scholarly journals Modelling of an Esaki Tunnel Diode in a Circuit Simulator

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Nikhil M. Kriplani ◽  
Stephen Bowyer ◽  
Jennifer Huckaby ◽  
Michael B. Steer
Keyword(s):  
Mathematical Model ◽  
Intermediate State ◽  
Tunnel Diode ◽  
Nonlinear Characteristic ◽  
Nonlinear Characteristics ◽  
Circuit Simulator ◽  
Strongly Nonlinear ◽  
State Variable

A method for circuit-level modelling a physically realistic Esaki tunnel diode model is presented. A paramaterisation technique that transforms the strongly nonlinear characteristic of a tunnel diode into two relatively modest nonlinear characteristics is demonstrated. The introduction of an intermediate state variable results in a physically realistic mathematical model that is not only moderately nonlinear and therefore robust, but also single-valued.

scholarly journals SIMULATION OF TRUCKING MODE CARS WITH A COMBINED ELASTIC ELEMENT IN THE REAR AXLE SUSPENSION

2021 ◽  
Vol 4 (4) ◽  
pp. 114-119
Author(s):  
Vladimir Pryadkin ◽  
Aleksandr Zavyalov
Keyword(s):  
Mathematical Model ◽  
Numerical Experiment ◽  
Elastic Element ◽  
Rear Axle ◽  
Nonlinear Characteristic ◽  
Nonlinear Characteristics ◽  
The Mathematical Model ◽  
Elastic Elements

The article analyzes elastic elements with a nonlinear characteristic. To improve the smoothness of a truck, a combined elastic element is proposed, including a semi-eleptic spring and an air cylinder, for installation in the rear axle suspension of a car. In order to assess the effect of a combined elastic element with a nonlinear characteristic on the smoothness of the ride, a mathematical model has been developed. The mathematical model allows for a numerical experiment taking into account the nature of the interaction of tires with unevenness of the roadway and the nonlinear characteristics of the combined elastic element.

scholarly journals Experimental evaluation of a vibro-impact model for two adjacent shear-building structures

2018 ◽  
Vol 211 ◽  
pp. 03004
Author(s):  
Marcus Varanis ◽  
Arthur Mereles ◽  
Anderson Silva ◽  
José Balthazar ◽  
Ângelo Tusset ◽  
...  
Keyword(s):  
Beam Theory ◽  
Rotor Blades ◽  
Contact Theory ◽  
Building Structures ◽  
Impact Model ◽  
Nonlinear Characteristics ◽  
Strongly Nonlinear ◽  
Shear Building ◽  
The Impact ◽  
Euler Bernoulli Beam

The vibro-impact phenomenon is found in many engineering applications, from impact of floating ice with ships to rubbing between the stator structure and rotor blades in turbomachinery, and in most cases it is important to know the implication of this phenomenon in the mechanical system. This is often done by proposing vibro-impact models for describing the behavior of the system when subjected to periodically impacts. However, this modelling may be challenging due to the strongly nonlinear characteristics of the impact phenomenon. Therefore, this paper presents a vibro-impact model of two shearbuilding structures positioned side by side, where one of them is driven by an unbalanced DC motor. The structures were modeled using the Euler-Bernoulli beam theory and the contact was modeled based on the Hertz contact theory. In order to validate the model their responses were compared with experimental signals.

Discrete Preisach Model of a Shape Memory Alloy Actuator

2016 ◽  
Vol 248 ◽  
pp. 227-234
Author(s):  
Waldemar Rączka ◽  
Jarosław Konieczny ◽  
Marek Sibielak ◽  
Janusz Kowal
Keyword(s):  
Mathematical Model ◽  
Shape Memory Alloy ◽  
Parameter Identification ◽  
Shape Memory ◽  
Preisach Model ◽  
Discrete Form ◽  
Nonlinear Characteristics ◽  
Shape Memory Alloy Actuator ◽  
Sma Actuator ◽  
Identification Model

