scholarly journals Analysis of the lateral vibrations of an unbalanced Jeffcott rotor

2018 ◽  
Vol 211 ◽  
pp. 18007
Author(s):  
Ali Alsaleh ◽  
Hassen M. Ouakad
Keyword(s):  
Mathematical Model ◽  
Vibration Monitoring ◽  
Flexible Rotor ◽  
Nonlinear Mathematical Model ◽  
Lagrange Method ◽  
Lateral Vibrations ◽  
Mass Unbalance ◽  
Jeffcott Rotor ◽  
Rigid Condition ◽  
Work Done

This paper examines experimentally and analytically the lateral vibrations of a Jeffcott rotor running at various unbalance states. Using a Bently Nevada RK-4 rotor kit, three states of eccentric mass unbalance were assumed in this study: 0.4g, 0.8g and 1.2g. Measurements of the startup data and the steady state data at rigid and flexible rotor condition were collected using a setup that mimics the vibration monitoring industrial practices. Lagrange method was assumed to construct a linear mathematical model of the investigated rotor, based on rigid rotor assumptions, that can predict analytically the lateral vibrations. The dynamic characteristics of the system, including the linearized bearing induced stiffness, were solely extracted from startup data. It was concluded that the developed twodegrees- of-freedom model was able to predict the lateral vibration at the rigid condition with an error around 5%. Whereas it failed to predict the response at flexible condition with matching accuracy. Unlike the majority of the work done in this field where complex, nonlinear mathematical model were used to model real systems, this work validates the applicability of using simple mathematical models in predicting the response of a real rotorsystem with an acceptable accuracy.

On the Coupling Between Torsional and Lateral Vibrations in a Rotor Dynamic System With Set-Valued Friction

2007 ◽  
Author(s):  
N. van de Wouw ◽  
H. Nijmeijer ◽  
N. Mihajlovic´
Keyword(s):  
Dynamic System ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Lateral Vibrations ◽  
Sustained Oscillations ◽  
Mass Unbalance ◽  
Stabilizing Effect ◽  
Set Up ◽  
Rotor Dynamic ◽  
Flexible Rotor Systems

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by mass-unbalance in an experimental rotor dynamic set-up. This study is performed on the level of both numerical and experimental bifurcation analyses. The results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Moreover, the analyses provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which supports the design of such flexible rotor systems.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

scholarly journals Turbogenerator: Part 1: Simulation

2018 ◽  
Vol 7 (3.15) ◽  
pp. 277
Author(s):  
Lev Yu. Lezhnev ◽  
Alexey P. Tatarnikov ◽  
Arсady A. Skvortsov ◽  
Igor A. Papkin ◽  
Aleksandr S. Nekrasov
Keyword(s):  
Mathematical Model ◽  
Power Generation ◽  
Comparative Analysis ◽  
Power Plants ◽  
Computational Analysis ◽  
Exhaust System ◽  
Electric Machine ◽  
Distributed Power Generation ◽  
Technical Solutions ◽  
Work Done

The article describes the process of developing a turbogenerator for power plants of small and distributed power generation. The analysis of the component base for the turbogenerator was carried out, and thereof a comparative analysis of possible technical solutions was conducted. The work considered the installation variants of a turbogenerator in the exhaust system, an electric machine of a turbogenerator, types of turbines of a generator. A mathematical model for computation of the output effective and geometric parameters of a turbogenerator was described. The results of computational analysis were presented, and the parameters of the turbogenerator being developed were selected. Based on the results of the work done the conclusions were made  

A Nonlinear Mathematical Model for Ship Turning Circle Simulation in Waves

2005 ◽  
Vol 49 (02) ◽  
pp. 69-79 ◽  
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo ◽  
Ming-Ling Lee
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Regular Waves ◽  
Nonlinear Mathematical Model ◽  
Ship Maneuvering ◽  
Sea Trial ◽  
Six Degrees Of Freedom ◽  
Strip Theory ◽  
Calm Water ◽  
Maneuvering Motion

In the paper, a simplified six degrees of freedom mathematical model encompassing calm water maneuvering and traditional seakeeping theories is developed to simulate the ship turning circle test in regular waves. A coordinate system called the horizontal body axes system is used to present equations of maneuvering motion in waves. All corresponding hydrodynamic forces and coefficients for seakeeping are time varying and calculated by strip theory. For simplification, the added mass and damping coefficients are calculated using the constant draft but vary with encounter frequency. The nonlinear mathematical model developed here is successful in simulating the turning circle of a containership in sea trial conditions and can be extended to make the further simulation for the ship maneuvering under control in waves. Manuscript received at SNAME headquarters February 19, 2003; revised manuscript received January 27, 2004.

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

Optimizing Series Repairable Systems with Imperfect Repair

2013 ◽  
pp. 83-93
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

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