Longitudinal Dynamic Response Research Articles

A coupling method for wheel–rail longitudinal interaction

Longitudinal wheel–rail interaction is often neglected in railway engineering research. In order to analyze the system dynamics with consideration of the braking force, a new longitudinal wheel–rail interaction model is proposed in this paper. Then, the reliability of the proposed model is verified by comparing the results obtained from the traditional vehicle-track coupled dynamic model. The calculated dynamic responses of the system with different time steps are compared to illustrate the stability of the proposed method. In the case study, the influence of the track irregularity on the dynamic response of the system is analyzed in detail, and it is found that the influence of the lateral track irregularity on the longitudinal dynamic response of the system is significant. In addition, the effect of the nonlinearity of ballasted bed longitudinal resistance on the longitudinal dynamic response, and it is found that the nonlinear characteristics of the ballast bed cannot be ignored.

Longitudinal Dynamic Response of a Large-Diameter-Bored Pile Considering the Bottom Sediment and Radial Unloading of the Surrounding Soil

The longitudinal dynamic response of a large-diameter-bored pile is investigated considering the bottom sediment and the radial unloading of the surrounding soil. First, the sediment between the pile tip and the bedrock is treated as a fictitious soil pile with a cross-sectional area similarto that of the pile tip. The large-diameter-bored pile (including the fictitious soil pile) is considered as a Rayleigh–Love rod and is divided into finite segments. Under theseconditions, the three-dimensional (3D) effect of the wave propagation along the pile is indirectly simulated by considering the transverse inertia of the pile to avoid complicated calculations. Meanwhile, the surrounding soil is divided into finite annular zones in the radial direction, with the soil properties varying radially as well to simulate the radial unloading of the surrounding soil during construction. The governing equation for each soil zone is built and solved, from zone to zone, to obtain the shear stress acting on the pile. Then, the governing equation for the fictitious soil pile (i.e., the sediment) is solved to derive the dynamic action at the pile tip. In a similar manner to that ofthe fictitious soil pile and together with the recursion method, the governing equation for the pile is solved to obtain the pile’s complex impedance and velocity response. The proposed solution is verified and then introduced to portray the coupling effect of the sediment, pile parameters and radial unloading of the surrounding soil on the longitudinal dynamic response of the large-diameter-bored pile.

Investigations on the Effects of Rail Longitudinal Forces in Train-Track Dynamic Interaction

Nowadays, attention to railways has been increased as one of the important transportation methods. Various factors can cause longitudinal forces on the railway tracks, so the most important factors are the temperature changes due to the rail contraction and expansion (thermal forces), train braking system forces and acceleration, etc. Increasing longitudinal force can lead to buckling phenomena in railway tracks. In this paper, the effects of tensile and compressive longitudinal forces on the parameters of rail, sleeper, and ballast layers under vertical moving loads are investigated by using the finite element method. In this regard, by performing sensitivity analyses for different values of longitudinal forces and train speeds dynamic responses (displacement, velocity, and acceleration) of railway track components like rail, sleeper, and ballast have been studied. The results show that increasing the values of longitudinal axial force from –2000 [kN] up to 2000 [kN] as well as increasing the train speed from 10 [m/s] (36 [km/h]) up to 100 [m/s] (360 [km/h]) increases the rail displacement and velocity in the range of 25% up to 37% also the rail acceleration in the range of 9% up to 14%. The velocity and acceleration of the sleeper also the ballast velocity increase in the range of 24% up to 30% and 7% up to 9%, respectively, by increasing the speed of the train from 10 [m/s] (36 [km/h]) to 100 [m/s] (360 [km/h]) in all three modes without applying axial force, considering compressive and tensile one in the train-track interaction system.

