Oscillators and Oscillatory Signals from Smooth to Discontinuous

This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford's algebras, give rise to the essentially nonlinear quasi-impact methodology based on the idea of non-smooth temporal substitutions. In the years since Nonlinear Dynamics: Between Linear and Impact Limits, the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.

Presents an improved picture of non-smooth temporal transformations using impact systems as a basis for various analyses Includes new examples of recent applications for problems in energy absorption/harvesting and resonance interactions Describes a complementarity principle with a range of applications from smooth to discontinuous oscillatory processes

Auteur

Dr. Valery N. Pilipchuk is Associate professor of Mechanical Engineering at Wayne State University, Detroit, Michigan, USA.

Contenu

Introduction.- Smooth Oscillating Processes.- Nonsmooth Processes as Asymptotic Limits.- Nonsmooth Temporal Transformations (NSTT).- Sawtooth Power Series.- NSTT for Linear and Piecewise-Linear Systems.- Periodic and Transient Nonlinear Dynamics under Discontinuous Loading.- Strongly Nonlinear Vibrations.- Strongly Nonlinear Waves.- Impact Modes and Parameter Variations.- Principal Trajectories of Forced Vibrations.- NSTT and Shooting Method for Periodic Motions.- Essentially Non-periodic Processes.- Spatially-Oscillating Structures.