A Fractional Derivative Model for Rubber Spring of Primary Suspension in Railway Vehicle Dynamics

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Dawei Zhang ◽  
Shengyang Zhu
Keyword(s):  
Fractional Derivative ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Coupled System ◽  
Dynamic Responses ◽  
Viscous Force ◽  
Railway Vehicle ◽  
Spring Model ◽  
The Difference ◽  
Amplitude Dependency

This paper presents a nonlinear rubber spring model for the primary suspension of the railway vehicle, which can effectively describe the amplitude dependency and the frequency dependency of the rubber spring, by taking the elastic force, the fractional derivative viscous force, and nonlinear friction force into account. An improved two-dimensional vehicle–track coupled system is developed based on the nonlinear rubber spring model of the primary suspension. Nonlinear Hertz theory is used to couple the vehicle and track subsystems. The railway vehicle subsystem is regarded as a multibody system with ten degrees-of-freedom, and the track subsystem is treated as finite Euler–Bernoulli beams supported on a discrete–elastic foundation. Mechanical characteristic of the rubber spring due to harmonic excitations is analyzed to clarify the stiffness and damping dependencies on the excitation frequency and the displacement amplitude. Dynamic responses of the vehicle–track coupled dynamics system induced by the welded joint irregularity and random track irregularity have been performed to illustrate the difference between the Kelvin–Voigt model and the proposed model in the time and frequency domain.

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.

Study on Dynamic Responses of Human-Structure Interaction System

2013 ◽  
Vol 438-439 ◽  
pp. 775-778
Author(s):  
Yi He Wang ◽  
Na Yang
Keyword(s):  
Dynamic System ◽  
Fundamental Frequency ◽  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Coupled System ◽  
Dynamic Responses ◽  
Major Topic ◽  
Integer Multiple ◽  
Structure Interaction

t has previously been shown that human-structure dynamic system received much attention as a major topic in the serviceability performance and safety problems. In this study, the structure occupied by human are considered as a two degrees-of-freedom system. The dynamic characteristics of human-structure system are investigated by deriving the eigenvalue equation of the system. The response of structure to a person walking across it at various rates of walking is also researched. The results show that the pair natural frequencies of coupled system have a contrary trend when the crowd densities increase. It also demonstrates that the resonant situation occurs when structural fundamental frequency is equal to or an integer multiple of the pacing frequency.

Passenger Comfortability Studies of Electric Vehicle under ISO-2631 Criteria

2014 ◽  
Vol 699 ◽  
pp. 975-980
Author(s):  
Wibowo ◽  
Ubaidillah ◽  
Ipnu Candra ◽  
Muhammad Nizam
Keyword(s):  
Electric Vehicle ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Dynamic Responses ◽  
Stiffness Coefficient ◽  
Vehicle Model ◽  
Passive Suspension ◽  
Suspension Stiffness ◽  
Passive Suspension System ◽  
Iso 2631

The study focuses on the vertical, longitudinal and lateral responses of ride performance of an electric vehicle. Issues related to the design of vehicle model with passive suspension system are discussed. A full-car seven-degrees-of-freedom model is used to investigate the dynamic responses by applying road disturbances in sinusoidal road input excitation. Frequency response of the heave, roll and pitch of the sprung mass is obtained for the need of studying the effects of given variations of the suspension stiffness coefficient and the suspension damping coefficient. Finally, using the ISO-2631 criteria, the result of the responses in frequency domain are evaluated to evaluate the passenger comfortability.

scholarly journals Fault Diagnosis of Wheel Flat Using Empirical Mode Decomposition-Hilbert Envelope Spectrum

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Hua Jiang ◽  
Jianhui Lin
Keyword(s):  
Empirical Mode Decomposition ◽  
Degrees Of Freedom ◽  
Frequency Component ◽  
Dynamic Responses ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Mode Decomposition ◽  
Hilbert Envelope ◽  
Wheel Flat ◽  
Envelope Spectrum

We establish the Injury Model of Wheel Flats with 10 degrees of freedom and calculate the dynamic responses of the railway vehicle system, which include different vehicle speeds and different length flats. The Hilbert envelope spectrum method based on Empirical Mode Decomposition (EMD) is proposed according to the nonstationary characteristics of axle box acceleration (ABA) signal. The vibration characteristics of the ABA are studied thoroughly. And then the effects concerning speed and flat length on the diagnosis results are analyzed. The simulation results show the amplitude corresponding to the frequency component of wheel flats raise with the increasing of the wheel flat length when the single or double wheel flats impact the track at the same vehicle speed. In other words, the longer the wheel flat is, the greater the magnitude of the decomposition result is. In the same vehicle speed, the amplitude corresponding to the frequency component of wheel flat is minimum when the two flats’ phase difference is 180°. With the same flat length (single or double wheel flats), the amplitude corresponding to the frequency components of wheel flats decreases with the increasing of the speed. This method could accurately and effectively identify the frequency of wheel flats.