Quantitative research on vehicle energy consumptions based on the longitudinal-vertical dynamics of the tracked vehicle

In this paper, a longitudinal-vertical coupling tracked vehicle dynamic model is established to simultaneously describe the longitudinal, vertical and pitch dynamic responses of the tracked vehicle under off-road conditions. The road wheels are subjected to variable longitudinal-vertical forces due to the terrain unevenness and the excitations are transmitted to the vehicle body through the torsion suspension system. An experiment by means of a scaled-down tracked vehicle was carried out. The comparisons between the field test results and simulation results verified the effectiveness of the coupling dynamic model on predicting the vehicle dynamics. Taking advantage of the coupling tracked vehicle dynamic model, the energy computation formulas are further derived to quantitatively study the vehicle energy consumptions. The energy consumption distributions of the tracked vehicle on uneven road and paved road at different velocities are analysed. The computation results indicate that the developed energy computation method is reliable on predicting the energy generation and dissipation of the tracked vehicle. It has been found that the proportions of damping dissipation energy and road roughness caused energy consumption to total energy consumption are both higher at a greater speed.

Longitudinal Seismic Analysis of Tunnels with Nonuniform Strata Considering the Effect of Karst

The longitudinal direction of shield tunnels is prone to seismic damage due to excessive deformation under seismic action, especially in nonuniform stratum. In this paper, the longitudinal dynamic response of the tunnel under different seismic effects is calculated based on the longitudinal equivalent stiffness model using the stratigraphic load model, and the seismic indexes such as longitudinal corner, tube sheet and joint bolt stresses are verified. The calculation results show that the longitudinal seismic weakness of the shield tunnel is in the interface between soft and hard strata and karst development. The longitudinal axial force of the structure is larger during the longitudinal excitation of seismic waves, and the maximum bending moment is mainly in the vertical plane, i.e., the vertical bending moment. The axial force of the tunnel is smaller during the transverse excitation of seismic waves. The maximum bending moment is mainly the bending moment in the horizontal plane, i.e., the transverse moment. The South Lake section of the Two Lakes Tunnel has good seismic performance in the event of a rare earthquake with a 50-year exceedance probability of 2%. The investigation can guide the seismic design of the South Lake section of the Two Lakes Tunnel.

Associations of clinical features and dynamic immune response with the duration of viral RNA shedding in patients with COVID-19

<sec><strong>Background</strong> Clinical features and the dynamic changes of the immune response in coronavirus disease-2019 (COVID-19) patients play essential roles in the disease courses. We hypothesized that clinical features and longitudinal dynamic immune response of COVID-19 patients might be associated with viral shedding duration. </sec><sec><strong>Methods</strong> In this retrospective study, we documented 413 adult patients with laboratory-confirmed COVID-19 from Wuhan Huoshenshan Hospital. Demographic, clinical, and laboratory data were extracted from electronic medical records. Risk factors associated with viral shedding duration were examined using odds ratios (ORs) and 95% confidence intervals (CIs) in the multivariable logistic regression models. </sec><sec><strong>Results</strong> The median duration of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral shedding was 48 days (interquartile range, 40–58 days) among all patients. Fever symptom (OR, 2.23; 95% CI, 1.46–3.44), delayed admission after symptom onset (OR, 15.33; 95% CI, 9.14–26.65), CD8⁺ T cells (OR, 1.93; 95% CI, 1.10–3.44) were associated with prolonged viral shedding. In contrast, shorter viral shedding was associated with CD4⁺ T cells (OR, 0.38; 95% CI, 0.16–0.88), the ratios of CD4⁺ T cells to CD8⁺ T cells (OR, 0.79; 95% CI, 0.63–0.98). Longitudinal dynamic analyses demonstrate that sustained monocyte level was associated with shorter viral shedding (OR, 0.41; 95% CI, 0.22–0.76). More importantly, the associations of CD4⁺ T cells, CD8⁺ T cells, the ratio of CD4⁺ T cells to CD8⁺ T cells, and sustained monocyte level were confined to male patients. </sec><sec><strong>Conclusions</strong> Higher CD4⁺ T cells, sustained monocyte level, and lower CD8⁺ T cells might shorten the disease course. The male-specific associations supported the contribution of sex-dependent immune responses to the disease courses. </sec>

Identification of the tire model and road adhesion coefficient based on vehicle dynamic response data and the BP neural network algorithm

The longitudinal and lateral dynamic responses of a vehicle are essentially determined by the forces resulting from the contact between the tire and road surface. Therefore, identifying the tire model and road adhesion coefficient plays an important role in vehicle dynamics control. At present, the identification of a nonlinear tire model essentially assumes that slip ratio-longitudinal force data or wheel side slip angle-lateral force data are known and that nonlinear fitting is performed, and the road adhesion coefficient based on the dynamic response is also identified on the premise of a known tire model. In this paper, the characteristic of approximating arbitrary nonlinear mapping relationships by a BP neural network is taken advantage of, and an off-line identification method of the Dugoff tire model based on onboard sensors and vehicle dynamics response is proposed. On this basis, an online identification method for the road adhesion coefficient is subsequently proposed. Finally, vehicle experiments on steering and braking are performed to verify the accuracy of the method in the Simulink-CarSim joint simulation environment.

