Rigid Bar Research Articles

Stability of vibrations of a moving railway vehicle along an infinite complex three-part viscoelastic beam/foundation system

Vibrations of a railway vehicle that moves on a long three-part viscoelastic system can become unstable because of elastic waves that the railway vehicle generates in the structure. A typical example of the railway vehicle that can experience such instability is a high-speed train. Moving with a sufficiently high speed, this train could generate in the railway track elastic waves, whose reaction might destabilize vibrations of the train. In this paper, an improved procedure and parametric analysis of stability of vibrations of a railway vehicle system were carried out with the emphasis on the effects of damping of the secondary suspension of the railway vehicle, stiffness of the secondary suspension of railway vehicle, mass of the railway vehicle, wheelbase and positions of the supports. The d-decomposition method and the principle of the argument are adopted to handle cumbersome expressions that occur due to the present railway vehicle system model. The railway vehicle system is modeled by elastically connected rigid bars on identical supports. Identical supports are modeled as a system of springs and dashpots attached to the bars on one side, which interact with the beam through the concentrated masses on the other side. The paper analyzes the case when the railway vehicle system exceeds the minimum phase velocity of waves in the beam, which may lead to the vibration of the system becoming unstable. The instability intervals are determined for varying parameters and important conclusions are performed.

Effect of a viscoelastic target on the impact response of a flat-nosed projectile

Taylor impact is a widely used strategy in which a flat-nosed projectile is fired onto a rigid anvil directly to determine the dynamic strength of rod specimens. Nowadays, the rigid anvil is often replaced by an output target bar to ensure the accuracy of measurement via recording strain signals in the output bar. For testing the dynamic strength of low-density materials, a low-impedance target bar, which exhibits viscoelastic characteristics is often employed. In this paper, an extended Taylor model is proposed to improve the idealization of treating the target bar as perfectly rigid material in the classic Taylor model, and the viscoelastic effect of the target bar is incorporated. The viscoelastic target bar is depicted by two elastic springs and one dashpot. Based on the plastic shock wave theory in the flat-nosed projectile associated with the viscoelastic wave analysis in the target bar, the viscoelastic effect of the target bar on the impact response of the flat-nosed projectile is investigated. The finite element simulation is also carried out to verify the theoretical model, and good agreement is found. The present theoretical model is also called the Taylor-cylinder Hopkinson impact, which provides a more accurate way to identify the dynamic material parameters. The dynamic responses of the present model are further compared with previous elastic and rigid target bar models. It is found that the viscoelastic effect of the target bar should be taken into consideration in the Taylor-cylinder Hopkinson impact test for low-impedance materials.

Dynamic stability of vibrations and critical velocity of a complex bogie system moving on a flexibly supported infinity track

The paper studies vibrations of a complex bogie system moving along a high order shear deformable beam on a viscoelastic foundation. The complex bogie system is modeled by elastically connected rigid bars on identical supports. An elastic coupling between the bars is introduced to simulate a rigid or flexible (transverse or/and rotational) connection. Identical supports are modeled as a system of springs and dashpots attached to the bars on one side, which interact with the beam through the concentrated masses on the other side. It is assumed that the masses and the beam are always in contact. A new analytically determined critical velocity of the system is presented. The paper analyzes the case when the complex bogie system exceeds the minimum phase velocity of waves in the beam, which may lead to the vibration of the system becoming unstable. The effect of the elastic coupling between the bars on the stability of the system is also analyzed. The instability regions are found for the complex bogie system by applying the principle of the argument and the D-decomposition method.

03.28: Performance of cruciform finite elements that model 2D steel joints with beams of unequal depth in frame analysis

