Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book. First systematic description for the non smooth time transformations and related analytical and numerical algorithms Bridges the gap between linear and strongly nonlinear dynamics by showing how to switch the physical basis when approaching the area of severe (impact) nonlinearities Presents a unified physical basis for analyses of vibrations with essentially non-harmonic or discontinuous temporal shapes INDICE: Part 1 Introduction.- Part 2 Smooth Oscillating Processes.- Part 3Nonsmooth Processes as Asymptotic Limits.- Part 4 Nonsmooth Temporal Transformations (NSTT).- Part 5 Sawtooth Power Series.- Part 6 NSTT for Linear and Piecewise-Linear Systems.- Part 7 Periodic and Transient Nonlinear Dynamics underDiscontinuous Loading.- Part 8 Strongly Nonlinear Vibrations.- Part 9 Strongly Nonlinear Waves.- Part 10 Impact Modes and Parameter Variations.- Part 11 Principal Trajectories of Forced Vibrations.- Part 12 NSTT and Shooting Method for Periodic Motions.- Part 13 Essentially Non-periodic Processes.- Part 14 Spatially-Oscillating Structures
- ISBN: 978-3-642-12798-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 360
- Fecha Publicación: 30/05/2010
- Nº Volúmenes: 1
- Idioma: Inglés