Awrejcewicz J. Chaos in Structural Mechanics 2008 Rep

Textbook in PDF format

This monograph is devoted to construction of novel theoretical approaches of modeling non-homogeneous structural members as well as to development of new and economically efficient (simultaneously keeping the required high engineering accuracy) computational algorithms of nonlinear dynamics (statics) of strongly nonlinear 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 existing 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 algorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the fields of bifurcation, chaos, control, and stability of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs), and may have a positive impact on interdisciplinary fields of nonlinear mechanics, physics, and applied mathematics. We show, for the first time in a book, the complexity and fascinating nonlinear behavior of continual mechanical objects, which cannot be found in widely reported bifurcational and chaotic dynamics of lumped mechanical systems, i.e., those governed by nonlinear ODEs