Gull dynamic pitch stability is controlled by wing morphing

Birds perform astounding aerial maneuvers by actuating their shoulder, elbow, and wrist joints to morph their wing shape. This maneuverability is desirable for similar-sized uncrewed aerial vehicles (UAVs) and can be analyzed through the lens of dynamic flight stability. Quantifying avian dynamic stability is challenging as it is dictated by aerodynamics and inertia, which must both account for birds' complex and variable morphology. To date, avian dynamic stability across flight conditions remains largely unknown. Here, we fill this gap by quantifying how a gull can use wing morphing to adjust its longitudinal dynamic response. We found that it was necessary to adjust the shoulder angle to achieve trimmed flight and that most trimmed configurations were longitudinally stable except for configurations with high wrist angles. Our results showed that as flight speed increases, the gull could fold or sweep its wings backward to trim. Further, a trimmed gull can use its wing joints to control the frequencies and damping ratios of the longitudinal oscillatory modes. We found a more damped phugoid mode than similar-sized UAVs, possibly reducing speed sensitivity to perturbations, such as gusts. Although most configurations had controllable short-period flying qualities, the heavily damped phugoid mode indicates a sluggish response to control inputs, which may be overcome while maneuvering by morphing into an unstable flight configuration. Our study shows that gulls use their shoulder, wrist, and elbow joints to negotiate trade-offs in stability and control and points the way forward for designing UAVs with avian-like maneuverability.

Green's functions based on the Timoshenko beam model for the longitudinal seismic dynamic response of tunnels crossing soft and hard rock strata

Weathered rocks typically exist in the portal section of mountain tunnels where the tunnels in the portal section often cross soft and hard rock strata. The interface between the soft and hard rocks is the control point in the seismic design of tunnels. However, there is currently no seismic design method based on dynamic methods that consider tunnels crossing soft and hard rock strata along their longitudinal direction. In this study, two elastic foundation beams in different rock strata were used to model the behaviour of a tunnel crossing soft and hard rock strata. Based on the Timoshenko beam vibration response theory, the higher-order differentials of the beam dynamic governing equation are transformed into algebraic equations using the Laplace transform. The closed-form solution of the dynamic response of the entire beam is derived by combining the boundary and deformation coordination conditions of two elastic foundation beams. Subsequently, the dynamic response of any point along the longitudinal direction of the elastic foundation beam (tunnel) crossing the soft and hard rock strata was obtained using Green's function. The validity of the method was verified by comparing it with a finite difference model. Finally, a parametric analysis was performed based on the analytical method derived in this study to investigate the influences of parameters such as the liner elastic modulus, liner thickness, modulus of elasticity ratio of hard rock to soft rock, and axial forces, on the seismic response of tunnels crossing soft and hard rock strata. The results suggest that with an increase in lining thickness, the bending moment and shear force of the tunnel become increasingly significant, but the transverse displacement response of the tunnel was slightly affected. With an increase in the elastic modulus of the lining, the difference in the peak values of the bending moment and shear force increases, whereas the transverse displacement response is slightly diminished. With an increase in the elastic modulus ratio of hard rock to soft rock, the difference in the peak values of the bending moment, shear force, and transverse displacement of the tunnel, varied more along the tunnel axis. With the increase in the axial force, the seismic responses from the bending moment and shear force on the tunnel cross-section were significantly weakened.