Shape Memory Alloy is a material used to designing actuators. These actuators have many advantages. They are light, strong and silent. They are building in laboratory and tested because beside advantages they have disadvantages too. SMA actuators have nonlinear characteristics with hysteresis loop.In the first part of the paper Shape Memory Alloys are shortly described. Next mathematical model was formulated. In the paper the Preisach model was developed. Discrete form of the model was considered and implemented. After parameter identification model was implemented in LabView. Tests of the model were conducted and results were worked. Obtained characteristics of the SMA actuator are shown in the paper. At the end of the paper the conclusions were formulated.

scholarly journals Chaos Predictability in a Chemical Reactor

2020 ◽  
Vol 30 (11) ◽  
pp. 2050221
Author(s):  
Marek Berezowski
Keyword(s):  
Mathematical Model ◽  
Chemical Reactor ◽  
Transient Chaos ◽  
Distant Future ◽  
State Variable ◽  
First Case ◽  
Start Up ◽  
System Temperature ◽  
Intermittent Chaos ◽  
The Mathematical Model

The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor.

Longitudinal Instability in Braked Landing Gear

1981 ◽  
Vol 103 (3) ◽  
pp. 259-265 ◽  
Author(s):  
R. R. Allen ◽  
R. C. O’Massey
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Analytical Methods ◽  
Design Guidelines ◽  
Landing Gear ◽  
Nonlinear Mathematical Model ◽  
Nonlinear Characteristics ◽  
Aircraft Landing ◽  
Design Variables ◽  
Aircraft Landing Gear

An instability in the form of a self-excited, bounded longitudinal oscillation may occur in aircraft landing gear when one or more wheels lock due to excessive braking. The instability usually appears at ground speeds below 40 knots (20 m/s) and results from interaction between structural elasticity and the nonlinear characteristics of tire-runway friction. A nonlinear mathematical model is developed to study the dynamics of this divergence in a braked, dual tire landing gear. Analytical methods are presented to determine critical ground speeds in terms of runway friction characteristics and to predict the amplitude of steady-state oscillations. The effect of design variables on longitudinal stability is evaluated and design guidelines are presented which insure reduction of the severity of this divergent dynamic behavior.

scholarly journals FAMILIES OF SCROLL GRID ATTRACTORS

2002 ◽  
Vol 12 (01) ◽  
pp. 23-41 ◽  
Author(s):  
MÜŞTAK E. YALÇIN ◽  
JOHAN A. K. SUYKENS ◽  
JOOS VANDEWALLE ◽  
SERDAR ÖZOĞUZ
Keyword(s):  
State Space ◽  
Equilibrium Points ◽  
Strange Attractors ◽  
Current Feedback ◽  
Nonlinear Characteristics ◽  
State Variable ◽  
New Family ◽  
2D And 3D

In this paper a new family of scroll grid attractors is presented. These families are classified into three called 1D-, 2D- and 3D-grid scroll attractors depending on the location of the equilibrium points in state space. The scrolls generated from 1D-, 2D- and 3D-grid scroll attractors are located around the equilibrium points on a line, on a plane or in 3D, respectively. Due to the generalization of the nonlinear characteristics, it is possible to increase the number of scrolls in all state variable directions. A number of strange attractors from the scroll grid attractor families are presented. They have been experimentally verified using current feedback opamps. Also Lur'e representations are given for the scroll grid attractor families.

scholarly journals Математична модель антени з нелінійними характеристиками для розрахунку елект-ромагнітного поля у зоні Френеля

2021 ◽  
pp. 46-58
Author(s):  
Дмитро Вячеславович Грецьких ◽  
Василь Олександрович Алєксєєв ◽  
Андрій Володимирович Гомозов ◽  
Віктор Олександрович Катрич ◽  
Михайло Васильович Нестеренко
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Compatibility ◽  
Phase Distribution ◽  
Mutual Influence ◽  
Fresnel Zone ◽  
Nonlinear Effects ◽  
Arbitrary Field ◽  
Mathematical Methods ◽  
Nonlinear Characteristics ◽  
Transmitting Antenna

