e e) ω 2 pe . Here, ω ce = eB 0/ m e c is the electron gyrofrequency, ω pe =(4 πn e e 2/ m e ) 1/2 is the electron plasma frequency, and n b and n e are the ion and electron number densities.

Numerical study for the two-beam instability due to ions in electron-storage rings

We discuss the two-beam instability which is caused by interactions between ions and the electron beam in electron storage rings. Motion of beam and ions trapped in the beam potential was studied by using a simulation method based on a rigid Gaussian beam model. We consider two types of the two beam instability depending on the trapped time. One is the so-called ion trapping instability, in which ions are accumulated every revolution. The growth of the coupled bunch mode, which was obtained by simulations, was consistent with experiments in the KEK-photon factory. The other is the fast ion instability, in which ions are trapped during only the passage of a single series of bunches (bunch train). Simulations gave the growth of the couple bunch mode for the KEK-B factory.

The influence of damping on the ion hose instability

The ion hose instability in the ion-focused regime is analyzed using a rigid beam model with phenomenological damping terms. Values of the instability wavelength, e-folding length, and group velocity are calculated and compared with numerical results. The impulse response function for this model is also obtained.

Nonlinear stage of development of resistive hose instability of a high-current relativistic electron beam in a plasma

The nonlinear stage in the development of a resistive hose instability of a highcurrent relativistic electron beam in a finite-conductivity plasma has been studied in the rigid-beam model. The attenuation of the force of the interaction of the beam with the magnetic field of the total current for large beam displacements is shown to result in the stabilization of the instability. The stabilization time and the amplitudes of the oscillations in the saturation regime are determined as functions of the parameters of the beam in the plasma.

Seismic analysis of a rotor‐bearing system

AbstractThe seismic analysis of a rotor‐bearing system is presented in the time domain. The governing equations of motion for the rotor are derived including the effects of rotatory inertia, shear deformation, gyroscopic effects, axial force, axial torque, stiffness and damping provided by the lubricants in the bearings, base translation and base rotation. A simple and efficient finite rotor element based on a Galerkin formulation is proposed to model the rotor. The effects of disks and flywheels mounted on the rotor are also included in the analysis. An example problem for a rotor‐bearing system is solved using El Centro earthquake data. Four cases are investigated that will permit one to study the influence of spin, base rotation, comparison between rigid body model and beam model and the influence of axial force and axial torque. The results of the above study show that the gyroscopic effects amplify the response of the rotor‐bearing system. The base rotations of the rotor‐bearing system under seismic excitation contribute significantly to the response.

Coupled dipole oscillations in an intense relativistic electron beam

The stability properties of coupled dipole resonance oscillations in a relativistic electron-beam–plasma system are investigated within the framework of a rigid beam model. The analysis is carried out assuming sharp-boundary rectangular density profiles, and distinguishing the two cases: (a) beam-electron–plasma-electron dipole resonance oscillations and (b) the ion resonance instability for an intense relativistic electron beam partially charge neutralized by background ions. In case (a), it is shown that the system is most unstable for zero fractional charge neutralization and that the instability growth rate can be significantly reduced by increasing the density ratio ?e’/?e, where ?e’ and ?e are the beam-electron and plasma-electron densities, respectively. Moreover, the characteristic growth rate for the electron-electron dipole resonance instability can be a substantial fraction of the beam-electron cyclotron frequency. In case (b), it is found that the instability growth rate is enhanced considerably by increasing the beam density and energy and that, for sufficiently small fractional charge neutralization, the most unstable mode occurs for long axial wavelengths (kz=0). The characteristic growth rate for the ion resonance instability is also found to be a substantial fraction of the beam-electron cyclotron frequency.