Regular and Irregular Vibrations of a Non-Ideal Autoparametric System

Volume 2 ◽  
2004 ◽  
Author(s):  
Danuta Sado ◽  
Maciej Kot
Keyword(s):  
Energy Source ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Resonance Region ◽  
The Body ◽  
Damping Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Time Histories ◽  
Limited Power

This paper studies the regular and irregular vibrations of two degrees of freedom autoparametrical system, when the excitation is made by an electric motor (with unbalanced mass), which works with limited power supply. The investigated system consists of a pendulum of the length l and mass m, and a body of mass M suspended on the flexible element. It was assumed that the damping force acting on the body of mass M and resistive moment acting on the pedulum are non-linear. In this case, the excitation has to be expressed as an equation describing how the energy source supplies the energy to the system. The non-ideal source of power adds one degree of freedom, and then the system has three degrees of freedom. The system has been researched for known characteristic of the energy source (DC motor). The equations of motion have been solved numerically what permit to enrich the investigations and to examine not only small and steady state oscillations but also large-amplitude oscillations in transient states. The influence of motor’s speed on the phenomenon of energy transfer has been researched. Near the internal and external resonance region, except different kind of periodic vibration, the chaotic vibration has been observed. For characterizing an irregular chaotic response bifurcation diagrams and time histories, power spectral densities, Poincare´ maps and maximal exponents of Lyapunov have been constructed.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

Control of Maglev Suspension Systems

1996 ◽  
Vol 2 (3) ◽  
pp. 349-368 ◽  
Author(s):  
Y. Cai ◽  
S.S. Chen
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Vehicle Suspension ◽  
Semiactive Control ◽  
One Dimensional ◽  
Suspension Systems ◽  
Maglev Vehicle ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Control Designs

This study investigates alternate designs for control of maglev vehicle suspension systems. Active and semiactive control-law designs are introduced into primary and secondary suspensions of maglev vehi cles. A one-dimensional vehicle with two degrees of freedom, simulating the German Transrapid Magiev System, is used. The transient and frequency responses of suspension systems and power spectral densities of vehicle accelerations are calculated to evaluate different control designs. The results show that both active and semiactive control designs improve vehicle response and provide acceptable ride comfort for maglev systems.

scholarly journals Modelling of propeller shaft dynamics at pulse load

2008 ◽  
Vol 15 (4) ◽  
pp. 52-58 ◽  
Author(s):  
Andrzej Grządziela
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Model Identification ◽  
Experimental Results ◽  
Real Object ◽  
Pulse Load ◽  
Propeller Shaft ◽  
Matlab Simulink ◽  
External Agents ◽  
Time Histories

Modelling of propeller shaft dynamics at pulse load The article discusses a method of modelling of propeller shaft dynamics at the presence of virtually introduced underwater detonation effects. The propeller shaft model has four degrees of freedom, which provides opportunities for introducing shaft displacements and rotations similar to those observed in a real object. The equations of motion, taking into account the action of external agents, were implemented to the Matlab SIMULINK environment. The obtained time-histories and their spectra were compared with the experimental results of the tests performed on the marine testing ground. The performed model identification confirmed its sensitivity to changing parameters of motion and external actions.

Computer Based Model of Vibro-Impact Driving

1999 ◽  
Author(s):  
Howe Ping Lok ◽  
Richard D. Neilson ◽  
Albert A. Rodger
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Laboratory Model ◽  
Side Resistance ◽  
Time Histories ◽  
Computer Based ◽  
Impact Driving ◽  
Penetration Time

Abstract A computer based model of a novel vibro-impact ground moling system is presented as an aid to designing such systems. The equations of motion governing the system are presented and a corresponding laboratory model is described. The model includes elasto-plastic modelling of the end resistance and Coulomb terms for side resistance between the soil and the body of the moling system. Results for both penetration time histories and end resistance time histories from both the model and the rig are presented which show that the model can adequately predict the motion of the mole for design purposes.

On Chaotic Dynamics of a Double Pendulum Arm Excited by a Nonlinear Shaker Based RLC Circuit

2013 ◽  
Author(s):  
Danuta Sado ◽  
José M. Balthazar ◽  
Jorge L. P. Felix
Keyword(s):  
Magnetic Field ◽  
Chaotic Dynamics ◽  
Nonlinear Term ◽  
Nonlinear Function ◽  
Double Pendulum ◽  
Bifurcation Diagrams ◽  
Power Spectral ◽  
Rlc Circuit ◽  
Power Spectral Densities ◽  
Time Histories

The chaotic dynamics of a double pendulum arm coupled to a nonlinear shaker based RLC circuit through a magnetic field is studied numerically. The nonlinear term, in the circuit, is introduced by considering that the voltage of the capacitor is a nonlinear function of the instantaneous electric charge. For the identification of the response of the system various techniques, including chaos techniques as bifurcation diagrams and time histories, power spectral densities (FFT), Poincaré maps and exponents of Lyapunov are used. This electromechanical system will represent a basic subsystem of any robot.

