Dynamic Behavior of Damaged Bridge with Multi-Cracks Under Moving Vehicular Loads

2017 ◽  
Vol 17 (02) ◽  
pp. 1750019 ◽  
Author(s):  
Xinfeng Yin ◽  
Yang Liu ◽  
Lu Deng ◽  
Xuan Kong
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Coupled System ◽  
Interaction Force ◽  
Vehicle Model ◽  
Coupled Equations ◽  
Contact Points ◽  
Local Flexibility ◽  
Bridge Structures ◽  
Road Surface Roughness

When studying the vibration of a bridge–vehicle coupled system, most researchers mainly focus on the intact or original bridge structures. Nonetheless, a large number of bridges were built long ago, and most of them have suffered serious deterioration or damage due to the increasing traffic loads, environmental effect, material aging, and inadequate maintenance. Therefore, the effect of damage of bridges, such as cracks, on the vibration of vehicle–bridge coupled system should be studied. The objective of this study is to develop a new method for considering the effect of cracks and road surface roughness on the bridge response. Two vehicle models were introduced: a single-degree-of-freedom (SDOF) vehicle model and a full-scale vehicle model with seven degrees of freedom (DOFs). Three typical bridges were investigated herein, namely, a single-span uniform beam, a three-span stepped beam, and a non-uniform three-span continuous bridge. The massless rotational spring was adopted to describe the local flexibility induced by a crack on the bridge. The coupled equations for the bridge and vehicle were established by combining the equations of motion for both the bridge and vehicles using the displacement relationship and interaction force relationship at the contact points. The numerical results show that the proposed method can rationally simulate the vibrations of the bridge with cracks under moving vehicular loads.

scholarly journals The Normal Modes of Nonlinear n-Degree-of-Freedom Systems

1962 ◽  
Vol 29 (1) ◽  
pp. 7-14 ◽  
Author(s):  
R. M. Rosenberg
Keyword(s):  
Linear System ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Minimum Problem ◽  
Infinite Class ◽  
Coupled Equations ◽  
Geometrical Problem ◽  
Maximum Minimum

A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form.

Dynamic Interaction Analysis of Maglev-Guideway System Based on a 3D Full Vehicle Model

2017 ◽  
Vol 17 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Dong-Ju Min ◽  
Myung-Rag Jung ◽  
Moon-Young Kim ◽  
Jong-Won Kwark
Keyword(s):  
Dynamic Equilibrium ◽  
Interaction Analysis ◽  
Equations Of Motion ◽  
Dynamic Interaction ◽  
Surface Irregularity ◽  
Superposition Method ◽  
Vehicle Model ◽  
Equilibrium Equations ◽  
Coupled Equations ◽  
Maglev Vehicle

The purpose of this paper is to develop a detailed 3D maglev vehicle and guideway model and investigate the dynamic response characteristics of the coupled system. For this, the maglev vehicle is modeled as one cabin and four bogies having eight electromagnetics, four sensors, and four secondary suspensions based on the Urban Transit Maglev (UTM) system in Korea. The 3D dynamic equilibrium equations of the cabin and bogies are derived by considering the actively controlled electromagnetic forces. Also, the equations of motion for the guideway are derived using the modal superposition method for vertical, lateral, and torsional modes. The resulting coupled equations of motion are then solved using a predictor–corrector iterative algorithm. Finally, through the numerical simulation of the developed system, the responses using the 3D maglev vehicle model are compared with those obtained by the corresponding 2D model. The effects of surface irregularity on the dynamic interaction behaviors are then evaluated for increasing vehicle speeds. Particularly, the 3D resonance conditions of the guideway girder and the maglev vehicle are presented considering the resonance conditions due to equidistant moving loads. In addition, some resonance phenomena are rigorously explored, including the lateral resonance by a series of vehicles running on a girder.

scholarly journals Modeling and Validation of 2-DOF Rail Vehicle Model Based on Electro–Mechanical Analogy Theory Using Theoretical and Experimental Methods

2018 ◽  
Vol 8 (6) ◽  
pp. 3603-3608
Author(s):  
F. Pehlivan ◽  
C. Mizrak ◽  
I. Esen
Keyword(s):  
Degrees Of Freedom ◽  
Similarity Theory ◽  
Equations Of Motion ◽  
Vehicle Model ◽  
Rail Vehicle ◽  
Free Body Diagram ◽  
Model Transfer ◽  
Simulation Results ◽  
Free Body ◽  
Secondary Suspension

This paper presents theoretical and experimental results on modeling and simulation of two degrees of freedom rail vehicle by using electro-mechanical similarity theory. In this study, the equations of motion were derived using Newton’s second law of motion and then mechanical and equivalent electrical circuits were obtained with the help of a free body diagram. A schema in Simulink allowing analyzing of the behavior of the primary and secondary suspension was created. In order to verify the electrical model, transfer function and schema were developed in Simulink. The simulation results were compared with the experimental data and the comparison showed that the results of the mechanical experiments were close to the simulation results, but the electrical results showed better periodic behavior.

