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.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
M. Chapron ◽  
P. Velex ◽  
J. Bruyère ◽  
S. Becquerelle
Keyword(s):  
Equations Of Motion ◽  
Integration Scheme ◽  
Time Varying ◽  
Time Step ◽  
Planetary Gears ◽  
Contact Algorithm ◽  
Beam Elements ◽  
Internal Gear ◽  
Gear Meshes ◽  
Optimum Profile

This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (PGTs) with regard to dynamic mesh forces. To this end, a dynamic model is presented based on 3D two-node gear elements connected to deformable ring-gears discretized into beam elements. Double-helical gears are simulated as two gear elements of opposite hands which are linked by shaft elements. Symmetric tip relief on external and internal gear meshes are introduced as time-varying normal deviations along the lines of contact and time-varying mesh stiffness functions are deduced from Wrinckler foundation models. The equations of motion are solved by coupling a Newmark time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear PMs for helical and double-helical PGTs are optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the sensitivity of these optimum PMs to speed and load is analyzed.

Performance Characteristics of a Smart Flexible Beam With Distributed ACLD Elements

2002 ◽  
Author(s):  
L. C. Hau ◽  
Eric H. K. Fung
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Element Model ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Optimal Output ◽  
Modes Of Vibration ◽  
Original Size

The finite element method, in conjunction with the Golla-Hughes-McTavish (GHM) viscoelastic model, is employed to model a clamped-free beam partially treated with active constrained layer damping (ACLD) elements. The governing equations of motion are converted to a state-space form for control system design. Prior to this, since the resultant finite element model has too many degrees of freedom due to the addition of dissipative coordinates, a model reduction is performed to revert the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different element configurations, with various spacing and locations, on the vibration control performance of a “smart” flexible ACLD treated beam. Results are presented for the damping ratios of the first two modes of vibration. It is found that improvement on the second mode damping can be achieved by splitting a single ACLD element into two and placing them at appropriate positions of the beam.

On the Efficiency of Some Recently Developed Integration Algorithms for Offshore Problems

1983 ◽  
Vol 105 (1) ◽  
pp. 73-77 ◽  
Author(s):  
T. K. Datta ◽  
A. M. Sood
Keyword(s):  
Degrees Of Freedom ◽  
Large Time ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Response Analysis ◽  
Time Step ◽  
Beam Elements ◽  
Integration Schemes ◽  
Large Time Step ◽  
Integration Algorithms

The efficiency of some recently developed integration schemes, namely, Hilber’s ∝-method, collocation schemes and large time step integration schemes developed by Argyris, is evaluated by applying them to the response analysis of an idealized offshore tower. The tower is fixed at the base, having an additional mass at the top. For the analysis the tower has been modeled as an assemblage of 2-D beam elements. The dynamic degrees of freedom at each node are taken as those corresponding to the rotational and sway degrees of freedom. Using the normal mode theory the equations of motion have been decoupled except for the generalized loading vector which appear nonlinearly coupled, thus requiring iterative solution at every time step. The results of the study show that the large time step integration schemes developed by Argyris are more efficient than other integration methods considered here.

Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Planetary Gears With Flexible Ring-Gears

2015 ◽  
Author(s):  
Matthieu Chapron ◽  
Philippe Velex ◽  
Jérôme Bruyère ◽  
Samuel Becquerelle
Keyword(s):  
Equations Of Motion ◽  
Integration Scheme ◽  
Mesh Stiffness ◽  
Time Step ◽  
Planetary Gears ◽  
Contact Algorithm ◽  
Beam Elements ◽  
Internal Gear ◽  
Gear Meshes ◽  
Optimum Profile

This paper deals with the optimization of tooth profile modifications in planetary gears. A dynamic model is proposed based on 3D two-node gear elements connected to a deformable ring-gear discretized into beam elements. Symmetric tip relief on external and internal gear meshes are introduced as normal deviations along the lines of contact superimposed on a stiffness distribution aimed at simulating position- and time-varying mesh stiffness functions. The equations of motion are solved by the combination of a Newmark’s time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear profile modifications are then optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the interest of the corresponding optimum profile modifications with regard to speed and torque variations is analyzed.

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.

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.

An Efficient Algorithm for Nonlinear Analysis of Vehicle/Track Interaction Problems

2016 ◽  
Vol 16 (08) ◽  
pp. 1550040 ◽  
Author(s):  
J. Sadeghi ◽  
A. Khajehdezfuly ◽  
M. Esmaeili ◽  
D. Poorveis
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Dynamic Interaction ◽  
Integration Scheme ◽  
Equilibrium Equations ◽  
Track System ◽  
Newton Raphson ◽  
Interaction Problem

In this paper, a new algorithm for solving the vehicle/track dynamic interaction problem is developed, aimed at reducing the computational cost. The algorithm called Advanced Solver Algorithm (ASA) uses the full Newton–Raphson incremental-iterative method in conjunction with the Newmark integration scheme to solve the equilibrium equations of the coupled vehicle/track system in time domain. Considering the track as a beam resting on a viscoelastic foundation and each vehicle as a wagon with ten degrees of freedom, the governing differential equations of motion of the vehicle/track system were derived. The wheel/rail contact was considered as a nonlinear Hertz spring and consequently the vehicle/track nonlinear dynamic interaction problem was solved. A comparison between the results of the ASA and those of the most advanced algorithm available was made to evaluate the efficiency of the ASA. It is confirmed that using the ASA can result in 40–70 % of reduction in computational cost.

scholarly journals Modelling of Shaft Orbiting with 3-D Solid Finite Elements

1999 ◽  
Vol 5 (1) ◽  
pp. 53-65 ◽  
Author(s):  
J. Yu ◽  
A. Craggs ◽  
A. Mioduchowski
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Rotating Frame ◽  
Circular Orbits ◽  
Bending Vibration ◽  
Solid Finite Elements ◽  
Beam Theories

A 3-D solid finite element model which can include bending, torsional, axial and other motions is proposed to analyse dynamic responses of shafts. For uniform shafts, this model shows consistency with beam theories when bending vibration is examined. For non-uniform shafts such as tapered ones, however, this model gives much more reliable and accurate results than beam theories which use an assumption that plane sections remain plane. Reduction procedures can be applied which involve only small matrix operations for such a system with a large number of degrees of freedom. The equations of motion have been consistently derived in a rotating frame. Shaft orbiting motion is then defined in this frame, giving a clear view of its trajectories. Forced responses due to excitation in the rotating frame have been examined to find some characteristics of the orbiting shaft. Resonant orbiting frequencies, i.e., natural frequencies of rotating shafts, can be determined in terms of the rotating or fixed frame. Trajectories of transverse displacements have been found to be varying with the forcing frequencies. At resonance, a uniform shaft will only have forward or backward orbiting motion with circular orbits. For other forcing frequencies, however, even a uniform shaft could present both forward and backward orbiting motions with non-circular orbits at different locations along its length. It is anticipated that modelling of shaft orbiting in the rotating frame with the proposed 3-D solid finite elements will lead to accurate dynamic stress evaluation.

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