scholarly journals Simplified Vibration Model and analysis of a single-conductor transmission line with dampers

2016 ◽  
Vol 231 (22) ◽  
pp. 4150-4162 ◽  
Author(s):  
O Barry ◽  
R Long ◽  
DCD Oguamanam
Keyword(s):  
Transmission Line ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Proposed Model ◽  
Vibration Model ◽  
Mass Spring ◽  
Discrete Mass

A novel model is developed for a vibrating single-conductor transmission line carrying Stockbridge dampers. Experiments are performed to determine the equivalent viscous damping of the damper. This damper is then reduced to an equivalent discrete mass-spring-mass and viscous damping system. The equations of motion of the model are derived using Hamilton’s principle and explicit expressions are determined for the frequency equation, and mode shapes. The proposed model is verified using experimental and finite element results from the literature. This proposed model excellently captures free vibration characteristics of the system and the vibration level of the conductor, but performs poorly in regard to the vibration of the counterweights.

Free Vibration Analysis of a Beam Under Axial Load Carrying a Mass-Spring-Mass

2012 ◽  
Author(s):  
O. R. Barry ◽  
Y. Zhu ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Equations Of Motion ◽  
Tensile Load ◽  
Free Vibration Analysis ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Mass System ◽  
Mass Spring

This paper deals with the free vibration analysis of a beam subjected to an axial tensile load with an attached in-span mass-spring-mass system. The equations of motion are derived by means of the Hamilton principle and an explicit expression of the frequency equation is presented. The formulation is validated with results in the literature and the finite element method. Parametric studies are done to investigate the effect of the axial load, the magnitude and location of the mass-spring-mass system on the lowest five natural frequencies and mode shapes. The results indicate that the fundamental mode is independent of the tension and the in-span mass. However, a significant change in all modes is observed when the position of the mass-spring-mass is varied.

Nonlinear Dynamics of Stockbridge Dampers

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
O. Barry ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Nonlinear Frequency ◽  
Modulation Equations ◽  
Proposed Model ◽  
Cantilevered Beams ◽  
Stockbridge Damper

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

Experimental Modal Analysis of a Fixed-Fixed Beam Under Axial Force

2017 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Khaled Alghemlas ◽  
Adam Betancourt
Keyword(s):  
Analytical Model ◽  
Axial Force ◽  
Experimental Approach ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Governing Equations ◽  
Experimental Procedure ◽  
Resonance Frequencies ◽  
Fixed Beam

In this paper, an experimental procedure is proposed for determining the resonance frequencies and mode shapes of vibration of a fixed-fixed beam. Since it is fixed at both ends, the beam may sustain an axial force due to several factors including the fasteners and/or change of temperature. The analytical governing equations of motion, frequency equation, and mode shapes of vibration are presented. The analytical model is used to justify the experimental approach as well as interpretation of the experiment data. In this study, a hammer is used to excite the beam, and then the vibration of the beam is observed and recorded at two different points on the beam using two laser Doppler vibrometers. The data from the vibrometers are used to extract the resonance frequencies and mode shapes of vibrations. Using the analytical model, the axial force in the beam is estimated.

A New Dynamical Model of Flexible Cracked Wind Turbines for Health Monitoring

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
M. A. Ben Hassena ◽  
F. Najar ◽  
B. Aydi ◽  
S. Choura ◽  
F. H. Ghorbel
Keyword(s):  
Health Monitoring ◽  
Large Scale ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Crack Size ◽  
Mode Shapes ◽  
Horizontal Axis Wind Turbine ◽  
Proposed Model ◽  
Monitoring Applications ◽  
Bem Theory

We develop a mathematical model of a large-scale cracked horizontal axis wind turbine (HAWT) describing the flapping flexure of the flexible tower and blades. The proposed model has enough fidelity to be used in health monitoring applications. The equations of motion account for the effect of the applied aerodynamic forces, modeled using the blade element momentum (BEM) theory, and the location and shape of a crack introduced into one of the blades. We first examine the static response of the HAWT in presence of the crack, and then we formulate the eigenvalue problem and determine the natural frequencies and associated mode shapes. We show that both shape and location of the crack influence the first four natural frequencies. The dynamic response of the HAWT subjected to wind and gravity is obtained using a Galerkin procedure. We conduct a parametric analysis to investigate the influence of the crack on the eigenstructure and overall dynamics. The simulations depict that the first four natural frequencies are reduced as the crack size become more important. We also conclude that the tower root moment may be considered as potential indicators for health monitoring purposes.

