scholarly journals Synchronization and Stability of Two Unbalanced Rotors with Fast Antirotation considering Energy Balance

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yongjun Hou ◽  
Pan Fang
Keyword(s):  
Energy Balance ◽  
Theoretical Analysis ◽  
Differential Equations ◽  
Computer Simulations ◽  
Stability Criterion ◽  
Induction Motors ◽  
Energy Balance Method ◽  
Analytical Analysis ◽  
The Stability ◽  
Vibrating Systems

We consider synchronization and stability of two unbalanced rotors reversely and fast excited by induction motors fixed on an oscillating body. We explore the energy balance of the system and show how the energy is transferred between the rotors via the oscillating body allowing the implementation of the synchronization of the two rotors. An approximate analytical analysis, energy balance method, allows deriving the synchronization condition, and the stability criterion of the synchronization is deduce by disturbance differential equations. Later, to prove the correctness of the theoretical analysis, many features of the vibrating system are computed and discussed by computer simulations. The proposed method may be useful for analyzing and understanding the mechanism of synchronization, stability, and energy balance of similar fast rotation rotors excited by induction motors in vibrating systems.

scholarly journals Synchronization and Stability of Elasticity Coupling Two Homodromy Rotors in a Vibration System

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Yongjun Hou ◽  
Mingjun Du ◽  
Pan Fang ◽  
Yuwen Wang ◽  
Liping Zhang
Keyword(s):  
Theoretical Analysis ◽  
Computer Simulations ◽  
Stability Criterion ◽  
Mechanical Model ◽  
Induction Motors ◽  
Simplified Model ◽  
Vibration System ◽  
Analysis Method ◽  
Lagrange Equations ◽  
Synchronous State

The mechanical model of an elasticity coupling 1-DOF system is proposed to implement synchronization; the simplified model is composed of a rigid body, two induction motors, and a connecting spring. Based on the Lagrange equations, the dynamic equation of the system is established. Moreover, a typical analysis method, the Poincare method, is applied to study the synchronization characteristics, and the balanced equations and stability criterion of the system are obtained. Obviously, it can be seen that many parameters affect the synchronous state of the system, especially the stiffness of the support spring, the stiffness of the connecting spring, and the installation location of the motors. Meanwhile, choose a suitable stiffness of the connecting spring (k), which would play a significant role in engineering. Finally, computer simulations are used to verify the correctness of the theoretical analysis.

Dynamics of n Coupled Double Pendula Suspended to the Moving Beam

2014 ◽  
Vol 14 (08) ◽  
pp. 1440028 ◽  
Author(s):  
Piotr Koluda ◽  
Piotr Brzeski ◽  
Przemyslaw Perlikowski
Keyword(s):  
Energy Balance ◽  
Periodic Solutions ◽  
Natural Frequency ◽  
Balance Method ◽  
Energy Balance Method ◽  
Analytical Analysis ◽  
Stability Properties ◽  
Moving Beam ◽  
The Stability

We consider the synchronization of n self-excited double pendula. For such pendula hanging on the same beam, different synchronous configurations can be obtained (in-phase and anti-phase states). An approximate analytical analysis allows to derive the synchronization condition and explain the observed types of synchronization for any number of coupled double pendula. The energy balance method is used to show how the energy between the pendula is transferred via the oscillating beam allowing their synchronization. We compute periodic solutions for n = 2, 3, 4, 5 coupled double pendula, based on analytical predictions. For all obtained periodic solutions, we investigate how the stability properties change with the varying natural frequency of the beam.

scholarly journals Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Supassorn Aekthong ◽  
Chontita Rattanakul
Keyword(s):  
Metabolic Disease ◽  
Parathyroid Hormone ◽  
Theoretical Analysis ◽  
Bone Formation ◽  
Postmenopausal Women ◽  
Computer Simulations ◽  
Impulsive Differential Equations ◽  
System Parameters ◽  
Theoretical Predictions ◽  
The Stability

Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.

scholarly journals FRACTAL DIMENSION OF FRACTIONAL BROWNIAN MOTION BASED ON RANDOM SETS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040020
Author(s):  
RUISHUAI CHAI
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Stability Criterion ◽  
Random Sets ◽  
Stochastic Comparison ◽  
Calculation Methods ◽  
The Stability

The fractal dimension of fractional Brownian motion can effectively describe random sets, reflecting the regularity implicit in complex random sets. Data mining algorithms based on fractal theory usually follow the calculation of the fractal dimension of fractional Brownian motion. However, the existing fractal dimension calculation methods of fractal Brownian motion have high time complexity and space complexity, which greatly reduces the efficiency of the algorithm and makes it difficult for the algorithm to adapt to high-speed and massive data flow environments. Therefore, several existing fractal dimension calculation methods of fractional Brownian motion are summarized and analyzed, and a random method is proposed, which uses a fixed memory space to quickly estimate the associated dimension of the data stream. Finally, a comparison experiment with existing algorithms proves the effectiveness of this random algorithm. Second, in the sense of two different measures, based on the principle of stochastic comparison, the stability of the stochastic fuzzy differential equations is derived using the stability of the comparison equations, and the practical stability criterion of two measures according to probability is obtained. Then, the stochastic fuzzy differential equations are discussed. The definition of stochastic exponential stability is given and the stochastic exponential stability criterion is proved.

A THEORETICAL ANALYSIS OF A PERCOLATION MODEL

2012 ◽  
Vol 26 (26) ◽  
pp. 1250169
Author(s):  
SENCER TANERI
Keyword(s):  
Partial Differential Equations ◽  
Theoretical Analysis ◽  
Differential Equations ◽  
Random Environment ◽  
String Model ◽  
Percolation Model ◽  
Partial Differential ◽  
Analytical Analysis ◽  
Invading Species ◽  
Published Research

This is an analytical analysis of a previously published research for a percolation simulation. In that research the effect of mutations on adaptability was investigated in a bit-string model of invading species in a random environment. However, analytical analysis was missing which will be the topic here. The Hausdorff dimensions are calculated for the fractals and the conditions on invasion are analyzed analytically by manipulation of partial differential equations. Thus, various conclusions may be reached without having to run long simulations.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

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