The Effect of Centrifugal Force and Coriolis Force on Vehicle-Flexible Bridge Vertical Vibration

2012 ◽  
Vol 455-456 ◽  
pp. 1480-1485
Author(s):  
Xiang Xiao ◽  
Wei Xin Ren ◽  
Wen Yu He
Keyword(s):  
Centrifugal Force ◽  
Coriolis Force ◽  
Mass Matrix ◽  
Interaction Model ◽  
Vertical Motion ◽  
Vertical Vibration ◽  
Time Deformation ◽  
Damping Matrix ◽  
Load Vector ◽  
Bridge System

Considering centrifugal force and Coriolis force caused by the real-time deformation of bridge, a vehicle-bridge interaction model is established. Take simply supported bridge subjected to an one-axle vehicle for example, the mass matrix, damping matrix, stiffness matrix and load vector of the vehicle-bridge system are derived via modal analysis method, thus the vertical motion equation of vehicle-bridge system, which can better reflect the operation characteristics of vehicles running on the bridge, has been established.

Dynamic Responses of Beam With Sloping Support Traversed by a Moving Mass

2010 ◽  
Author(s):  
Guolai Yang ◽  
James Yang ◽  
Chen Qiang ◽  
Jianli Ge ◽  
Qiang Chen
Keyword(s):  
Structural Design ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Inertial Force ◽  
Variable Cross Section ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Variable Cross ◽  
Matrix Stiffness ◽  
Damping Matrix

This paper contributes to investigation on vibration analysis for cradle subjected to the moving barrel. The tipping part of the gun is simplified by a beam with sloping support traversed by a moving mass. The cradle structure is modeled by Euler-Bernoulli variable cross-section beam and the elevating strut is modeled by elastic supporting rod. The beam and supporting rod are discretized into finite elements, and then the main mass matrix, stiffness matrix, and damping matrix can be formulated. Gravity and inertial force are described by external nodal load vectors. The time-varying additional mass matrix, stiffness matrix, and damping matrix are derived. Numerical computation is conducted to analyze the effect of the barrel velocity on dynamic response of system, which can provide theoretical foundation to structural design of such system.

Comparison of Vertical Model and Spatial Model for Vehicle-Track-Bridge Coupling Vibration System

2011 ◽  
Vol 243-249 ◽  
pp. 4307-4310
Author(s):  
Yuan Zhang ◽  
Wei Lin ◽  
Ze Ming Wang
Keyword(s):  
Vertical Vibration ◽  
Coupling Vibration ◽  
Spatial Coupling ◽  
Advantages And Disadvantages ◽  
Vibration Model ◽  
Spectrum Density ◽  
Exciting Source ◽  
Vibration Responses ◽  
Track Bridge ◽  
Bridge System

In this paper, models for vertical and spatial coupling vibration of vehicle-track-bridge system are established separately. The track vertical irregularity sample in time domain is established by power spectrum density and taken as the exciting source to analyze the coupling vibration of vehicle-track-bridge system of two models. The advantages and disadvantages and applicability of the vertical vibration model and the spatial vibration model are analyzed by comparing the vertical vibration responses of the two models under excitation with same level of track vertical irregularity.

The effect of spanwise system rotation on Dean vortices

1994 ◽  
Vol 274 ◽  
pp. 243-265 ◽  
Author(s):  
O. John E. Matsson ◽  
P. Henrik Alfredsson
Keyword(s):  
Centrifugal Force ◽  
Coriolis Force ◽  
Travelling Waves ◽  
Streamwise Vortices ◽  
Longitudinal Vortices ◽  
Smoke Visualization ◽  
Rotation Rates ◽  
Dean Vortices ◽  
System Rotation ◽  
Secondary Instabilities

An experimental study is reported of the flow in a high-aspect-ratio curved air channel with spanwise system rotation, utilizing hot-wire measurements and smoke visualization. The experiments were made at two different Dean numbers (De), approximately 2 and 4.5 times the critical De for which the flow becomes unstable and develops streamwise vortices. For the lower De without system rotation the primary Dean instability appeared as steady longitudinal vortices. It was shown that negative spanwise system rotation, i.e. the Coriolis force counteracts the centrifugal force, could cancel the primary Dean instability and that for high rotation rates it could give rise to vortices on the inner convex channel wall. For positive spanwise system rotation, i.e. when the Coriolis force enhanced the centrifugal force, splitting and merging of vortex pairs were observed. At the higher De secondary instabilities occurred in the form of travelling waves. The effect of spanwise system rotation on the secondary instability was studied and was found to reduce the amplitude of the twisting and undulating motions for low negative rotation. For low positive rotation the amplitude of the secondary instabilities was unaffected for most regions in parameter space.

Spline-Based Finite Element Analysis in Composite Laminates Mechanical Properties

2011 ◽  
Vol 138-139 ◽  
pp. 673-680
Author(s):  
Feng Xiang You ◽  
Fei Zhang ◽  
Buo Lei Zuo
Keyword(s):  
Finite Element ◽  
Composite Laminates ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Normal Displacement ◽  
Laminated Plate ◽  
Element Analysis ◽  
Damping Matrix ◽  
Spline Finite Element

The geometric parameters of the composite laminate in the engineering structure tend to have random properties. It is of great significance on how to study sensitivity of random parameters of laminated plates and carry on the optimized analysis to the parameteranalys when accurately estimating the reliability of structural design. According to the first order shear deformation theory, by using the spline finite element method, we can infer and the establish a laminated plate vibration equation, the stiffness matrix, mass matrix, proportional damping matrix, before making solution of the antisymmetric laminated plates response sensitivity formula, and analyzing the normal displacement, the sensitivity, the natural frequency of compound materials laminated plate. The Numerical examples verify the effectiveness of this algorithm.

