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Deterministic Chaos In One Dimensional Continuous Systems (Hardcover)
Loot Price: R5,343
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Deterministic Chaos In One Dimensional Continuous Systems (Hardcover)
Series: World Scientific Series on Nonlinear Science Series A, 90
Expected to ship within 12 - 17 working days
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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.
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