ABSTRACTThis paper deals with the performance evaluation of cruciform finite elements with 4 nodes and 12 degrees of freedom that model 2D steel joints with beams of unequal depth in frame analysis. These elements are capable of modelling joints that have double rectangular panels, with or without horizontal stiffeners in the panel zone, due to beams of different depths at both sides of the joint. In addition, these cruciform elements are suitable for simple, rigid and semi‐rigid connections and therefore can be used for the global analysis of semi‐rigid steel frames. The performance of these elements is assessed by analysing steel frames under different loading conditions, and comparing the results with complete finite element models.The characteristics of these elements (stiffness and resistance) are generated by a previously proposed displacement based modal approach. All the forces and moments coming from the adjacent beams and columns concur at the joint, therefore, the complete force field in the panel zones is known with no need for a transformation parameter β (EC3‐Part 1.8). The proposed element also avoid the use of mechanical models (composed of springs and rigid bars) for frame analyses, which add complexity, numerical overhead —consequence of the larger number of degrees of freedom— and possible round off errors (due to the rigid bars) in the solution process.In addition, since the real dimensions of the joint are included in the proposed elements, the eccentric moments are automatically taken into account. Also, the interaction between the deep and the shallow sides of the column double panels are considered. Numerical simulations and comparison with complete finite element models are carried out that show the validity and computational efficiency of these elements.

Hybrid foetus with an FE head for a pregnant occupant model for vehicle safety investigations

ABSTRACT‘Expecting’, a computational pregnant occupant model, developed to simulate the dynamic response to crash impacts, possesses anthropometric properties of a fifth percentile female at around the 38th week of pregnancy. The model is complete with a finite element uterus and a multi-body foetus which is a novel feature in models of this kind. In this paper, the effect of incorporating a foetus with a finite element head into ‘Expecting’ is investigated. The finite element head was developed using detailed anatomic geometry and projected material properties. Then it was integrated with the ‘Expecting’ model and validated using the lap belt loading and the rigid bar impact tests. The model is then used to simulate frontal impacts at a range of crash severities with seatbelt and airbag, seatbelt only, airbag only as well as no restraint cases to investigate the risk of placental abruption and compare it with the model featuring the original multi-body foetus. The maximum strains developed in the utero-placental interface are used as the main criteria for foetus safety. The results show comparable strain levels to those from the multi-body foetus. It is, therefore, recommended to use the multi-body foetus in simulations as the computation time is more favourable.

Hencky bar-net model for plate buckling

This paper presents the Hencky bar-net model (HBM) for elastic buckling analysis of rectangular plates with any combination of edge conditions. HBM comprises a grid (or net) of rigid bar segments joined by rotational springs as well as a torsional spring system in each grid panel. The HBM is developed from the finite difference plate model that allows researchers to perform plate buckling analysis via solving a set of algebraic equations instead of solving a fourth order partial differential equation. The elastic spring stiffnesses for the HBM that provides the flexibility for deformation are established for the first time for elastic rotationally restrained edges and free edges. Some plate buckling problems were solved by using the developed HBM and the solutions shown to converge to those of the continuum plate counterparts when the grid size becomes very small; thereby verifying the validity of the model.

Estimation accuracy vs. engineering significance of contact parameters for solid dampers

AbstractAll numerical models of friction-damped bladed arrays require knowledge or information of contact-friction parameters. In the literature, these parameters are typically tuned so that the experimental Frequency Response Function (FRF) of a damped blade matches its numerical counterpart. It is well known that there exist multiple combinations of contact parameters capable of satisfying a given experimental-numerical FRF match. A better approach towards a finer tuning could be based on directly measuring contact forces transmitted between blade platforms through the damper: in this case friction coefficients are estimated through tangential over normal force components during those hysteresis segments which are safely identified as being in a slip condition. This has been applied by these authors to rigid bar (solid) dampers. Unfortunately, the four contact stiffness values (left and right damper-platform contact, normal and tangential) are more than the measurements available in the technique presented by these authors. Therefore, the problem is underdetermined. The purpose of this paper is twofold,i.e., to propose an alternative way to estimate contact stiffness values (i.e.thus solving the under-determinacy mentioned above) and to check the effective significance of such estimates from a practical engineering point of view. The contact parameter estimation technique proposed by these authors produces, for each contact parameter, a best-fit value and an uncertainty band. It will be shown that the uncertainty affecting each contact parameter results in an uncertainty on the equivalent damping and stiffness indicators at blade level which is lower than 5%.

강체전차선을 이용한 직류전기철도용 이동식 전차선 시스템 개발 및 성능검증에 관한 연구

강체전차선을 이용한 직류전기철도용 이동식 전차선 시스템 개발 및 성능검증에 관한 연구

How to produce pre-shaped rigid arch bars using low-cost 3D printing technology-A technical note.