Study of Vehicle Vibration Model Based on Lagrange Method

2013 ◽  
Vol 328 ◽  
pp. 585-588
Author(s):  
Ming Yang ◽  
Xin Xiang Zhou ◽  
De Chen Zhang ◽  
Xiu E Wu ◽  
Xi Chen
Keyword(s):  
Kinetic Energy ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Dissipation Function ◽  
Mode Shapes ◽  
Energy Potential ◽  
Lagrange Method ◽  
Vibration Model ◽  
Vehicle Systems ◽  
Vehicle Vibration Model

The vibrating behavior of multiple DOF vehicle systems is very much dependent to their natural frequencies and mode shapes. These characteristics can be determined by solving an eigenvalue and an eigenvector problem. The kinetic energy, potential energy, and dissipation function of the system was defined by quadratures and the equations of motion were derived by applying the Lagrange method. Numerical example was calculated. The results show that the method is correct and it lay a good foundation for further research on vehicle vibration.

Axisymmetrical Vibrations of Underwater Hemispherical Shells

1976 ◽  
Vol 98 (3) ◽  
pp. 941-947
Author(s):  
F. C. Chen ◽  
T. C. Huang
Keyword(s):  
Equations Of Motion ◽  
Hydrodynamic Pressure ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Legendre Functions ◽  
Water Field ◽  
Fluid Solid Interaction ◽  
Interaction Problem ◽  
Hemispherical Shells

Free vibrations of an underwater elastic hemispherical thin shell with fixed edge have been investigated based on the bending theory. The solution of this fluid-solid interaction problem involves the differential equations of motion of underwater spherical shells, the velocity potential of the water field, the hydrodynamic pressure, and the continuity and boundary conditions. A transcedental frequency equation in terms of Legendre functions is derived and the normal and tangential mode shapes are found. Examples are given and results are plotted for natural frequencies and modes shapes.

Vibration Modes and Frequencies of Timoshenko Beams With Attached Rigid Bodies

1995 ◽  
Vol 62 (1) ◽  
pp. 193-199 ◽  
Author(s):  
M. W. D. White ◽  
G. R. Heppler
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Rigid Bodies ◽  
The Body ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
First Moment

The equations of motion and boundary conditions for a free-free Timoshenko beam with rigid bodies attached at the endpoints are derived. The natural boundary conditions, for an end that has an attached rigid body, that include the effects of the body mass, first moment of mass, and moment of inertia are included. The frequency equation for a free-free Timoshenko beam with rigid bodies attached at its ends which includes all the effects mentioned above is presented and given in terms of the fundamental frequency equations for Timoshenko beams that have no attached rigid bodies. It is shown how any support / rigid-body condition may be easily obtained by inspection from the reported frequency equation. The mode shapes and the orthogonality condition, which include the contribution of the rigid-body masses, first moments, and moments of inertia, are also developed. Finally, the effect of the first moment of the attached rigid bodies is considered in an illustrative example.

Modal Estimation of Gyroscopic Effect in Rotordynamic Systems

2001 ◽  
Author(s):  
Jerzy T. Sawicki
Keyword(s):  
Decay Rate ◽  
Natural Frequency ◽  
Controller Design ◽  
Equations Of Motion ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
New Approach ◽  
Technical Interest ◽  
Gyroscopic Effects ◽  
Gyroscopic Systems

Abstract A new approach for uncoupling the equations of motion typical for rotordynamical systems is presented. The method does not neglect the speed dependent effects, like gyroscopic effects, and can be particularly valuable in the controller design of actively controlled rotors. In the presence of hysteretic type of damping, the resulting uncoupled gyroscopic systems come with an equivalent viscous damping, equivalent in a sense of the same natural frequency and decay rate. The approach is illustrated through the example of technical interest. The generated results demonstrate that the developed approach is correct and straightforward.

The Effect of Rolling Speed and Friction on Cold Rolling Mill Stability

2012 ◽  
Author(s):  
Y. S. Kim ◽  
N. Zhang ◽  
J. C. Ji ◽  
W. Y. D. Yuen
Keyword(s):  
Friction Coefficient ◽  
Rolling Force ◽  
Equations Of Motion ◽  
Rolling Speed ◽  
Vibrational Modes ◽  
Proposed Model ◽  
Vibration Model ◽  
Steady State Rolling ◽  
The Given ◽  
Negative Gradient

In order to investigate the validity of a coupled mill vibration model presented in the dynamic rolling formulation, this paper presents the results of dynamic characteristics examining rolling force variations in response to rolling parameters. Under the given steady state rolling condition, the unstable vibrational modes with corresponding frequencies are identified and stability analysis is also performed to demonstrate that the proposed model is highly dependent on the rolling speed and friction coefficient with an assumed negative gradient of friction coefficient. To further find the transient characteristics and the direct influences of the friction coefficient and rolling speed on the mill chatter, the derived equations of motion of the system are solved using Runge-Kutta numerical integration method. Simulations are carried out to reveal the chatter sources, which gives rise to unstable rolling vibrations.

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