Dynamic interaction of vehicles moving on uniform bridges

2002 ◽  
Vol 216 (4) ◽  
pp. 343-350 ◽  
Author(s):  
N Jalili ◽  
E Esmailzadeh
Keyword(s):  
Degrees Of Freedom ◽  
Practical Importance ◽  
Beam Theory ◽  
Bending Moment ◽  
Dynamic Interaction ◽  
Suspension Bridges ◽  
Vehicle Speed ◽  
Varying Coefficients ◽  
Moving Vehicles ◽  
Time Varying Coefficients

The dynamic interaction problem of moving vehicles on uniform suspension bridges is studied. The resulting variable moving loads acting on the bridge are of great practical importance to both bridge and automotive engineers. The vehicle, including the occupants, is modelled as a planar half-car with six degrees of freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. However, the numerical simulations presented here are for the case of a vehicle travelling at a constant speed on a bridge with simply supported end conditions. Owing to the continuously moving location of the loads on the bridge, the governing differential equations will have time-varying coefficients and hence become rather complicated. The relationship between the bridge vibration characteristics and the vehicle speed is established, resulting in a search for a particular speed that determines the maximum values of dynamic deflection and the bending moment of the bridge.

Induced Vibration of Suspension Bridges Traversed by Moving Vehicles

2001 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Nader Jalili
Keyword(s):  
Degrees Of Freedom ◽  
Beam Theory ◽  
Bending Moment ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Vehicle Speed ◽  
Moving Vehicle ◽  
Varying Coefficients ◽  
Moving Vehicles ◽  
Time Varying Coefficients

Abstract An investigation into the dynamics of vehicle-structure interaction of a suspension bridge traversed by a moving vehicle is presented. The vehicle including the occupants is modeled as a half-car model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory. Due to the continuously moving location of the loads on the bridge, the governing differential equations will have time-varying coefficients and hence, become rather complicated. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span (±3%), while the maximum bending moment is found at ±20% of the mid-span. It is shown that one can find a critical speed at which the maximum values of bridge dynamic deflection and bending moment attain their global maxima.

Vibration Analysis of Axially Loaded Bridges Traversed by Accelerating Vehicles With Passenger Dynamics

Volume 2 ◽  
2004 ◽  
Author(s):  
P. Hassanpour Asl ◽  
H. Mehdigholi ◽  
E. Esmailzadeh
Keyword(s):  
Timoshenko Beam ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Bending Moment ◽  
Timoshenko Beam Theory ◽  
The Body ◽  
Suspension Bridges ◽  
Vehicle Speed ◽  
Damping Force ◽  
Shock Absorbers

An investigation into the dynamics of vehicle-passenger-structure-induced vibration of suspension bridges traversed by accelerating vehicles is carried out. The vehicle including the driver and passengers is modeled as a half-car planer model with six degrees-of-freedom. In addition, the stiffness of compliant bushings at the connecting points of the shock absorbers to the body is considered. The bridge is assumed to obey the Timoshenko beam theory with axial load and arbitrary conventional boundary conditions. The roughness of the bridge is assumed as a differentiable function of location. Due to continuously moving the location of the variable loads on the bridge, and in the presence of damping force, the governing differential equations become complicated. The numerical simulations presented here are for the case of a vehicle traveling at a constant acceleration on a uniform bridge with rough surface and simply supported end conditions. The relationship between the bridge vibration characteristics, bridge roughness, and the vehicle speed and acceleration is rendered, which yields into search for a particular acceleration and speed that determines the maximum value of the dynamic deflection and the bending moment of the bridge. Results obtained from the Timoshenko beam theory are compared with those from the Euler-Bernoulli beam for which full agreements are found. Finally, the maximum deflection of the beam under moving loads is compared with that of the case with static loading.