NONLINEAR RESPONSES OF A STRING-BEAM COUPLED SYSTEM WITH FOUR-DEGREES-OF-FREEDOM AND MULTIPLE PARAMETRIC EXCITATIONS

2009 ◽  
Vol 19 (01) ◽  
pp. 225-243 ◽  
Author(s):  
D. X. CAO ◽  
W. ZHANG
Keyword(s):  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Coupled System ◽  
Dynamic Responses ◽  
Governing Equations ◽  
Chaotic Motions

The nonlinear dynamic responses of a string-beam coupled system subjected to harmonic external and parametric excitations are studied in this work in the case of 1:2 internal resonance between the modes of the beam and string. First, the nonlinear governing equations of motion for the string-beam coupled system are established. Then, the Galerkin's method is used to simplify the nonlinear governing equations to a set of ordinary differential equations with four-degrees-of-freedom. Utilizing the method of multiple scales, the eight-dimensional averaged equation is obtained. The case of 1:2 internal resonance between the modes of the beam and string — principal parametric resonance-1/2 subharmonic resonance for the beam and primary resonance for the string — is considered. Finally, nonlinear dynamic characteristics of the string-beam coupled system are studied through a numerical method based on the averaged equation. The phase portrait, Poincare map and power spectrum are plotted to demonstrate that the periodic and chaotic motions exist in the string-beam coupled system under certain conditions.

scholarly journals Numerical modelling of the oscillatory flow effect around submarine pipeliness

2020 ◽  
Author(s):  
Marian Yegres ◽  
Armando Blanco Álvarez
Keyword(s):  
Numerical Model ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Cross Flow ◽  
Uniform Flow ◽  
Incident Flow ◽  
Drag Forces ◽  
Numerical Predictions ◽  
Underwater Pipeline ◽  
The Difference

This work describes the dynamics of an underwater pipeline subjected to an incident flow composed of a uniform flow and a sinusoidal component. The motion equations of the pipeline and the fluid flow around the pipeline are solved simultaneously with a numerical model that considers in-line oscillations (one degree of freedom) and a second numerical model that additionally includes cross flow (two degrees of freedom). The amplitude response and drag forces on the pipe are compared for both models considering parameters such as the difference between the excitation and natural frequencies of pipelines and the relative value between the sinusoidal and uniform components of the incident flow. Important differences in numerical predictions of both models are observed when the excitation frequency is greater than the natural frequency of the system and when the amplitude of the oscillatory component of the incident flow is greater than the amplitude of the uniform flow.

Effects of intermediate support stiffness on nonlinear dynamic response of transmission system

2020 ◽  
Vol 26 (9-10) ◽  
pp. 851-862
Author(s):  
Jinli Xu ◽  
Jiwei Zhu ◽  
Lei Wan
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Nonlinear Differential Equations ◽  
Great Influence ◽  
Coupled System ◽  
Transmission System ◽  
Dynamic Responses ◽  
Axial Stiffness ◽  
Parameter Method ◽  
Intermediate Support

This study is aimed at investigating the effects of intermediate support stiffness on nonlinear vibration response of transmission system. A coupled bending–torsional–lateral dynamic model with 14 degrees of freedom of transmission system is proposed comprehensively considering rubber dynamic stiffness, time-varying stiffness, static transmission error, and backlash. Meanwhile, a model of intermediate support with rubber nonlinear properties is developed to improve the accuracy of analysis. On the basis of the nonlinear differential equations derived by the lumped-parameter method, the dynamic responses of the key parts in the transmission system are obtained using the Runge–Kutta method and the effects of intermediate support stiffness on the dynamic characteristics are analyzed. Numerical results show that complicated interaction occurs and intermediate support stiffness has a great influence on the vibration of the coupled system. With the increase in the intermediate support stiffness, the vibration displacements in the three directions of the gear are progressively reduced and the nature frequencies are changed. The influence of the radial stiffness is greater than that of the axial stiffness. An experiment is performed subsequently to validate the effect of intermediate support stiffness on system, and the experimental results are consistent with numerical ones.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

Workspace, dexterity and dimensional optimization of microhexapod

2015 ◽  
Vol 35 (4) ◽  
pp. 341-347 ◽  
Author(s):  
E. Rouhani ◽  
M. J. Nategh
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Screw Theory ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Content Type ◽  
Workspace Analysis ◽  
The Difference ◽  
Flexure Joints ◽  
6 Degrees Of Freedom

Purpose – The purpose of this paper is to study the workspace and dexterity of a microhexapod which is a 6-degrees of freedom (DOF) parallel compliant manipulator, and also to investigate its dimensional synthesis to maximize the workspace and the global dexterity index at the same time. Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Design/methodology/approach – Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Findings – It has been shown that the proposed procedure for the workspace calculation can considerably speed the required calculations. The optimization results show that a converged-diverged configuration of pods and an increase in the difference between the moving and the stationary platforms’ radii cause the global dexterity index to increase and the workspace to decrease. Originality/value – The proposed algorithm for the workspace analysis is very important, especially when it is an objective function of an optimization problem based on the search method. In addition, using screw theory can simply construct the homogeneous Jacobian matrix. The proposed methodology can be used for any other micromanipulator.

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