Stability of synchronous regimes in unbalanced rotors on elastic base

2020 ◽  
pp. 095440622092032
Author(s):  
Arkadiy I Manevich
Keyword(s):  
Numerical Simulation ◽  
Parametric Instability ◽  
Elastic Base ◽  
First Approximation ◽  
Unbalanced Rotor ◽  
Synchronous Rotation ◽  
The Stability ◽  
Conditions Of Stability ◽  
Nonuniform Rotation ◽  
Driving Torque

The stationary dynamics of an unbalanced rotor (vibrator) on a movable base (linear oscillator) under excitation by a driving torque is studied with focusing on the stability of 1:1 stationary regimes of rotation and oscillation. This problem was well studied previously in the first approximation, dealing, in fact, with averaged regimes, mainly in the framework of asymptotic procedures. We use an efficient analytical procedure, proposed in our previous works for another problem, which sequentially separates the averaged regimes and deviations from them. Describing in the first approximation the known features of the synchronous stationary regimes under consideration, this approach in the second approximation results in the analytical solution for nonuniform rotation whose exactness is confirmed in the numerical simulation. The solution enables us to reveal possibility of parametric instability for oscillations of the rotor angular velocity and to describe two possible mechanisms of this instability. It is shown that the known condition of stability of stationary synchronous rotation-oscillation regimes is only necessary but not sufficient criterion, and two additional necessary conditions of stability are obtained and confirmed by the numerical simulation.

scholarly journals Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 173 ◽  
Author(s):  
Sameh S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Numerical Simulation ◽  
Fixed Points ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Dynamic Effects ◽  
One Dimensional ◽  
First Case ◽  
The Stability ◽  
Conditions Of Stability ◽  
Dynamic Duopoly

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

The Compliance Method for Measurement of Near Surface Residual Stresses—Analytical Background

1994 ◽  
Vol 116 (4) ◽  
pp. 550-555 ◽  
Author(s):  
M. Gremaud ◽  
W. Cheng ◽  
I. Finnie ◽  
M. B. Prime
Keyword(s):  
Numerical Simulation ◽  
Residual Stresses ◽  
Random Errors ◽  
Residual Stress Field ◽  
Near Surface ◽  
Surface Residual Stresses ◽  
Zero Shift ◽  
Stress States ◽  
The Stability ◽  
Piecewise Functions

Introducing a thin cut from the surface of a part containing residual stresses produces a change in strain on the surface. When the strains are measured as a function of the depth of the cut, residual stresses near the surface can be estimated using the compliance method. In previous work, the unknown residual stress field was represented by a series of continuous polynomials. The present paper shows that for stress states with steep gradients, superior predictions are obtained by using “overlapping piecewise functions” to represent the stresses. The stability of the method under the influence of random errors and a zero shift is demonstrated by numerical simulation.

Basic Experimental and Numerical Investigations on Chip Pressing

2013 ◽  
Vol 554-557 ◽  
pp. 630-637 ◽  
Author(s):  
Martin Grüner ◽  
Marion Merklein
Keyword(s):  
Numerical Simulation ◽  
Aluminium Alloys ◽  
Testing Machine ◽  
Material Model ◽  
Extrusion Process ◽  
Milling Process ◽  
Numerical Investigations ◽  
Compression Direction ◽  
Universal Testing ◽  
The Stability