Theoretical and Experimental Study of the Nonlinearly Coupled Heave, Pitch, and Roll Motions of a Ship in Longitudinal Waves

1993 ◽  
Author(s):  
I. G. Oh ◽  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Force Response ◽  
Governing Equations ◽  
Response Curves ◽  
Varying Coefficients ◽  
Jump Phenomena ◽  
Time Varying Coefficients ◽  
Three Degrees Of Freedom

Abstract The loss of dynamic stability and the resulting large-amplitude roll of a vessel in a head or following sea were studied theoretically and experimentally. A ship model with three degrees of freedom (roll, pitch, heave) was considered. The governing equations for the heave and pitch modes were linearized and their harmonic solutions were coupled with the nonlinear equation governing roll. The resulting equation, which has time-varying coefficients, was used to predict the response in roll. The principal parametric resonance was considered in which the excitation frequency is twice the natural frequency in roll. Force-response curves were obtained. The existence of jump phenomena and multiple stable solutions for the case of subcritical instability was observed in the experiments and found to be in good qualitative agreement with the results predicted by the theory. The experiments also revealed that the large-amplitude roll is dependent on the location of the model in the standing waves.

Effect of Prestress on Bridge–Vehicle Interactions

2015 ◽  
Author(s):  
Hai Zhong ◽  
Mijia Yang
Keyword(s):  
Degrees Of Freedom ◽  
Virtual Work ◽  
Interaction Model ◽  
Dynamic Interaction ◽  
Vertical Acceleration ◽  
Vehicle Speed ◽  
Principle Of Virtual Work ◽  
Vehicle Model ◽  
Multiple Vehicles ◽  
4 Degrees Of Freedom

Prestress applied on bridges affects the dynamic interaction between bridges and vehicles traveling over them. In this paper, the prestressed bridge is modeled as a beam subjected to eccentric prestress force at the two ends, and a half-vehicle model with 4 degrees of freedom is used to represent the vehicle passing the bridge. A new bridge–vehicle interaction model considering the effect of prestress with eccentricity is developed through the principle of virtual work. The correctness and accuracy of the model are validated with literature results. Based on the developed model, numerical simulations have been conducted using the Newmark’s β method to study the effects of vehicle speed, eccentricity and amplitude of the prestress, and presence of multiple vehicles. It is shown that prestress has an important effect on the maximum vertical acceleration of vehicles, which may provide a good index for detecting the change of prestress. It is also interesting to find that the later-entering vehicle on the prestressed bridge will largely reduce the maximum vertical acceleration of the vehicle ahead of it.

Dynamic Analysis of Vehicle-Guideway Interaction in a Maglev Cargo Transportation System

2012 ◽  
Author(s):  
Bun Buth ◽  
Bei Lu
Keyword(s):  
Permanent Magnets ◽  
Magnetic Levitation ◽  
Beam Theory ◽  
Element Model ◽  
Transportation System ◽  
Dynamic Interaction ◽  
Vehicle Speed ◽  
Euler Beam ◽  
Spring System ◽  
Halbach Arrays

The dynamic response of a magnetic levitation (maglev) transportation system has important consequences for guideway design and system costs. The objective of this research is to develop a framework to analyze the dynamic interaction between a flexible guideway structure and a maglev vehicle named Electric Cargo Conveyor (ECCO). Different from other maglev vehicles, which use either electromagnetic or electrodynamic suspension technologies, the ECCO is the only system utilizing the Inductrack levitation technology, where the permanent magnets are arranged as so-called Halbach arrays to create a levitating force. The theoretical dynamic model of the ECCO system is derived in this paper. The guideway structure is modeled as a simply supported beam based on Bernoulli-Euler beam theory. The vehicle is modeled as a two-degree-of-freedom mass-damper-spring system. They are coupled with each other through nonlinear magnetic forces. To investigate the dynamic interaction between the vehicle and guideway, a finite element model of the ECCO system is created in COMSOL Multiphysics using its equation-based modeling interface. Numerical simulations are conducted to examine the effects of different factors such as the cargo weight and the vehicle speed.