Analytical Solution for Longitudinal Dynamic Responses of Long Tunnels under Arbitrary Excitations

In this paper, an analytical solution is proposed for longitudinal dynamic responses of long tunnels under arbitrary excitations. For the derivation, the tunnel is assumed as a Timoshenko beam resting on a visco-Pasternak foundation. The Timoshenko beam theory is employed to consider both effects of the shear distortion as well as the rotary inertia of the tunnel, which are neglected by the Euler–Bernoulli beam. The visco-Pasternak foundation is applied to represent the viscoelastic compressive and shear resistance of soil. The governing equations of motion are transformed from partial differential forms into algebraic forms through integral transformations, and thus the solutions are conveniently obtained. The analytical solutions of the tunnel under several specific dynamic loads, including impulsive loads, moving line loads as well as traveling loads, are presented in detail and verified by comparing to the known degraded solution in literature and finite element results. Several examples are also conducted to investigate the influence of the relative stiffness ratio between the soil and the tunnel structure on the tunnel responses.

Longitudinal aerodynamic modeling and verification for air-launch-to-orbit system during stage separation

The stage separation is one of key issues for air-launch-to-orbit system. In this process, the elastic deformation of carrier causes periodic pulsation in interference aerodynamics and may lead to modal coupling and dynamics instability of spacecraft. The dynamic responses and stability of the two vehicles should be considered carefully. The CFD-based dynamic simulation method has high accuracy but requires large computation cost. In this study, a new reduced-order modeling method is developed, which is for unsteady aerodynamics of the air-launch-to-orbit system with considering the elastic deformations of carrier. Based on the physical mechanism of interference aerodynamics factors, the model input parameters are decoupled and the modeling difficulty is reduced. By coupling the unsteady aerodynamic model, structural dynamics equations and rigid body dynamic equations, the longitudinal dynamic responses of air-launch-to-orbit system during stage separation are simulated. Through comparison, those results have good agreement with traditional CFD-based method, and the simulation efficiency of new method is improved greatly. The new modeling method is applicable to the air-launch-to-orbit system and can provide guidance for similar engineering issues.

Synthesis of landing dynamics on land-base high performance aircraft considering multi-variate landing conditions

Consideration of standard landing cases from technical guideline document is the traditional design practice followed to ascertain aircraft landing loads. A rationale approach on landing load generation and its impact on flexible airframe dynamic response is explored, considering multi-variate landing conditions for the first time on land-base high performance aircraft. Methodology on nonlinear landing dynamic response simulation is developed by amalgamating inputs such as nonlinear nose and main landing gear dynamic models, aircraft rigid body dynamics, low speed aerodynamic and thrust forces. True representation of landing gear nonlinear oleo-pneumatic strut and tire characteristics, variable geometric strut structural stiffness and nonlinear spin-up friction resulted in satisfactory correlation of vertical and longitudinal dynamic response simulation with experimental drop test results. The adequacy of lateral dynamic model is established from the compatibility condition of landing gear and tire dynamics. A down selection methodology is worked out considering total probability and first order sensitive multi-variate landing parameters such as pitch, roll and vertical descent speed, taking into account the plausible statistical variation. Transient dynamic response simulation is then performed for the critical landing cases, on a flexible airframe finite element model by inputting landing load time history as base excitation motion. The dynamic amplification of acceleration response on flexible fuselage nose location from the simulation, is verified with flight data accelerometer frequency response. The application of flexible dynamic responses in ensuring the structural integrity of airframe is elaborated. The proposed methodology on landing load generation is pragmatic, in comparison with the traditional design practice and provides insight during early design phase thereby achieving landing gear subsystem development in-unison with airframe structural clearance aspects.

Analysis of longitudinal vibration acceleration based on continuous time-varying model of high-speed elevator lifting system with random parameters

In this paper, for studying the influence of the randomness of structural parameters of high-speed elevator lifting system (HELS) caused by manufacturing error and installation error, a continuous time-varying model of HELS was constructed, considering the compensation rope mass and the tension of the tensioning system. The Galerkin weighted residual method is employed to transform the partial differential equation with infinite degrees of freedom (DOF) into the ordinary differential equation. The five-order polynomial is used to fit the actual operation state curve of elevator, and input as operation parameters. The precise integration method of time-varying model of HELS is proposed. The determination part and the random part response expression of the longitudinal dynamic response of HELS are derived by the random perturbation method. Using the precise integration method, the sensitivity of random parameters is determined by solving the random part response expression of time-varying model of HELS, and the digital characteristics of the acceleration response are analyzed. It is found that the line density of the hoisting wire rope has the maximum sensitivity on longitudinal vibration velocity response, displacement response and acceleration response, and the sensitivity of the elastic modulus of the wire rope is smallest.

