Generalized mathematical model of the multiple-mass dynamical system of a vibration machine

The article describes the methodology for the study of the dynamics of vibrating machines for surface processing of products by mathematical modeling, which is presented in four main stages. The first stage: analysis of classes of vibrating machines for surface treatment of products, choice of basic for solving the technological problem, project of a unified calculation scheme of the machine. The second stage: development of a nonlinear mathematical model for describing the dynamics of the vibration machine working body and its filling, development of elements of automated calculations of the machine. The third stage: the study of the influence of the parameters of the vibrating machine, product sets and tools (with their various combinations) on the factors of the intensity of products surface processing. The fourth stage: recommendations for choosing vibrating machine parameters and machining bodies that will maximize the processing performance of products with the selected intensity criterion. A mathematical model for describing the motion of a vibrating machine for surface treatment of articles by a set of unrelated bodies of small size is created. It has two unbalance units that generate oscillations of its working body and a spring suspension-mounting of the working chamber (container). The model is parametric and nonlinear, incorporating key dynamic, kinematic and geometric parameters of the vibrating machine in symbolic format. It is constructed by: descriptions of the plane-parallel movement of the mechanical system, the rotational motion of the material point and the body; second-order Lagrange equation; asymptotic (approximate) methods of nonlinear mechanics. With the help of the model it is possible: to describe the oscillatory movement of the working chamber (container) of the vibrating machine; to study the influence of the machine parameters on the efficiency of performance of the set technological task, the conditions of occurrence of non-stationary modes of operation of the vibrating machine and the ways of their regulation.

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Fuzzy Approximation by a Novel Levenberg–Marquardt Method for Two-Degree-of-Freedom Hypersonic Flutter Model

Journal of Vibration and Acoustics ◽

10.1115/1.4027524 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 2

Author(s):

Y. H. Wang ◽

L. Zhu ◽

Q. X. Wu ◽

C. S. Jiang

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Approximation Scheme ◽

Degree Of Freedom ◽

Human Knowledge ◽

Marquardt Method ◽

Fuzzy Approximation ◽

Levenberg Marquardt ◽

Modification Factor ◽

Two Degree Of Freedom

The two-degree-of-freedom (2DOF) hypersonic flutter dynamical system has strong aeroelastic nonlinearities, and it is very difficult to obtain a more precise mathematical model. By considering varying learning rate and σ-modification factor, a novel Levenberg– Marquardt (L–M) method is proposed, based on which, an online fuzzy approximation scheme for 2DOF hypersonic flutter model is established without any human knowledge. Compared with the standard L–M method, the proposed method can obtain faster converge speed and avoid parameter drift. Numerical simulations approve the advantages of the proposed scheme.

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The synchronization of coupled stochastic systems driven by symmetric α-stable process and Brownian motion

Filomat ◽

10.2298/fil1806219a ◽

2018 ◽

Vol 32 (6) ◽

pp. 2219-2245

Author(s):

Shahad Al-Azzawi ◽

Jicheng Liu ◽

Xianming Liu

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Brownian Motion ◽

Gaussian Noise ◽

Stochastic Systems ◽

Stable Process ◽

Symmetric Stable Process ◽

And Brownian Motion ◽

Coupled Dynamical System ◽

Non Gaussian

The synchronization of stochastic differential equations (SDEs) driven by symmetric ?-stable process and Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, another one is driven by non- Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.

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New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

Mathematical Problems in Engineering ◽

10.1155/2020/2640629 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18

Author(s):

Jiri Petrzela

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

High Frequency ◽

Piecewise Linear ◽

Chaotic Oscillator ◽

Chaotic Dynamical System ◽

Transient Behaviour ◽

Local Polynomial ◽

Good Accordance ◽

Class C

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.

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STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL

Glasgow Mathematical Journal ◽

10.1017/s0017089508004485 ◽

2009 ◽

Vol 51 (1) ◽

pp. 1-17 ◽

Cited By ~ 4

Author(s):

LE HUY CHUAN ◽

TOHRU TSUJIKAWA ◽

ATSUSHI YAGI

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Infinite Number ◽

Kinematic Model ◽

Stationary Solutions ◽

Cross Diffusion ◽

Stability And Instability ◽

Math Biol ◽

Forest Boundary ◽

Boundary Dynamics

AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.

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Autopoiesis and Cognition

Artificial Life ◽

10.1162/1064546041255557 ◽

2004 ◽

Vol 10 (3) ◽

pp. 327-345 ◽

Cited By ~ 97

Author(s):

Paul Bourgine ◽

John Stewart

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Boundary Conditions ◽

Living System ◽

Random Dynamical System ◽

Sensory Inputs ◽

Autopoietic System ◽

Definition Of

This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: “An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain.” We propose a modified definition of autopoiesis: “An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network.” We also propose a definition of cognition: “A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint.” It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: “A system that is both autopoietic and cognitive is a living system.”

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Analysis of a Model for Coronavirus Spread

Mathematics ◽

10.3390/math8050820 ◽

2020 ◽

Vol 8 (5) ◽

pp. 820 ◽

Cited By ~ 1

Author(s):

Youcef Belgaid ◽

Mohamed Helal ◽

Ezio Venturino

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Global Stability ◽

Basic Reproduction Number ◽

Local Stability ◽

Reproduction Number ◽

Early Stage ◽

Asymptomatic Individuals ◽

Restrictive Measures ◽

Disease Free

The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

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