Comparative Study of the Linear and Non-Linear Locomotive Response

1979 ◽  
Vol 101 (3) ◽  
pp. 263-271 ◽  
Author(s):  
E. H. Chang ◽  
V. K. Garg ◽  
C. H. Goodspeed ◽  
S. P. Singh
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Design Parameters ◽  
Suspension Systems ◽  
Damping Characteristics ◽  
Time Histories ◽  
Steady State Responses ◽  
Stiffness And Damping ◽  
State Responses

A mathematical model for a six-axle locomotive is developed to investigate its dynamic response on tangent track due to vertical and/or lateral track irregularities. The model represents the locomotive as a system of thirty-nine degrees of freedom. The nonlinearities considered in the model are primarily associated with stiffness and damping characteristics of the primary suspension system. The transient and steady-state responses of the locomotive are obtained for the linear and nonlinear primary suspension systems. The response time-histories of the locomotive obtained by integrating the generalized equations of motion are presented. The potential uses of the model are indicated for studying the influence of different design parameters and predicting subsequent dynamic response.

scholarly journals Swimming Hydrodynamics and Maneuverability in C-Start of Zebrafish Larvae: An Integrated Computational Study

2011 ◽  
Author(s):  
Gen Li ◽  
Hao Liu ◽  
Ulrike K. Mu¨ller ◽  
Johan L. van Leeuwen
Keyword(s):  
Vortex Ring ◽  
Degrees Of Freedom ◽  
Computational Study ◽  
Equations Of Motion ◽  
The Body ◽  
Free Swimming ◽  
Double Row ◽  
Zebrafish Model ◽  
Larval Zebrafish ◽  
Ring Structures

Fishes often exhibit stable body undulating in body and caudal fin (BCF) mode during cyclic swimming, but can perform remarkable maneuverability with significantly different swimming modes in case of C-start. Aiming at unveiling the mechanisms of swimming hydrodynamics and maneuverability of C-start, we have developed an integrated computational framework to model a free-swimming larval zebrafish (Danio rerio) by coupling the equations of 3DoF (Degrees of Freedom) motion and Navier-Stokes (NS) equations. Unsteady hydrodynamics is resolved by integrating models of realistic fin-body morphology and body-undulatory kinematics with an in-house NS solver. The instantaneous forces and moments on the body provided by the NS-solutions serve as input for 3DoF equations of motion. In this study, with a specific focus on a C- start as well as a subsequent transient phase till the cyclic swimming phase, we construct a larval zebrafish model, which can mimics realistic body motions and deformations based on measurements. Validation of the simulation is discussed by comparing model predictions with experimental measurements, which indicates that the present integrated model is capable to accurately predict free-swimming dynamics and hydrodynamics. The model successfully simulated a swimming bout of C-start and cyclic swimming: a wake topology of double row vortex ring structures is observed behind the fish; and a strong jet is visible at the center of the vortex ring, pushing water backward as the fish accelerates.

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.

A New Control Algorithm for Vehicle Stability Control

2008 ◽  
Author(s):  
Seyed Hossein Tamaddoni ◽  
Saied Taheri
Keyword(s):  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Equations Of Motion ◽  
Stability Control ◽  
The Body ◽  
Vehicle Stability ◽  
Relaxation Length ◽  
New Approach ◽  
Vehicle Stability Control

A new control algorithm and the adaptation laws required for estimation of unknown vehicle parameters have been developed for vehicle stability control (VSC). This algorithm is based on the Lyapunov Direct Method. A vehicle model with two degrees of freedom (DOF) was used to develop the control algorithm. In developing the equations of motion for this simple model, a new approach for introducing the needed stabilizing forces and moments was developed. In addition, an eight DOF model was developed for control algorithm evaluation. The model includes lateral, longitudinal, yaw, and roll motions of the body plus the rotational DOFs for all of the four wheels. Also included in the model is a transient tire model taking into account the tire lateral relaxation length. Using the validated 8 DOF simulation model, the new control algorithm was evaluated and the results show the advantages of using such an approach for enhancing vehicle stability during emergency steering maneuvers.

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