Mathematical Models of Non-Linear Mechanical and Electrical Systems and Their Qualitative Behavior

1991 ◽  
Author(s):  
Mark Levi
Keyword(s):  
Mathematical Models ◽  
Qualitative Behavior ◽  
Electrical Systems ◽  
Non Linear

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

2021 ◽  
Vol 316 ◽  
pp. 936-941
Author(s):  
Natalya Ya. Golovina
Keyword(s):  
Mathematical Models ◽  
Strain Curve ◽  
Variational Model ◽  
Linear Deformation ◽  
Plastic Materials ◽  
Non Linear ◽  
Linear Sections ◽  
Elastic Plastic Materials ◽  
Deformation Section ◽  
St3sp Steel

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

Strange Attractors and Chaos in Nonlinear Mechanics

1983 ◽  
Vol 50 (4b) ◽  
pp. 1021-1032 ◽  
Author(s):  
P. J. Holmes ◽  
F. C. Moon
Keyword(s):  
Mathematical Models ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
Nonlinear Differential Equations ◽  
Homoclinic Orbits ◽  
Strange Attractors ◽  
Electrical Systems ◽  
Nonlinear Mechanical ◽  
Sensitive Dependence

We review several examples of nonlinear mechanical and electrical systems and related mathematical models that display chaotic dynamics or strange attractors. Some simple mathematical models — iterated piecewise linear mappings — are introduced to explain and illustrate the concepts of sensitive dependence on initial conditions and chaos. In particular, we describe the role of homoclinic orbits and the horseshoe map in the generation of chaos, and indicate how the existence of such features can be detected in specific nonlinear differential equations.

scholarly journals Wind Power Extraction Optimization by Dynamic Gain Scheduling Approximation Based on Non-Linear Functions for a WECS Based on a PMSG

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2028
Author(s):  
José Genaro González-Hernández ◽  
Rubén Salas-Cabrera
Keyword(s):  
Wind Speed ◽  
Mathematical Models ◽  
Synchronous Generator ◽  
Absolute Error ◽  
Gain Scheduling ◽  
Angular Speed ◽  
Linear Functions ◽  
Direct Drive ◽  
Power Extraction ◽  
Non Linear

Mathematical models and algorithms for maximizing power extraction have become an essential topic in renewable energies in the last years, especially in wind energy conversion systems. This study proposes maximum power point tracking using gain scheduling approximations for an emulated wind system in a direct-drive connection. Power extraction is obtained by controlling the duty cycle of a Multilevel Boost Converter, which directly varies the rotational speed of a permanent magnet synchronous generator directly coupled to a three-phase induction motor that emulates the wind turbine. The system’s complexity is linked to the inherent non-linearities associated with the diverse electrical, mechanical, and power electronic elements. In order to present a synthesized model without losing the system dynamic richness, several physical tests were made to obtain parameters for building several mathematical approaches, resulting in non-linear dynamic equations for the controller gains, which are dependant on wind speed. Thirty real operational wind speeds considering typical variations were used in several tests to demonstrate the mathematical models’ performance. Results among these gain scheduling approaches and a typical controller constant gains mathematical model were compared based on standard deviations, absolute error, and the time for reaching the optimum generator angular speed related to every wind speed.

scholarly journals ON INTERACTION OF A LIQUID FILM WITH AN OBSTACLE

2002 ◽  
Vol 7 (2) ◽  
pp. 327-342 ◽  
Author(s):  
A. Zemitis
Keyword(s):  
Liquid Film ◽  
Mathematical Models ◽  
Numerical Experiments ◽  
Impinging Jets ◽  
Numerical Results ◽  
Qualitative Behavior ◽  
Different Shapes ◽  
The Wire ◽  
The Difference

In this paper are discussed mathematical models for the liquid film generated by impinging jets. These models describe only the film shape under special assumptions about processes. Attention is stressed on the interaction of the liquid film with some obstacle. The idea is to generalize existing models and to investigate qualitative behavior of liquid film using numerical experiments. G.I. Taylor [Proc. R. Soc. London Ser. A 253, 313 (1959)] found that the liquid film generated by impinging jets is very sensitive to properties of the wire which was used as an obstacle. The aim of this presentation is to propose a modification of the Taylor's model, which allows to simulate the film shape in cases when the angle between jets is different from 180°. Numerical results obtained by discussed models give two different shapes of the liquid film similar as in Taylors experiments. These two shapes depend on the regime: either droplets are produced close to the obstacle or not. The difference between two regimes becomes larger if the angle between jets decreases. Existence of such two regimes can be very essential for some applications of impinging jets, if the generated liquid film can have a contact with obstacles.

The Testing Filtering and Majorized Algorithm of a Kind of Nonstationary Stochastic Transmission System in Intelligence Control

2014 ◽  
Vol 926-930 ◽  
pp. 3581-3584
Author(s):  
Xiao Nan Xiao
Keyword(s):  
Stochastic Process ◽  
Optimal Control ◽  
Mathematical Models ◽  
Incomplete Data ◽  
Transmission System ◽  
Linear Filtering ◽  
Optimal Coding ◽  
Non Linear ◽  
Intelligence Control ◽  
Nonstationary Stochastic Process

In intelligence control, applying the method of optimal non-linear filtering and majorized algorithm, this paper discusses the optimal control of a kind of incomplete data and continuous nonstationary stochastic process; yields two optimal control mathematical models in these two situations; illustrates how to establish the optimal coding and decoding of the nonstationary stochastic process; and provides an effective and reliable approach for the optimal control of such a process.

Modeling management decision making in the socially oriented business structures

2021 ◽  
Vol 96 (3) ◽  
pp. 78-86
Author(s):  
L. I. Kulakova ◽  
◽  
A. V. Polyanin ◽  
V. V. Tarnovskiy ◽  
◽  
...  
Keyword(s):  
Mathematical Models ◽  
Management Decision ◽  
Phase System ◽  
Management Decisions ◽  
Managerial Decision ◽  
Two Phase ◽  
Managerial Decisions ◽  
Non Linear ◽  
Management Decision Making ◽  
Business Structures

The article discusses the main economic and mathematical models used in making and implementing management decisions. It has been established that the beginning of making a managerial decision is determined by the nature of solution of managerial problem: creative and standard, implementation of a managerial decision is subordinate to the certainty of the result, that is, its probabilistic or deterministic outcome. The procedure and modeling of the process of making and implementing management decisions will be linear or non-linear. On this basis, the types of mathematical models for solving managerial problems are considered when making and implementing managerial decisions to optimize the chosen option. The author's model is proposed based on a two-phase system from the theory of queues with elements of nonlinear programming for making and implementing managerial decisions in socially oriented business structures. The model includes a combination of linear and non-linear programming. Since when conducting business, socially oriented entrepreneurial structures are aimed at obtaining two types of effects, both commercial and social.

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