Corrigendum/Addendum in ‘Georgiades, F., 2018, Equilibrium Points with Their Associated Normal Modes Describing Nonlinear Dynamics of a Spinning Shaft with Non-Constant Rotating Speed, Journal of Vibration Testing and System Dynamics, 2(4), 327-373’

2019 ◽  
Vol 3 (2) ◽  
pp. 233-235
Author(s):  
Fotios Georgiades
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Equilibrium Points ◽  
Normal Modes ◽  
Vibration Testing ◽  
Rotating Speed ◽  
Spinning Shaft

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

scholarly journals Non-smooth analysis in a national electricity market model: a complex approach

Memorias ◽  
2018 ◽  
pp. 58-66
Author(s):  
Johnny Valencia ◽  
Gerard Olivar ◽  
Johan Manuel Redondo ◽  
Danny Ibarra Vega ◽  
Carlos Peña Rincón
Keyword(s):  
System Dynamics ◽  
Electricity Market ◽  
Equilibrium Points ◽  
Supply And Demand ◽  
Market Model ◽  
National Network ◽  
Demand Growth ◽  
Zero Rate ◽  
National Electricity Market ◽  
Business Approach

In this paper, we show the preliminary results in a proposed a model for the supply and demand of electricity in a domestic market based on system dynamics. Additionally, the model indicates piecewise smooth differential equations arising from the diagram of flows and levels, using dynamical systems theory for the study of the stability of the equilibrium points that have such a system. A bifurcation analysis approach is proposed to define and understand the complex behavior. Until now, no work has been reported related to this topic using bifurcations criteria. The growing interest in personal ways of self-generation using renewable sources can lead the national grid to a standstill and low investment in the system. However, it is essential to preserve the national network as a power supply support to domestic and enterprise demand. To understand this scenario, we include an analysis of zero-rate demand growth. Under this hypothesis, a none smooth bifurcation appears related to a policy which involves the variation of the capacity charge. As a first significant result, we found that it is possible to preserve the investments in the market since, through the capacity charge parameter, the system dynamics can be controlled. Then, from a business approach, it is necessary to know the effects of the capacity charge as the strategic policy in the system generation price scheme.

scholarly journals Advances in classical and analytical mechanics: A reviews of author’s results

2013 ◽  
Vol 40 (2) ◽  
pp. 293-383 ◽  
Author(s):  
Katica Hedrih-Stevanovic
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Scientific Research ◽  
Order System ◽  
Analytical Mechanics ◽  
Mathematical Methods ◽  
Inertia Moment ◽  
Vector Method ◽  
Research Results ◽  
Scientific Results

A review, in subjective choice, of author?s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author?s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelic and Raskovic, as well as author?s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author?s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates.

Impact of Additive Allee Effect on the Dynamics of an Intraguild Predation Model with Specialist Predator

2020 ◽  
Vol 30 (16) ◽  
pp. 2050239
Author(s):  
Udai Kumar ◽  
Partha Sarathi Mandal
Keyword(s):  
System Dynamics ◽  
Equilibrium Point ◽  
Intraguild Predation ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Dimensional System ◽  
Global Dynamics ◽  
Interior Equilibrium ◽  
Trivial Equilibrium ◽  
The Impact

Many important factors in ecological communities are related to the interplay between predation and competition. Intraguild predation or IGP is a mixture of predation and competition which is a very basic three-dimensional system in food webs where two species are related to predator–prey relationship and are also competing for a shared prey. On the other hand, Allee effect is also a very important ecological factor which causes significant changes to the system dynamics. In this work, we consider a intraguild predation model in which predator is specialist, the growth of shared prey population is subjected to additive Allee effect and there is Holling-Type III functional response between IG prey and IG predator. We analyze the impact of Allee effect on the global dynamics of the system with the prior knowledge of the dynamics of the model without Allee effect. Our theoretical and numerical analyses suggest that: (1) Trivial equilibrium point is always locally asymptotically stable and it may be globally stable also. Hence, all the populations may go to extinction depending upon initial conditions; (2) Bistability is observed between unique interior equilibrium point and trivial equilibrium point or between boundary equilibrium point and trivial equilibrium point; (3) Multiple interior equilibrium points exist under certain parameters range. We also provide here a comprehensive study of bifurcation analysis by considering Allee effect as one of the bifurcation parameters. We observed that Allee effect can generate all possible bifurcations such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov–Taken bifurcation and Bautin bifurcation. Finally, we compared our model with the IGP model without Allee effect for better understanding the impact of Allee effect on the system dynamics.