Application of Generalized Newton-Euler Equations and Recursive Projection Methods to Dynamics of Deformable Multibody Systems

1989 ◽  
Author(s):  
R. A. Wehage ◽  
A. A. Shabana
Keyword(s):  
Euler Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Coupled System ◽  
Projection Methods ◽  
Open Loop ◽  
System Of Equations ◽  
Kinematic Chains ◽  
Deformable Bodies ◽  
Generalized Newton

Abstract A general symbolic-based method is presented for solving equations of motion for open-loop kinematic chains consisting of interconnected rigid and deformable bodies. The method utilizes matrix partitioning, recursive projection based on optimal block U-L factorization and generalized Newton-Euler equations to obtain an order n solution for the constrained equations of motion. Kinematic relationships between the absolute reference, joint and elastic coordinates are used with the generalized Newton-Euler equations for deformable bodies to obtain a large, loosely coupled system of equations. Taking advantage of the inertia matrix structure associated with elastic coordinates yields a recursive solution algorithm whose dimension is independent of the elastic degrees of freedom. The above solution techniques applied to this system of equations yield a much smaller operations count and can more effectively exploit vectorization and parallel processing. The algorithms presented in this paper are illustrated with the aid of cylindrical joints which are easily extended to revolute, prismatic, rigid and other joint types.

Dynamic Responses of the Beam Bridge under Moving Vehicular Loads

2013 ◽  
Vol 639-640 ◽  
pp. 1183-1186 ◽  
Author(s):  
Xin Feng Yin ◽  
Lei Zhang ◽  
C.S. Cai ◽  
Yang Liu
Keyword(s):  
Model Updating ◽  
Equations Of Motion ◽  
High Strength ◽  
Coupled System ◽  
Interaction Force ◽  
Dynamic Responses ◽  
Coupled Vibration ◽  
Beam Bridge ◽  
The Impact ◽  
Force Relationship

This paper presents a new method to study the impact factor of an old bridge strengthened with high strength materials based on the model updating technique. Using the genetic algorithm (GA) by minimizing an objective function of the residuals between the measured and predicted responses, the bridge and vehicle coupled vibration models were updated. Based on the displacement relationship and the interaction force relationship at the contact patches, the vehicle-bridge coupled system can be established by combining the equations of motion of both the bridge and vehicles. The simulated results show that the present method can simulate precisely the response of the tested bridge.

Wheelset Mechanics During Wheelclimb Derailment

1984 ◽  
Vol 51 (3) ◽  
pp. 680-686 ◽  
Author(s):  
A. Karmel ◽  
L. M. Sweet
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Nonlinear Dynamic Model ◽  
Normal Forces ◽  
Contact Points ◽  
Vertical Roll ◽  
Predicted Values ◽  
Railroad Vehicle

An analysis of the mechanics and dynamics of a railroad vehicle wheelset during flange contact and wheelclimb derailment is presented. The theoretical model includes wheelset lateral, vertical, roll, yaw, and axle rotation degrees of freedom, plus lateral displacement of the truck frame. The equations of motion are based on the kinematics and dynamics of the wheelset subject to constraints imposed by wheel/rail contact geometry. These constraints are used to compute creepages and normal forces at the wheel/rail contact points, needed as inputs to the Kalker Simplified Theory of rolling contact. Computational methods for simulation of the nonlinear dynamic model are discussed. Results of the simulation demonstrate the significance of the various degrees of freedom on wheelset motion and on predicted values of the derailment quotient (Q/P).