A methodology for calculating limit deceleration of flexible hoisting system: A case study of mine hoist

Mine hoist is a typical flexible lifting system. Due to the cable flexibility, the system is prone to severe shocks and even slippage during emergency braking. To establish a safe emergency braking operation for mine hoist, retarded velocity should be less than the limit deceleration value. The simplified mathematical model shows that the system dynamic response along the longitudinal axis of the wire rope (longitudinal dynamics) is a typical second-order underdamped one. Due to the inherent characteristics of the flexible lifting system, the longitudinal dynamic response under slippage condition exhibits the following characteristics: the response curve deviates from the input signal, that is, the retarded velocities of cable and pulley at their contact points are no longer equal. Based on this finding, deceleration deviation coefficient is defined to normalize the longitudinal response curves, which can help us to determine the extent to which the output signal deviates from the input one; and the sudden increase in the deceleration deviation coefficient is considered as an indicator of rope slippage during emergency braking. The proposed scheme is verified and evaluated by means of simulation model. Subsequent results indicate that the limit deceleration valves obtained by the proposed approach have the same trend and magnitude as those obtained by conventional one, which illustrates that the proposed methodology is feasible. The advantage of the proposed approach is that the solution for each set of operating parameter is unique and certain. As for the conventional approach, the solution is not unique because of the introduction of safety factor, which will cause some trouble to the user. In subsequent work, a test bench will be set up to verify and optimize the proposed scheme.

Optimisation of Longitudinal Seismic Energy Dissipation System for Straddle-type Monorail-Cum-Road Long-Span Cable-Stayed Bridge

To investigate the optimal longitudinal seismic energy dissipation system of straddle-type monorail-cum-road long-span cable-stayed bridges, the Niutianyang Bridge was selected as the engineering background, and the explicit time-domain dimension-reduced iteration method was adopted to carry out nonlinear time-history analysis. To consider the dynamic characteristics of longitudinal movable supports, the static and dynamic responses of four kinds of energy dissipation systems were studied, including longitudinal unconstrained, elastic cable, viscous damper, and speed lock-up devices. The damping effect of four types of schemes in which viscous dampers were installed at piers or towers was analysed, and the parameters of the viscous dampers were optimised. The influences of the straddle-type monorail train braking force and the running vibration of the straddle-type monorail traffic on the parameters of the viscous dampers were analysed. This study shows that the viscous damper system had the lowest bending moment at the bottom of the tower and a smaller displacement response, and the energy dissipation was the best. Each viscous damper had the highest energy dissipation efficiency when they are installed only at the main tower. The damping effect was better when the damping coefficient c ranged from 3500 to 5000 kN⋅m/s−α and the velocity exponent α ranged from 0.35 to 0.5. The static friction of the straddle-type monorail-cum-road long-span cable-stayed bridge support can resist the trains’ braking force, and the parameters of the viscous damper can be selected regardless of train braking. A suitably large value of velocity exponent α may be required to increase the working velocity of the viscous damper to reduce the damper’s participation in the process of the train crossing the bridge.

THREE DIMENSIONAL NUMERICAL ANALYSIS OF DYNAMIC RESPONSE OF UNDERGROUND UTILITY TUNNELS DURING EARTHQUAKE

As underground utility tunnels are buried at shallow depths, the effects of Rayleigh waves should be considered in relevant seismic analysis. To investigate the dynamic response characteristics of utility tunnels subjected to Rayleigh waves and bottom earthquake acceleration, a three dimensional(3D) finite element(FE)numerical model for double-cabin utility tunnels was built. An advanced constitutive model characterized by hysteresis loops(HSS model) was used to simulate the soil mass. Rayleigh waves were generated by multiple pulse loads at the boundary. Upland waves, Kobe waves and Taft waves were applied horizontally at the bottom of the model. The results were compared with those derived from the conventional time-history analysis where only transverse force was taken into account. The research results showed that the transverse dynamic response of utility tunnels was mainly influenced by transverse seismic waves, while the longitudinal dynamic response was affected by Rayleigh waves that were incident along the axial direction of the structure. The dynamic response to the input of Rayleigh waves plus bottom seismic waves was more significant than that to the input of bottom seismic waves alone. When different earthquake acceleration time histories were input, the dynamic response rules of tunnels were similar but the impacts on them varied, which implied that the compatibility between bottom seismic waves and Rayleigh waves exerted a certain influence on the dynamic response of the structure. The research findings are expected to provide a reference for the fine numerical analysis of the dynamic response of earthquake-excited underground utility tunnels as well as their seismic design.