scholarly journals Nonlinear Dynamics Analysis of Tilting Pad Journal Bearing-Rotor System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
Jiayang Ying ◽  
Yinghou Jiao ◽  
Zhaobo Chen
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Journal Bearing ◽  
Rotor System ◽  
Moment Of Inertia ◽  
Dynamics Analysis ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

The nonlinear dynamics theory is increasingly applied in the dynamics analysis of tilting pad journal bearing-rotor system. However, extensive work on system dynamics done previously neglects the influence caused by the moment of inertia of the pad. In this paper, a comparison is made between the responses of the rotor in the bearings with and without pad inertia effect. Taking the Jeffcott rotor system as an example, the characteristics of bearing-rotor system, such as bifurcation diagram, cycle response, frequency spectrum, phase trajectories, and Poincaré maps, were attained within a certain rotation rate range. The pivotal oil-film force of tilting pad journal bearing was calculated by database method. The results directly demonstrate that considering the influence of the pad moment of inertia, system dynamics characteristics are found more complicated when rotor-bearing system works around natural frequency and system bifurcation is observed forward when rotor-bearing system works on high-speed range.

scholarly journals Modal and Nonmodal Perturbations of Monochromatic High-Frequency Gravity Waves: Primary Nonlinear Dynamics

2007 ◽  
Vol 64 (6) ◽  
pp. 1977-1994 ◽  
Author(s):  
Ulrich Achatz
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
High Frequency ◽  
Normal Modes ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Spatial Dimensions ◽  
Phase Direction ◽  
Parallel Mode ◽  
Boussinesq Fluid

The primary nonlinear dynamics of high-frequency gravity waves (HGWs) perturbed by their most prominent normal modes (NMs) or singular vectors (SVs) in a rotating Boussinesq fluid have been studied by direct numerical simulations (DNSs), with wave scales and values of viscosity and diffusivity characteristic for the upper mesosphere. The DNS is 2.5D in that it has only two spatial dimensions, defined by the direction of propagation of the HGW and the direction of propagation of the perturbation in the plane orthogonal to the HGW phase direction, but describes a fully 3D velocity field. Many results of the more comprehensive fully 3D simulations in the literature are reproduced. So it is found that statically unstable HGWs are subject to wave breaking ending in a wave amplitude with respect to the overturning threshold near 0.3. It is shown that this is a result of a perturbation of the HGW by its leading transverse NM. For statically stable HGWs, a parallel NM has the strongest effect, quite in line with previous results on the predominantly 2D instability of such HGWs. This parallel mode is, however, not the leading NM but a larger-scale pattern, seemingly driven by resonant wave–wave interactions, leading eventually to energy transfer from the HGW into another gravity wave with steeper phase propagation. SVs turn out to be less effective in triggering HGW decay but they can produce turbulence of a strength that is (as that from the NMs) within the range of measured values, however with a more pronounced spatial confinement.

Model Parameter Identification of Nonlinear Dynamics Systems by Trajectory Pattern Method

2010 ◽  
Author(s):  
Jahangir Rastegar ◽  
Dake Feng ◽  
Kavous Jorabchi
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Parameter Identification ◽  
System Stability ◽  
Model Parameters ◽  
System Dynamics Model ◽  
Dynamics Model ◽  
Higher Order Terms ◽  
Trajectory Pattern ◽  
Trajectory Pattern Method

In this paper, a new method is presented for model parameter identification of a large class of fully controlled nonlinear dynamics systems such as robot manipulators. The method uses trajectory patterns with feed-forward controls to identify model parameters of the system. The developed method ensures full system stability, does not require close initial estimated values for the parameters to be identified, and provides a systematic method of emphasizing on the estimation of the parameters associated with lower order terms of the system dynamics model and gradually upgrading the accuracy with which the model parameters, particularly those associated with the higher order terms of the system dynamics model are estimated. The developed method is based on Trajectory Pattern Method (TPM). In this method, for a pattern of motion the inverse dynamics model of the system is derived in algebraic form in terms of the trajectory pattern parameters. The system dynamics model parameters are then identified using a systematic algorithm which ensures system stability as well as accurate estimation of the model parameters associated with lower as well as higher order terms. Mathematical proof of convergence of the developed method and an example of its application are provided.

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