Aluminium alloys show a great potential for lightweight constructions due to their high strength and low density but the production of this material is very energy consuming. Also the recycling of aluminium alloys, e.g. chips from the milling process, shows different challenges. Beside contamination by cooling lubricant and oxidation of the surface of the chips the melting and rolling process for new semi finish products needs a high amount of energy. TEKKAYA shows a new approach for recycling of aluminium alloy chips by an extrusion process at elevated temperatures producing different kinds of profiles. A new idea is the production of components directly out of chips using severe plastic deformation for joining of the chips similar to the accumulative roll bonding process in sheet metal forming. In a first approach aluminium alloy chips out of a milling process were uniaxial compressed with different loads inside an axisymmetric tool installed in a universal testing machine. The compressed chip disks subsequently were tested with two experiments to gain information on their stability. First experiment is a disk compression test with the disk standing on its cylindrical surface, giving information on the stability perpendicular to the compression direction. Second experiment is a stacked disk compression test with three disks to investigate the stability parallel to compression direction. During all three tests force and displacement values are recorded by the universal testing machine. These data are also processed to calculate or identify input parameters for the numerical investigations. For numerical simulation ABAQUS in conjunction with the Drucker-Prager-Cap material model, which is often used for sintering processes, seems to be a good choice. By numerical simulation of the experiments and comparison with the experiments input parameters for the material model can be identified showing good accordance. This material model will be used in future numerical investigations of an extrusion process to identify tool geometries leading to high strains inside the material and by this to an increased stability of the parts.

Application of ABAQUS in Surrounding Rock Stability Analysis of Shallow Large Cross-Section Tunnel

2015 ◽  
Vol 777 ◽  
pp. 8-12 ◽  
Author(s):  
Lin Zhen Cai ◽  
Cheng Liang Zhang
Keyword(s):  
Numerical Simulation ◽  
Rock Mass ◽  
Strong Support ◽  
Surrounding Rock ◽  
Tunnel Engineering ◽  
Tunnel Excavation ◽  
Rock Stability ◽  
Rock Bolting ◽  
Excavation Support ◽  
The Stability

HuJiaDi tunnel construction of Dai Gong highway is troublesome, the surrounding-rock mass give priority to full to strong weathering basalt, surrounding rock integrity is poor, weak self-stability of surrounding rock, and tunnel is prone to collapse. In order to reduce disturbance, taking advantage of the ability of rock mass, excavation adopt the method of "more steps, short footage and strong support". The excavation method using three steps excavation, The excavation footage is about 1.2 ~ 1.5 m; The surrounding rock bolting system still produce a large deformation after completion of the first support construction, it shows that the adopted support intensity cannot guarantee the stability of the tunnel engineering. Using ABAQUS to simulate tunnel excavation support, optimizing the support parameters of the tunnel, conducting comparative analysis with Monitoring and Measuring and numerical simulation results, it shows that the displacement - time curves have a certain consistency in numerical simulation of ABAQUS and Monitoring and Measuring.

Some Relationship between Safety Factor of Earthquake Slope and Related Parameters

2011 ◽  
Vol 422 ◽  
pp. 688-692
Author(s):  
Xiao Hei He ◽  
Geng You Han ◽  
Rui Hua Xiao
Keyword(s):  
Numerical Simulation ◽  
Rock Mechanics ◽  
Safety Factor ◽  
Limit Equilibrium ◽  
Static Method ◽  
Acceleration Coefficient ◽  
The Wenchuan Earthquake ◽  
Stability Of Slope ◽  
The Stability ◽  
The Relationship

Abstract:Since the Wenchuan earthquake happened, the slope stability had been paid much more attention. The safety factor is an important parameter that can be used to evaluate the stability of slope. The pseudo-static method that based on limit equilibrium and the method of numerical simulation can calculate the safety factor accurately, but the velocity that gets the result is slow. If we can establish the relationship between safety factor and some other parameters, then we can calculate the safety factor by using the relationship more quickly. This paper establishes much relationship, such as the relationship between the rock mechanics parameters and the average danymic safety factor, the relationship between the rock mechanics parameters and the ratio of average danymic safety factor to static safety factor, the relationship between the rock mechanics parameters and the average earthquake acceleration coefficient, the relationship between the average earthquake acceleration coefficient and the ratio of average danymic safety factor to static safety factor, and the relationship between the earthquake acceleration coefficient and the ratio of danymic safety factor to static safety factor on the condition of different rock mass.

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