Deterministic chaos in one dimensional continuous systems

Jan Awrejcewicz, Vadim A. Krysko, Irina V. Papkova, Anton V. Krysko

Research output: Book/ReportBook

27 Citations (Scopus)

Abstract

This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

Original languageEnglish
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages562
ISBN (Electronic)9789814719704
ISBN (Print)9789814719698
DOIs
Publication statusPublished - 1 May 2016

Fingerprint

Hyperchaos
Deterministic Chaos
One-dimensional System
Continuous System
Chaos Control
Bifurcation and Chaos
Civil Engineering
Nonlinear Phenomena
Euler-Bernoulli Beam
Timoshenko Beam
Nonlinear Vibration
Rectangular Plate
Infinite Dimensions
Elastic Deformation
Computational Analysis
Nonlinear Dynamical Systems
Chaotic Dynamics
Plastic Deformation
Inclined
Buckling

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Awrejcewicz, J., Krysko, V. A., Papkova, I. V., & Krysko, A. V. (2016). Deterministic chaos in one dimensional continuous systems. World Scientific Publishing Co. Pte Ltd. https://doi.org/10.1142/9775

Deterministic chaos in one dimensional continuous systems. / Awrejcewicz, Jan; Krysko, Vadim A.; Papkova, Irina V.; Krysko, Anton V.

World Scientific Publishing Co. Pte Ltd, 2016. 562 p.

Research output: Book/ReportBook

Awrejcewicz, J, Krysko, VA, Papkova, IV & Krysko, AV 2016, Deterministic chaos in one dimensional continuous systems. World Scientific Publishing Co. Pte Ltd. https://doi.org/10.1142/9775
Awrejcewicz J, Krysko VA, Papkova IV, Krysko AV. Deterministic chaos in one dimensional continuous systems. World Scientific Publishing Co. Pte Ltd, 2016. 562 p. https://doi.org/10.1142/9775
Awrejcewicz, Jan ; Krysko, Vadim A. ; Papkova, Irina V. ; Krysko, Anton V. / Deterministic chaos in one dimensional continuous systems. World Scientific Publishing Co. Pte Ltd, 2016. 562 p.
@book{7e0c7e9442be42be97fbe93130d171c1,
title = "Deterministic chaos in one dimensional continuous systems",
abstract = "This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.",
author = "Jan Awrejcewicz and Krysko, {Vadim A.} and Papkova, {Irina V.} and Krysko, {Anton V.}",
year = "2016",
month = "5",
day = "1",
doi = "10.1142/9775",
language = "English",
isbn = "9789814719698",
publisher = "World Scientific Publishing Co. Pte Ltd",
address = "Singapore",

}

TY - BOOK

T1 - Deterministic chaos in one dimensional continuous systems

AU - Awrejcewicz, Jan

AU - Krysko, Vadim A.

AU - Papkova, Irina V.

AU - Krysko, Anton V.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

AB - This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

UR - http://www.scopus.com/inward/record.url?scp=84985954225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84985954225&partnerID=8YFLogxK

U2 - 10.1142/9775

DO - 10.1142/9775

M3 - Book

AN - SCOPUS:84985954225

SN - 9789814719698

BT - Deterministic chaos in one dimensional continuous systems

PB - World Scientific Publishing Co. Pte Ltd

ER -