The paper presents a mathematical model of radio-electronic systems (RES), which include antennas and their excitation paths with nonlinear characteristics. The model provides acceptable accuracy of RES quality indicator analysis and electromagnetic compatibility (EMC) for further practical design. General purpose: the development of a mathematical model of a transmitting multi-input radiating structure with nonlinear characteristics under the Fresnel zone. Objective: choice justification of a structural schema of a radiating multi-input system with a radiator that has a distributed nonlinear surface impedance; obtaining the nonlinear integral equations (NIE) related to the current density for radiators with distributed nonlinearity, excited by an arbitrary field distribution for solving the general analysis problem; obtaining a ratio for calculating focused electromagnetic fields (EMF) created by multi-input radiating structures with nonlinear characteristics in the Fresnel zone. The methods used in the paper are mathematical methods of electrodynamics and antennas theory with nonlinear elements (ANE), theory of microwave circuits, and multipoles. The following results were obtained. An electrodynamics approach is proposed to analyze the entire set of nonlinear effects arising in transmitting multi-input radiating structures with nonlinear characteristics. It allows considering the mutual influence of the transmitting and receiving antennas with nonlinear characteristics in the system itself and the electrodynamics interaction of the transmitting antenna with nonlinear characteristics with RES for other purposes. Component equations (NIE) of multi-input radiating structures that establish the relationship of amplitude-phase distribution at the inputs of radiators with distributed nonlinearity and amplitude-phase distribution on their surfaces are obtained. A mathematical model of multi-input radiator structures with nonlinear characteristics in the Fresnel zone for analysis purposes has been produced. Conclusions. The scientific novelty of the obtained results is as follows: a generalized theory of transmitting antennas of arbitrary configuration with nonlinear characteristics in the Fresnel zone, which makes it possible to analyze the characteristics of these antennas considering the positive and negative (beneficial and adverse) nonlinear effects that arise in them.

scholarly journals A Novel Voltage-Controlled Tri-Valued Memristor and Its Application in Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xiaoyuan Wang ◽  
Xue Zhang ◽  
Meng Gao
Keyword(s):  
Mathematical Model ◽  
Nonlinear Systems ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Chaotic Systems ◽  
Nonlinear Element ◽  
Nonlinear Characteristics ◽  
Nanometer Size ◽  
New Chaotic System

Memristor is a kind of passive nonlinear element, which is widely used in nonlinear systems, especially chaotic systems, because of its nanometer size, nonvolatile property, and good nonlinear characteristics. Compared with general chaotic systems, chaotic systems based on memristors have richer dynamic characteristics. However, the current research mainly focuses on the binary and continuous chaotic systems based on memristors, and studies on the tri-valued and multi-valued memristor chaotic systems are relative scarce. For this reason, a mathematical model of tri-valued memristor is proposed, and the circuit characteristics of the model are studied. Furthermore, based on this model, a new chaotic system is designed and analyzed. This innovation enriches the types of chaotic systems and lays the foundation for the application of tri-valued and multi-valued memristors in nonlinear systems.

Experimental Bifurcation Diagram of Furuta Pendulum

2018 ◽  
Author(s):  
Mate B. Vizi ◽  
Gabor Stepan
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Coulomb Friction ◽  
Control Strategies ◽  
Strongly Nonlinear ◽  
Nonlinear Mechanical ◽  
Two Degree Of Freedom ◽  
Experimental Rig ◽  
Stability Results ◽  
Mechanical Phenomena

The Furuta pendulum is a two degree of freedom mechanical system that serves as an excellent and simple device to check control strategies applied for strongly nonlinear mechanical structures. Stability results related to certain stationary motions of the Furuta pendulum are compared to experimental observations, and conclusions are obtained regarding some essential mechanical phenomena that are present in the experimental rig, but still not properly described in the standard mathematical model of the pendulum. The results call the attention for the importance of the identification of the Coulomb friction in the structure, which effect the control strategies to be implemented.

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