scholarly journals Fourier Series Approach for the Vibration of Euler–Bernoulli Beam under Moving Distributed Force: Application to Train Gust

2019 ◽  
Vol 2019 ◽  
pp. 1-21
Author(s):  
Shupeng Wang ◽  
Weigang Zhao ◽  
Guangyuan Zhang ◽  
Feng Li ◽  
Yanliang Du
Keyword(s):  
Fourier Series ◽  
Dynamic Response ◽  
High Speed ◽  
Dynamic Pressure ◽  
Superposition Method ◽  
Bernoulli Beam ◽  
Complex Procedure ◽  
A Site ◽  
Site Test ◽  
Euler Bernoulli Beam

The dynamic response of an Euler–Bernoulli beam under moving distributed force is studied. By decomposing the distributed force into Fourier series and extending them to semi-infinite sine waves, the complex procedure for solving this problem is simplified to three base models, which are calculated by the modal superposition method further. The method is proved to be highly accurate and computational efficient by comparing with the finite element method. For verifying the theory and exploring the relationship between dynamic pressure due to train gust and vibration of the structure, a site test was conducted on a platform canopy located on the Beijing-Shanghai high-speed railway in China. The results show the theory can be used to evaluate the dynamic response of the beam structure along the trackside due to the train gust. The dynamic behavior of a 4-span continuous steel purlin is studied when the structure is subjected to the moving pressure due to different high-speed train passing.

Multiple-Railcar High-Speed Train Subject to Braking

2017 ◽  
Vol 17 (07) ◽  
pp. 1750071 ◽  
Author(s):  
Minh Thi Tran ◽  
Kok Keng Ang ◽  
Van Hai Luong
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Contact Forces ◽  
Bernoulli Beam ◽  
Wheel Load ◽  
Braking Torque ◽  
Braking Distance ◽  
Train Speed ◽  
Euler Bernoulli Beam ◽  
Two Parameter

The dynamic response of a high-speed multiple-railcar train experiencing deceleration under braking condition over a straight track is investigated using the moving element method. Possible sliding of train wheels over the rails is accounted for. The train is assumed to comprise a locomotive as the leading railcar and several passenger railcars connected to each other through train couplers. Each railcar is modeled as a 15-DOF system of interconnected car body, two bogies and four wheels. The rail is modeled as an Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The train and rails are coupled through normal and tangential wheel–rail contact forces. The effects of various parameters, such as braking torque, coupler stiffness, coupler gap, wheel load, wheel–rail contact condition, initial train speed and partial failure in braking mechanism on the dynamic response of the train subject to braking are investigated. It is found that there is significant interaction between neighboring railcars when the braking torque is applied between the optimal and critical torques. The former is the torque that would result in the smallest braking distance with no occurrence of wheel sliding and the latter is the smallest torque to cause wheel sliding in all four wheels.

scholarly journals Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction

2021 ◽  
Author(s):  
Paul König ◽  
Patrick Salcher ◽  
Christoph Adam ◽  
Benjamin Hirzinger
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Element Model ◽  
Bernoulli Beam ◽  
Railway Bridges ◽  
Modal Expansion ◽  
High Speed Trains ◽  
Mass Spring ◽  
Track Bridge ◽  
Euler Bernoulli Beam

AbstractA new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving mass–spring–damper (MSD) system of the passing train using a discrete substructuring technique (DST). To validate the presented modeling approach, its results are compared with those of a finite element model. In an application, the influence of the soil–structure interaction, the track subsystem, and geometric imperfections due to track irregularities on the dynamic response of an example bridge is demonstrated.

Effects of Different Models on Natural Frequencies of Short Span Bridges Used in High Speed Rail

2015 ◽  
Author(s):  
Said I. Nour ◽  
Mohsen A. Issa
Keyword(s):  
Timoshenko Beam ◽  
High Speed ◽  
Natural Frequencies ◽  
Bernoulli Beam ◽  
High Speed Rail ◽  
Vertical Stiffness ◽  
Short Span ◽  
Elastically Supported ◽  
Euler Bernoulli Beam ◽  
Track Modulus

