Deterministic Chaos in One Dimensional Continuous Systems: 90 (World Scientific Series on Nonlinear Science Series A) - Hardcover

Book 9 of 17: World Scientific Series On Nonlinear Science Series A

Jan Awrejcewicz; Vadim A Krysko; Irina V Papkova; Anton V Krysko

 
9789814719698: Deterministic Chaos in One Dimensional Continuous Systems: 90 (World Scientific Series on Nonlinear Science Series A)
Hardcover
ISBN 10: 9814719692 ISBN 13: 9789814719698
Publisher: World Scientific Publishing Company, 2016

Synopsis

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 EulerBernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elasticplastic 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.

"synopsis" may belong to another edition of this title.

Publisher
World Scientific Publishing Company
Publication date
2016
Language
English
ISBN 10 
9814719692
ISBN 13 
9789814719698
Binding
Hardcover
Number of pages
576