Chaos in Structural Mechanics: Understanding Complex Systems

Theory of Non-homogeneous Shells.- Static Instability of Rectangular Plates.- Vibrations of Rectangular Shells.- Dynamic Loss of Stability of Rectangular Shells.- Stability of a Closed Cylindrical Shell Subjected to an Axially Non-symmetrical Load.- Composite Shells.- Interaction of Elastic Shells and a Moving Body.- Chaotic Vibrations of Sectoria Shells.- Scenarios of Transition from Harmonic to Chaotic Motion.- Dynamics of Closed Flexible Cylindrical Shells.- Controlling Time-Spatial Chaos of Cylindrical Shells.- Chaotic Vibrations of Flexible Rectangular Shells.- Determination of Three-layered Non-linear Uncoupled Beam Dynamics with Constraints.- Bifurcation and Chaos of Dissipative Non-linear Mechanical Systems of Multi-layer Sandwich Beams.- Nonlinear Vibrations of the Euler-Bernoulli Beam Subjected to Transversal Load and Impact Actions.

From the reviews:
"This monograph is devoted to nonlinear oscillations of homogeneous and composite beams, plates and shells. … The monograph is well written and well organized. Strength of the book is the quantity and variety of example of nonlinear systems. This book is accessible to readers with a fundamental knowledge of ordinary and partial differential equations and linear and nonlinear theory of plates and shells. The book can be highly recommended to experts in mechanics of thin-walled structures." (Igor Andrianov, Zentralblatt MATH, Vol. 1144, 2008)
"The monograph under review is devoted to modeling nonlinear and non-homogeneous structural elements as well as to developing efficient computational algorithms for investigating the strongly nonlinear behavior of either continuous or hybrid continuous/lumped interacting mechanical systems. … The complexity of nonlinear continuous mechanical systems revealed, together with the mathematical and numerical techniques developed for the analysis of such systems, is the main value of this monograph." (Minvydas Ragulskis, Mathematical Reviews, Issue 2009 g)

This volume introduces and reviews novel theoretical approaches to modeling strongly nonlinear behaviour of either individual or interacting structural mechanical units such as beams, plates and shells or composite systems thereof.
The approach draws upon the well-established fields of bifurcation theory and chaos and emphasizes the notion of control and stability of objects and systems the evolution of which is governed by nonlinear ordinary and partial differential equations. Computational methods, in particular the Bubnov-Galerkin method, are thus described in detail.

Dr. Jan Awrejcewicz is the Chairperson for Science of the Faculty of Mechanical Engineering of the Technical University of Lodz, Poland. He has authored or coauthored over 410 publications in scientific journals and conference proceedings, 28 monographs, 2 textbooks, 2 edited volumes, 9 conferences proceedings, 8 journal special issues, and 145 other books, commentaries, or unpublished reports. He has also delivered 80 lectures during international conferences and gave 32 invited seminars at renowned universities worldwide. He is a contributer to 45 different journals and to 100 conferences. His papers and research cover various disciplines of mechanics, biomechanics, mathematics, physics and computer oriented sciences. He has authored and coauthered several books previously published by Springer. Dr. Yuriy Pyryev is an Assistant Professor at the Technical University of Lodz, Poland. He is a member of the Committee of Fracture Mechanics of Ukraine, and a member of the Dynamical System of the Committee of Mechanics of PAS. He has authored or coauthored 4 monographs, 60 journal papers and chapters in books, 29 proceedings from international or national conferences, and 31 brief communications and reports. His research includes coupled thermodynamics, nonlinear contact problems, and nonlinear mechanics.