Chaos in Structural Mechanics: (Understanding Complex Systems)

This monograph is devoted to construction of novel theoretical approaches of m- eling non-homogeneous structural members as well as to development of new and economically ef?cient (simultaneously keeping the required high engineering ac- racy)computationalalgorithmsofnonlineardynamics(statics)ofstronglynonlinear behavior of either purely continuous mechanical objects (beams, plates, shells) or hybrid continuous/lumped interacting mechanical systems. In general, the results presented in this monograph cannot be found in the - isting literature even with the published papers of the authors and their coauthors. We take a challenging and originally developed approach based on the integrated mathematical-numerical treatment of various continuous and lumped/continuous mechanical structural members, putting emphasis on mathematical and physical modeling as well as on the carefully prepared and applied novel numerical - gorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the ?elds of bifurcation, chaos, control, and s- bility of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs),and may have a positive impact on interdisciplinary ? elds of n- linear mechanics, physics, and applied mathematics. We show, for the ?rst time in a book, the complexity and fascinating nonlinear behavior of continual mechanical objects, which cannot be found in widely reported bifurcational and chaotic dyn- ics of lumped mechanical systems, i. e. , those governed by nonlinear ODEs.

Table of Contents:
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.

Review :
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)