Deterministic chaos in one dimensional continuous systems

by Awrejcewicz, J., (Jan)

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Title Statements

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

Summary

"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."--Provided by publisher

Edition Statements

Publication Date:©2016.

Publication Statements

Publisher(s):World Scientific
Place of Publication:New Jersey
Language:eng
Publication Date:©2016.

The Physical Object

Description:1 online resource

Edition Identifiers

ISBN:9789814719704, 9814719706
oclc:ocn946058869
LC Classification:TA342
Dewey Decimal:624.1/7011857

Preface; 1. Bifurcational and Chaotic Dynamics of Simple Structural Members; 1.1 Beams; 1.2 Plates; 1.3 Panels; 1.4 Shells; 2. Introduction to Fractal Dynamics; 2.1 Cantor Set and Cantor Dust; 2.2 Koch Snowflake; 2.3 1D Maps; 2.4 Sharkovsky's Theorem; 2.5 Julia Set; 2.6 Mandelbrot's Set; 3. Introduction to Chaos and Wavelets; 3.1 Routes to Chaos; 3.1.1 Introduction; 3.1.2 On chaos definitions; 3.1.3 Landau-Hopf (LH) scenario; 3.1.4 Ruelle-Takens-Newhouse (RTN) scenario; 3.1.5 Feigenbaum scenario (F); 3.1.6 Pomeau-Manneville (PM) scenario; 3.1.7 Synchronization of chaos.

3.2 Quantifying Chaotic Dynamics3.2.1 Introduction; 3.2.2 Fourier Transformation (FT); 3.2.3 Types of Poincare maps; 3.2.4 Lyapunov characteristic exponents; 3.2.5 Melnikov's method; 3.2.6 Wavelet analysis; 3.2.6.1 Introduction; 3.2.7 Basic functions; 3.2.8 Properties and advantages of wavelets; 4. Simple Chaotic Models; 4.1 Introduction; 4.2 Autonomous Systems; 4.2.1 Lorenz mathematical model (LMM); 4.2.2 Rossler mathematical model (RMM); 4.2.3 Modified generator with inertial nonlinearity (MGIN); 4.2.4 Chua circuit; 4.2.5 Conservative and other systems; 4.3 Non-Autonomous Systems.

5. Discrete and Continuous Dis…

Subjects

building materials Buildings -- Vibration Construction -- Matériaux Construction Materials Constructions -- Vibrations Engineering mathematics Mathématiques de l'ingénieur Résistance des matériaux -- Mathématiqu… Strength of materials -- Mathematics TECHNOLOGY & ENGINEERING -- Civil