Numerous oral and maxillofacial procedures in dentate patients begin with the fixation of occlusions. While several techniques exist to perform mandibulo-maxillary fixation, many surgeons use arch bars in common practice. In cases of severe craniofacial traumas or jaw malformations, such as temporomandibular joint ankylosis, it may be impossible to use rigid arch bars. This technical note reports on the development of a technique to produce pre-shaped rigid arch bars using 3D printing technology. We take the case of a patient who presents Le Fort 1, Le Fort 2 and Le Fort 3 fractures as well as a central palatine disjunction, an angular mandibular fracture and bilateral zygomatic fractures. We specify the indications and limitations of this technique.

Euler elastica as a Γ-limit of discrete bending energies of one-dimensional chains of atoms

In the 1920s, Hencky proposed a discrete elastica model describing a chain of identical rigid bars connected by torsional springs. Hencky observed that this discrete elastica model converges to Euler’s elastica as the number of bars increases while their lengths decrease, and Hencky’s bar-chain model has been used primarily as an approximation of Euler’s elastica. A Hencky-type bar-chain model can also be incorporated into a Frenkel–Kontorova-type discrete atomistic model, where the joints and bars represent the atoms and interatomic bonds, respectively, while the entire chain of atoms interacts with either a substrate or other chains. The energy of a continuum system corresponding to this Frenkel–Kontorova-type model can then be recovered by taking an appropriate discrete-to-continuum limit. Developing a correct limiting procedure for the discrete elastica establishes the bending component of this continuum energy. In this paper we use Γ-convergence to rigorously show that as the bar length in the discrete elastica model we consider goes to 0, the bending energies of the chain Γ-converge to the continuum bending energy associated with Euler’s elastica.

Modeling and Stability Analysis of Tethered Kites at High Altitudes

A systematic analysis of the role played by several physical mechanisms in the longitudinal stability of a tethered kite is presented. A simple model, which artificially constrains the pitch motion of the kite and approximates the tether by a massless and rigid bar, is improved progressively to include the kite pitch motion as well as the tether inertia, flexibility, wind load, and elasticity. The models are presented as compact sets of ordinary differential equations without algebraic constraints, which are explicitly eliminated by making an extensive use of Lagrangian mechanics. The contributions of each physical mechanism on kite stability are investigated separately, and a tradeoff between the complexity and computational costs of the models against their accuracy and reliability is carried out. The wind load on the tether is identified as a key effect stabilizing the steady state of the kites. The optimal bridle design and tether length selections to compute the kite ceiling are discussed.

RETRACTED ARTICLE: Reality of virtual damage identification based on neural networks and vibration analysis of a damaged bridge under a moving vehicle

Presented here is a reality of virtual damage detection and vibration behaviour study of a discrete beam-like bridge with one or several non-propagating edge cracks subjected to a moving vehicle. In this model, the simply supported beam elements are replaced by a range of rigid bars, which are connected by transverse and rotational springs, while the mass and rotational moment of inertia may be lumped at various points along the beam. The adopted vehicle model here is a four degrees-of-freedom, two axes half-vehicle model with tires flexibility and linear suspensions. Damage can be modelled by altering the spring stiffness equation at the crack position according to predictions, which allows the inclusion of simple or complex damage. To simplify, damage is represented here by an open crack, and stiffness of a given element with damage is calculated by fracture mechanics. Both the discrete element and finite element methods are used to investigate vibration analysis of a discrete beam model subjected to a moving vehicle to confirm model feasibility in vibration analysis under a moving vehicle. Besides, some dynamic response laws are obtained. Considering an irregular road profile, the effects of the moving vehicle velocity, the moving vehicle mass, the crack location and the crack depth on dynamic response of a beam-like bridge are analysed by a numerical example, combining a vehicle–bridge coupled vibration MATLAB program with ANSYS. In addition, the neural network is used to identify the damage of the structure. Numerical results of the numerical model predictions, compared with those obtained from the continuous elements beam, support the accuracy of the discrete elements beam model in both cases of undamaged beam and damaged one. The evidence for condition assessment and damage identification of bridge is obtained from this simulation as obtaining the vibrational characteristics of the damaged beam structure subjected to a moving vehicle. And the inversion results show that the neural network method can identify the injury location and injury size of the structure accurately.