Tracking Control of Unmanned Surface Vehicles With Abkowitz Steering Model

2010 ◽  
Author(s):  
C. Nataraj ◽  
Ramesh Thimmaraya
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Linear Time ◽  
Time Varying ◽  
Unmanned Surface Vehicles ◽  
Varying Coefficients ◽  
Ship Steering ◽  
Time Varying Coefficients

This paper is concerned with the tracking control of unmanned surface vehicles. Steering dynamics is modeled using nonlinear equations with three degrees of freedom following Abkowitz. Tracking control of this nonlinear system leads to the need to derive a control algorithm for linear error equations which have time-varying coefficients. Next, a control algorithm has been derived for this set of linear time-varying equations. Lyapunov transformations have been applied to transform the error equation into a canonical form. A desired closed-loop PD-spectrum and the desired right PD-modal matrix have been chosen and the resulting Sylvester equation has been solved to obtain a matrix of time-varying controller gains. This leads to the closed loop equations for controlling the ship steering of an unmanned ship. The controller algorithm is applied to the motion control of ships with parametric values from published reports. Several tracking trajectories have been generated with and without obstacles, and time-varying control has been investigated and presented. The control algorithm is shown to be quite effective for tracking of unmanned surface vehicles. Stability conditions are derived to ensure convergence. Present work in experimental verification is outlined.

scholarly journals Effect of Prestress on Bridge–Vehicle Interactions

2017 ◽  
Vol 4 (3) ◽  
Author(s):  
Hai Zhong ◽  
Mijia Yang
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Interaction Model ◽  
Dynamic Interaction ◽  
Vertical Acceleration ◽  
Vehicle Speed ◽  
Principle Of Virtual Work ◽  
Vehicle Model ◽  
Multiple Vehicles

Prestress applied on bridges affects the dynamic interaction between bridges and vehicles traveling over them. In this paper, the prestressed bridge is modeled as a beam subjected to eccentric prestress force at the two ends, and a half-vehicle model with four degrees-of-freedom is used to represent the vehicle passing the bridge. A new bridge–vehicle interaction model considering the effect of prestress with eccentricity is developed through the principle of virtual work. The correctness and accuracy of the model are validated with literature results. Based on the developed model, numerical simulations have been conducted using Newmark's β method to study the effects of vehicle speed, eccentricity and amplitude of the prestress, and presence of multiple vehicles. It is shown that prestress has an important effect on the maximum vertical acceleration of vehicles, which may provide a good index for detecting the change of prestress. It is also interesting to find that the later-entering vehicle on the prestressed bridge will largely reduce the maximum vertical acceleration of the vehicle ahead of it.

scholarly journals Behavioral Dynamics of Pedestrians Crossing between Two Moving Vehicles

2020 ◽  
Vol 10 (3) ◽  
pp. 859 ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun-Chae Chung ◽  
Gyoo-Jae Choi ◽  
MooYoung Choi
Keyword(s):  
Traffic Accidents ◽  
Vehicle Speed ◽  
Mathematical Tool ◽  
Vehicle Type ◽  
Behavioral Dynamics ◽  
Moving Vehicles ◽  
Bearing Angle ◽  
Human Participants ◽  
Crossing Point ◽  
Insight Into

This study examines the human behavioral dynamics of pedestrians crossing a street with vehicular traffic. To this end, an experiment was constructed in which human participants cross a road between two moving vehicles in a virtual reality setting. A mathematical model is developed in which the position is given by a simple function. The model is used to extract information on each crossing by performing root-mean-square deviation (RMSD) minimization of the function from the data. By isolating the parameter adjusted to gap features, we find that the subjects primarily changed the timing of the acceleration to adjust to changing gap conditions, rather than walking speed or duration of acceleration. Moreover, this parameter was also adjusted to the vehicle speed and vehicle type, even when the gap size and timing were not changed. The model is found to provide a description of gap affordance via a simple inequality of the fitting parameters. In addition, the model turns out to predict a constant bearing angle with the crossing point, which is also observed in the data. We thus conclude that our model provides a mathematical tool useful for modeling crossing behaviors and probing existing models. It may also provide insight into the source of traffic accidents.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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