Non-Ideal System With Quadratic Nonlinearities Containing a Two-to-One Internal Resonance

2016 ◽  
Author(s):  
Rodrigo T. Rocha ◽  
Jose M. Balthazar ◽  
D. Dane Quinn ◽  
Angelo M. Tusset ◽  
Jorge L. P. Felix
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Coupled System ◽  
Dynamical Behaviour ◽  
Main System ◽  
Weakly Coupled System ◽  
Ideal System ◽  
Quadratic Nonlinearities

The dynamical behaviour of a non-ideal three-degrees-of-freedom weakly coupled system associated with the quadratic nonlinearities in the equations of motion is investigated. The main system consists of two nonlinear mechanical oscillators coupling with quadratic nonlinearities and in which possess a 2:1 internal resonance between their translational movements. Under these conditions, we analyzed the response when a DC unbalanced motor with limited power supply (non-ideal system) excites the main system. When the excitation frequency is near to second natural frequency of the main system, saturation and jump phenomena are presented. Then, this work will analyze some torques of the motor, which causes the phenomena, and due to high amplitudes of motion will be possible to look for a way to harvest energy in a future work.

Numerical Solution of Vehicle-Bridge Coupling Vibration

2013 ◽  
Vol 859 ◽  
pp. 76-79
Author(s):  
Ze Peng Wen
Keyword(s):  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Reliability And Validity ◽  
Element Model ◽  
Interaction Force ◽  
Integration Scheme ◽  
Coupled Vibration ◽  
Time Step ◽  
Coupling Vibration

The bridge simplified two-dimensional plane beam element model, Simplified to two degrees of freedom quarter vehicle model, The entire bridge system is divided into two subsystems vehicle and bridge, Using separate equations of motion of vehicles and bridges, Proposed bridge systems numerical solution of coupled vibration analysis, The law at the wheel in contact with the deck displacement compatibility conditions for a balanced relationship with the interaction force associated, At each time step using the Newmark-β integration scheme, Through this paper the numerical solution results do comparison with the literature, the results show that the proposed method is reliability and validity.

Energy Conserving Equations of Motion for Gear Systems

2004 ◽  
Vol 127 (2) ◽  
pp. 208-212 ◽  
Author(s):  
Sejoong Oh ◽  
Karl Grosh ◽  
James R. Barber
Keyword(s):  
Equations Of Motion ◽  
Interaction Force ◽  
Fundamental Principle ◽  
Step Change ◽  
Conservation Of Energy ◽  
Gear Design ◽  
Contact Points ◽  
Energy Conserving ◽  
External Forces ◽  
Work Done

A system of two meshing gears exhibits a stiffness that varies with the number of teeth in instantaneous contact and the location of the corresponding contact points. A classical Newtonian statement of the equations of motion leads to a solution that contradicts the fundamental principle of mechanics that the change in total energy in the system is equal to the work done by the external forces, unless the deformation of the teeth is taken into account in defining the direction of the instantaneous tooth interaction force. This paradox is avoided by using a Lagrange’s equations to derive the equations of motion, thus ensuring conservation of energy. This introduces nonlinear terms that are absent in the classical equations of motion. In particular, the step change in stiffness associated with the introduction of an additional tooth to contact implies a step change in strain energy and hence a corresponding step change in kinetic energy and rotational speed. The effect of these additional terms is examined by dynamic simulation, using a system of two involute spur gears as an example. It is shown that the two systems of equations give similar predictions at high rotational speeds, but they differ considerably at lower speeds. The results have implications for gear design, particularly for low speed gear sets.

scholarly journals Vibration Suppression of Wind/Traffic/Bridge Coupled System Using Multiple Pounding Tuned Mass Dampers (MPTMD)

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1133 ◽  
Author(s):  
Xinfeng Yin ◽  
Gangbing Song ◽  
Yang Liu
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Coupled System ◽  
Highway Bridges ◽  
Dynamic Responses ◽  
Viscoelastic Layer ◽  
Parameter Study ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
Coupled Equations

Dynamic responses of highway bridges induced by wind and stochastic traffic loads usually exceed anticipated values, and tuned mass dampers (TMDs) have been extensively applied to suppress dynamic responses of bridge structures. In this study, a new type of TMD system named pounding tuned mass damper (PTMD) was designed with a combination of a tuned mass and a viscoelastic layer covered delimiter for impact energy dissipation. Comprehensive numerical simulations of the wind/traffic/bridge coupled system with multiple PTMDs (MPTMDs) were performed. The coupled equations were established by combining the equations of motion of both the bridge and vehicles in traffic. For the purpose of comparing the suppressing effectiveness, the parameter study of the different numbers and locations, mass ratio, and pounding stiffness of MPTMDs were studied. The simulations showed that the number of MPTMDs and mass ratio are both significant in suppressing the wind/traffic/bridge coupled vibration; however, the pounding stiffness is not sensitive in suppressing the bridge vibration.

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