Design and Experimental Study of an L Shape Piezoelectric Energy Harvester

Piezoelectric energy harvesters of cantilevered beam type are studied in various fields due to simplicity. In general, these systems obtain electrical energy from mechanical strain by bending of cantilevered beam. However, conventional systems have disadvantages that they have low efficiency in frequency regions other than resonance frequency. To overcome the limitations, various energy harvesters to apply performance enhancement strategies are proposed and investigated. In this paper, a frequency-changeable L shape energy harvester which is form connected cantilever beam and rigid arm is proposed and investigated. The conventional piezoelectric energy harvester exhibits the principal frequency in the simple bending mode whereas the proposed system features the twisting mode resulting in a higher output voltage than the conventional system. The proposed energy harvester is simplified to a two-degree-of-freedom model and its dynamics are described. How the length of a rigid bar affects its natural frequencies is also studied. To evaluate the performance of the system, experiments by using a vertical shaker and numerical simulation are carried out. As a result, it is shown that the natural frequency for a twisting mode decreases as the arm length increased, and the higher output voltage is generated comparing with those of the conventional energy harvester.

A 2-DOF Model of an Elastic Rocket Structure Under Circulatory Force

It is intended, in this paper, to develop a mathematical and numerical model of an elastic space rocket structure as a Beck’s column excited by a follower (or circulatory) force. This force represents the rocket motor thrust that should be always in the direction of the tangent to the structure deformed axis at the base of the vehicle. We present a simplified two degree of freedom rigid bars discrete model. Its system of two second order nonlinear ordinary differential equations of motion are derived via Lagrange’s energy method, allowing for a general understanding of the main characteristics of the problem. The proposed equations consider up to third order (cubic) inertia, stiffness and forcing terms. Among other rich nonlinear dynamic behaviour of this model, depending on parameters and initial conditions choices, either stable or unstable limit cycle post-critical steady state solutions are possible. The latter is a form of flutter. Numerical simulations are carried out using Runge-Kutta’s 4th order algorithm in Matlab environment.

Deformable printed circuit boards that enable metamorphic electronics

A method to produce single-layer deformable and stretchable printed circuit boards is reported and applied to enable the realization of metamorphic electronic products that can take on new three-dimensional (3D) shapes. The models contain arrays with packaged surface mount devices and bare dies that integrate light-emitting diodes (LEDs) and transistors within a rubber matrix. The test structures morph from planar to spherical to cone-like topologies. In one approach, the thickness of the stretchable printed circuit board is locally adjusted to control the morphological changes. In addition, a three-dimensionally-shaped chaperon is introduced to enable more abrupt topological changes. A comparative study of various designs of the metallization layer and stress-relieving reinforcing elements identified a highly stretchable and deformable design (up to 315% or six thousand 150% stretch and release cycles), which shields the interface between the hard and non-stretchable components from high levels of stress. A slight tweak to normal fabrication procedures has enabled researchers develop circuit boards that turn into new three-dimensional shapes. Flexible electronic devices are usually made by depositing circuits onto rubberized substrates. But delaying the use of a stretchable support until the end of production makes it easier to design, test and process such materials, reports Heiko Jacobs from Technische Universität Ilmenau and colleagues. This approach enabled them to identify meandering metal ribbons and rigid reinforcement bars as ways to provide critical stress relief for ‘metamorphic’ electronics. After integrating light-emitting diodes and other surface-mounted devices into rubber matrices, the team transformed the flat materials into shapes such as spheres and cones by either adjusting the thickness of the rubber substrate or inflating them with the help of geometric ‘chaperones’. A novel approach to produce stretchable and deformable printed circuit boards is reported and applied to enable the realization of metamorphic electronic products, which conform to take on new three-dimensional shapes. The test structures morph from planar, to spherical, to cone-like topologies.

