Chaos in Structural Mechanics

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.

Contenu

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.