The natural frequencies of vibration of short span bridges used in high-speed rail were investigated. Three different models of increasing complexity were evaluated and their effects on the vibration frequency were compared to the first basic model of simply supported Euler-Bernoulli beam. In the second and third cases, the bridge was modeled as an Euler-Bernoulli and Timoshenko beam supported at its two ends by identical spring elements with an equivalent vertical stiffness to simulate elastomeric bearings and soil foundation. The boundary value problem was solved numerically to extract the bridge eigenfrequencies. In the case of Euler-Bernoulli beam, curve fitting techniques were used to deduce accurate simple empirical formulae to calculate the first six natural frequencies of an elastically supported bridge. In the case of a Timoshenko beam, graphical solutions were proposed to compute the fundamental frequency. Results confirmed that the use of Timoshenko beam theory reduces the natural frequency and the consideration of flexible supports further decreases the natural frequency. In the fourth model, the interaction of the track and the bridge was included. The bridge was modeled as an elastically supported beam and the track was modeled as a spring-damper element with an equivalent vertical stiffness resulting from track components like rail pads, cross-ties and ballast. A parametric study was performed to analyze the effects of the track stiffness on the natural frequencies of the bridge. Graphical solutions were presented to quantify the change of the normalized natural frequencies of the system with the increase in the track modulus. Results indicated that the changes in the track modulus have no significant effects in models with rigid supports. A decrease in the fundamental frequency was noticeable with softer track modulus as the support flexibility increased.

Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load

2020 ◽  
Vol 234 (24) ◽  
pp. 4801-4812 ◽  
Author(s):  
Rajendra K Praharaj ◽  
Nabanita Datta
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Load ◽  
Order Derivative ◽  
Viscoelastic Foundation ◽  
Bernoulli Beam ◽  
Integer Order ◽  
Foundation Model ◽  
Euler Bernoulli Beam

The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

scholarly journals Critical Velocity of High-Performance Yarn Transversely Impacted by Razor Blade

Fibers ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95 ◽  
Author(s):  
Boon Lim ◽  
Jou-Mei Chu ◽  
Benjamin Claus ◽  
Yizhou Nie ◽  
Wayne Chen
Keyword(s):  
Critical Velocity ◽  
High Speed ◽  
High Performance ◽  
Hertzian Contact ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Razor Blade ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Hertzian Contact Model

A ballistic parameter that influences the ballistic performances of a high-performance yarn is the critical velocity. The critical velocity is defined as the projectile striking velocity that causes instantaneous rupture of the yarn upon impact. In this study, we performed ballistic experiments to determine the critical velocity of a Twaron® yarn transversely impacted by a razor blade. A high-speed camera was integrated into the experimental apparatus to capture the in-situ deformation of the yarn. The experimental critical velocity demonstrated a reduction compared to the critical velocity predicted by the classical theory. The high-speed images revealed the yarn specimen failed from the projectile side toward the free end when impacted by the razor blade. To improve the prediction capability, the Euler–Bernoulli beam and Hertzian contact models were used to predict the critical velocity. For the Euler–Bernoulli beam model, the critical velocity was obtained by assuming the specimen ruptured instantaneously when the maximum flexural strain reached the ultimate tensile strain of the yarn upon impact. On the other hand, for the Hertzian contact model, the yarn was assumed to fail when the indentation depth was equivalent to the diameter of the yarn. The errors between the average critical velocities determined from experiments and the predicted critical velocities were around 19% and 48% for the Euler–Bernoulli beam model and Hertzian contact model, respectively.

Dynamic Modeling and Optimal Control of Rotating Euler-Bernoulli Beams

1997 ◽  
Vol 119 (4) ◽  
pp. 802-808 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Optimal Control ◽  
High Speed ◽  
Vibration Suppression ◽  
Large Angle ◽  
System Response ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Control Moment ◽  
Angular Velocities ◽  
Euler Bernoulli Beam

The nonlinear integro-differential equations, describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, are derived. The effects of both the linear and nonlinear elastic rotational couplings are investigated. The linear couplings are exactly accounted for in a decoupled Euler-Bernoulli beam model and their effects on the eigensolutions and response are significant for a small ratio of hub-to-beam inertia. The nonlinear couplings with a resultant stiffening effect are negligible for small angular velocities. A discretized model, suitable for the study of large angle, high speed rotation of a nonuniform beam, is presented. The optimal control moment for simultaneous vibration suppression of the beam at the end of a prescribed rotation is determined. Influences of the nonlinearity, nonuniformity, maneuver time, and inertia ratio on the optimal control moment and system response are discussed.

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