Decentralized structure-integrated spatial force measurement in machine tools

New manufacturing processes and extended movability of modern machine tools, such as five-axis kinematics or hexapods, increase the demand for in-process measurement of spatial forces and torques in up to 6 degrees of freedom (DoF). The approach proposed in this paper is based on the idea of integrating 6 single-axis force sensors into the machine’s structure and converting these sensor forces to spatial forces and torques at the tool centre point (TCP) using a measurement model. This concept is advantageous to costs, ruggedness and available workspace when compared to state-of-the-art 6 DoF force/torque transducers. At the same time, the achievable measuring accuracy is similar and also significantly better than the accuracy of drive current based force evaluation. On the other hand, structure and machine influences have to be addressed by suitable measurement models. This article presents design, parametrization, verification, and characterisation of these measurement models on the example of four integration concepts, two in rigid bar frameworks and two in bar kinematics. Further, experimental results are shown which are classified in comparison to a 6 DoF F/T sensor and drive current based force measurement. Finally, other influences, such as structural design and deformations, as well as the integration of sensors and models into the machine’s control software are discussed.

Singular Space-Time Transformations. Towards One Method For Solving the Painlevé Problem

We develop the method of singular space-time transformations for systems with impact and friction. We consider a mathematical model of a Painleve problem concerning impacts of an absolutely rigid bar with a rough surface. Using the method of singular space-time change of variables, we obtain the model of an absolutely rigid body by passing to the limit as the generalized rigidity parameter tends to infinity.

Parameter optimization of tetrahedral tuned mass damper for three-directional seismic response reduction

An optimization approach is presented for design of a tetrahedral tuned mass damper called TD-TMD for three-directional seismic response reduction of structures. The mass damper consists of a viscous damper and a mass connected by springs and a rigid bar. By utilizing flexibility of the springs, movement of the mass in three-directions and elongation of the viscous damper are amplified, and vibration energy of the structure is effectively dissipated by the viscous damper. The objective function of the parameter optimization problem is the mean norm of the response displacements of the structure. The bounds of parameters are determined by solving an auxiliary nonlinear programming problem to maximize the minimum deformation of the damper against unit static loads in various directions. Approximate optimal solutions are found using a heuristic approach called simulated annealing combined with pure random search that generates efficient initial solutions. The TD-TMD is attached to a simple three-degree-of-freedom structure, and the seismic responses are compared with those with conventional single-directional tuned mass dampers.

Soft mobile robots driven by foldable dielectric elastomer actuators

A cantilever beam with elastic hinge pulled antagonistically by two dielectric elastomer (DE) membranes in tension forms a foldable actuator if one DE membrane is subject to a voltage and releases part of tension. Simply placing parallel rigid bars on the prestressed DE membranes results in enhanced actuators working in a pure shear state. We report design, analysis, fabrication, and experiment of soft mobile robots that are moved by such foldable DE actuators. We describe systematic measurement of the foldable actuators and perform theoretical analysis of such actuators based on minimization of total energy, and a good agreement is achieved between model prediction and measurement. We develop two versions of prototypes of soft mobile robots driven either by two sets of DE membranes or one DE membrane and elastic springs. We demonstrate locomotion of these soft mobile robots and highlight several key design parameters that influence locomotion of the robots. A 45 g soft robot driven by a cyclic triangle voltage with amplitude 7.4 kV demonstrates maximal stroke 160 mm or maximal rolling velocity 42 mm/s. The underlying mechanics and physics of foldable DE actuators can be leveraged to develop other soft machines for various applications.

Pre-optimization of Asymmetrical Underplatform Dampers

The numerical coupled optimization of an underplatform damper is the exploration of its dynamics through a finite element model which includes both the damper and the blades. This is an effective approach if the initial damper mass and geometry have been previously selected (i.e., pre-optimized) in such a way that those parameter combinations leading to undesirable damper behavior are ruled out a priori: —ensure that damper jamming is avoided by ruling out the undesirable combinations of platform and friction angles; —ensure that damper lift-off is avoided through an appropriate choice of the shape and position of the damper-platform flat contact surface and the position of the damper mass center; —set upper and lower to the value of damper-platform contact forces (as a multiple of the damper centrifugal force), the first being related to friction and wear problems, and the second to the very existence of bilateral contacts. The above is strongly dependent on the effective values of friction coefficients, which can vary by a factor of over two with temperature, frequency and contact pressure. The paper illustrates the pre-optimization procedure using, as an example, a rigid bar damper with a curved-flat cross section. In order to validate the method against experimental data and to determine the necessary real contact parameters, the paper capitalizes on already developed tools presented in the previous ASME papers: the test rig developed at the AERMEC lab, the numerical model representing the damper dynamics, and the automatic random sampling tuning procedure.