scholarly journals Numerical study of the vertical vibration of a vehicle model with variable speed

2021 ◽  
Vol 1199 (1) ◽  
pp. 012087
Author(s):  
M Sága ◽  
M Vaško ◽  
Z Ságová ◽  
L Jakubovičová ◽  
M Handrik
Keyword(s):  
Numerical Study ◽  
Numerical Procedure ◽  
Vertical Motion ◽  
Random Excitation ◽  
Vertical Vibration ◽  
Railway Vehicle ◽  
Model Parameters ◽  
Variable Speed ◽  
Gaussian Random Process ◽  
Stationary Random Function

Abstract The paper deals with the numerical analysis of the general model of vehicle oscillations considering the non-stationarity of random excitation. The model parameters of the applied railway vehicle are deterministic functions. The non-stationary random function will be modelled by the variable speed of the vehicle and the vertical unevenness of the track. The so-called evolutionary Gaussian random process will be considering. The proposed comparative study of the dynamics of the vertical motion of the analysed railway vehicle will be realized using Monte Carlo simulation and a numerical procedure based on the theory of Markov processes. The originality of the article can be found in the implementation and algorithmization of the principles of solving non-stationary oscillation problems of machines. A universal methodology applicable in the dynamics of machines of various purposes is presented.

Closed Form Solutions to the Equation of Motion Avoiding Mass Matrix Inversion and Eigenvectors Decomposition

2001 ◽  
Author(s):  
Karine Reaud ◽  
Claude Vallee ◽  
Danielle Fortune
Keyword(s):  
Closed Form ◽  
Mass Matrix ◽  
Equation Of Motion ◽  
Matrix Inversion ◽  
Matrix Exponential ◽  
Linear Case ◽  
Closed Form Solutions ◽  
Damping Matrix ◽  
Ill Conditioned Matrices ◽  
Damping Systems

Abstract Solutions of the vibrations equations are generally obtained, in the linear case, by methods involving either matrix exponential computation or matrix eigendecomposition. However, these methods lead to a loss of symmetry because of the necessary inversion of the mass matrix. In doing so, one can introduce ill-conditioned matrices and, thus, compute eigenvectors with poor accuracy. In order to avoid these inconveniences, our method, which is an extension of Le Verrier-Souriau algorithm, provides solutions to the vibrations equations without inverting the mass matrix or computing eigenvectors. Moreover, we can solve damping systems even when the damping matrix has no specific properties such as the Basile property.

Dynamic Structural Analysis of Large Dams by Fourier SEM

2013 ◽  
Vol 838-841 ◽  
pp. 1726-1732
Author(s):  
Ping Tan ◽  
Nan Sheng Li ◽  
Qun Jiang
Keyword(s):  
Dynamic Analysis ◽  
Structural Engineering ◽  
Spectral Element ◽  
Static And Dynamic Analysis ◽  
Damping Matrix ◽  
Large Dams ◽  
Load Vector ◽  
Spatial Domains ◽  
Equivalent Load ◽  
Element Method

Spectral element method (SEM), which combines the ideas of the finite element method (FEM) with the theory of spectral method, is being in the initial stage of developing for the static and dynamic analysis of large dams. The best advantage of SEM is that it can arrive at so-called spectral accuracy out of FEMs reach. In this paper, the Fourier SEM has been first used in dynamic analysis of large dams in order to improve the accuracy and efficiency of numerical results and procedure. The study begins with the governing equation of motion of large dams, then deduces the corresponding SEM stiffness, mass (damping) matrix and equivalent load vector taking advantage of the Fourier interpolation polynomials to approximate the unknowns in spatial domains. This paper also reveals the valuable application of SEM in complicated structural engineering. The formulation proposed in this paper can also be applied to the general dynamic analysis of physical structures.

scholarly journals Numerical Flow Analysis in a Rotating Square Duct and a Rotating Curved-Duct

2000 ◽  
Vol 6 (1) ◽  
pp. 1-9
Author(s):  
Je Hyun Baekt ◽  
Chang Hwan Ko
Keyword(s):  
Laminar Flow ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Centrifugal Force ◽  
Coriolis Force ◽  
Axial Velocity ◽  
Numerical Study ◽  
Axial Direction ◽  
Square Duct ◽  
Rotation Rates

A numerical study is conducted on the fully-developed laminar flow of an incompressible viscous fluid in a square duct rotating about a perpendicular axis to the axial direction of the duct. At the straight duct, the rotation produces vortices due to the Coriolis force. Generally two vortex cells are formed and the axial velocity distribution is distorted by the effect of this Coriolis force. When a convective force is weak, two counter-rotating vortices are shown with a quasi-parabolic axial velocity profile for weak rotation rates. As the rotation rate increases, the axial velocity on the vertical centreline of the duct begins to flatten and the location of vorticity center is moved near to wall by the effect of the Coriolis force. When the convective inertia force is strong, a double-vortex secondary flow appears in the transverse planes of the duct for weak rotation rates but as the speed of rotation increases the secondary flow is shown to split into an asymmetric configuration of four counter-rotating vortices. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration. Also, a numerical study is conducted on the laminar flow of an incompressible viscous fluid in a90°-bend square duct that rotates about axis parallel to the axial direction of the inlet. At a90°-bend square duct, the feature of flow by the effect of a Coriolis force and a centrifugal force, namely a secondary flow by the centrifugal force in the curved region and the Coriolis force in the downstream region, is shown since the centrifugal force in curved region and the Coriolis force in downstream region are dominant respectively.

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