Longitudinal dynamic impedance of a static drill rooted nodular pile embedded in layered soil

ABSTRACTThe static drill rooted nodular (SDRN) pile is a new type of precast pipe pile with equally spaced nodes distributed along the shaft and wrapped by the surrounding cemented soil. In this paper, the longitudinal dynamic response of the SDRN pile embedded in layered soil is investigated with respect to the complexity of the pile body structure and the pile–soil contact condition. First, the shear complex stiffness transfer model is used to simulate the radial inhomogeneity of the surrounding soil. Then, the governing Equations of the pile–soil system subjected to longitudinal dynamic loading are established. The analytical solution for the dynamic response at the pile head is obtained by the shear complex stiffness transfer method and the impedance function transfer method. The degenerate case of the present solution is compared with the published solution to verify its reliability, and the complex impedance of the SDRN pile is compared with that of the precast pipe pile and the bored pile. Finally, a parametric study is conducted to investigate the influence of pile–soil parameters on the complex impedance at the pile head within the low frequency range concerned in the design of the dynamic foundation.

Flight dynamics model for preliminary design of PrandtlPlane wing configuration with sizing of the control surfaces

This paper deals with the evaluation of the flight dynamics response of aircraft with a PrandtlPlane configuration by means of simple models to be used during the preliminary design. The study is completed by a method for an initial sizing of the elevators and the ailerons (positioned on both the front and the rear wing) in order to achieve adequate handling qualities. The flight dynamics model considers the rigid aircraft, the steady aerodynamics, and separating the longitudinal and the lateral-directional motions. The force derivatives are extrapolated through a VLM solver whose the reliability of the results has been proven. The methods have been applied on the IDINTOS aircraft with the conclusion that we obtain a proper longitudinal dynamic response with a reduced Margin of Stability because of the very high values of the aerodynamic damping Mq and the pitch stiffness Malpha.

Experimental analysis of occupational whole-body vibration exposure of agricultural tractor with large square baler

This study investigates longitudinal whole-body vibration in agricultural tractors powering a large square baler. The aim is to test the hypothesis that four-wheel drive has an influence on the longitudinal dynamic response. A number of experimental measurements are carried out on a specific vehicle combination driving uphill and downhill. The whole-body vibration exposure is measured at the operator seat under different conditions.The statistic results show a significant difference on the whole-body vibration exposure depending on operating conditions. Driving uphill and downhill with four-wheel drive activated showed the highest difference with increased vibration level at downhill driving.The results indicate that four-wheel drive influences the longitudinal dynamics and hence the whole-body vibration exposure on tractors with large square balers. Relevance to industryThe findings of this work are highly relevant to the manufacturers of agricultural tractors and machinery as well advisers within occupational health. The paper demonstrates potential in reducing damaging vibrations by simple manual or automatic control of four-wheel drive.

Una metodología de cálculo para la determinación de la respuesta dinámica longitudinal de estructuras altas bajo la acción del viento

The optimization of computing methods along with the advance of construction technology of civil structures, allow nowadays to design and build lighter and low stiffness and damping structures, turning them into elements of high sensitivity against wind-induced dynamic effects. The purpose of this work is to describe and to apply a simple calculation methodology that enables the determination of the longitudinal dynamic response of tall buildings in time domain. The wind velocity field is reproduced by velocity series that incorporate the coherence function which then are transformed into fluctuating nodal forces using the quasi-static loading model. Furthermore, to include the effect of imperfect averaging associated with the discretized nodes, the aerodynamic admittance function is added.Through the proposed methodology two structures widely studied by other authors are analyzed: a steel tower and the CAARC Standard Tall Building. The results thus obtained show agreement with those reported in the literature.