Details

A Smooth and Discontinuous Oscillator

Theory, Methodology and Applications
Springer Tracts in Mechanical Engineering

von: Qingjie Cao, Alain Léger
106,99 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	27.09.2016
ISBN/EAN:	9783662530948
Sprache:	englisch

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Beschreibungen

Titelbeschreibung

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Inhaltsverzeichnis

Background: Nonlinear Systems.- An Smooth and Discontinuous (SD) Oscillator.- Bifurcation Behaviour.- Periodic Motions of the Perturbed SD Oscillator.- The Exact Solutions.- Chaotic Motions of the SD Oscillator.- Experimental Investigation of the SD Oscillator.- Applications in Structural Dynamics.- Applications in Engineering Isolation.- Challenges and the Open Problems.

Back cover copy

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest.  Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Sonderbeitrag

Clearly illustrates the nature of nonlinear phenomena by introducing a real mechanical model, the SD oscillator, which offers an effectives model for describing geometrical nonlinearitiesOpens a new perspective on the inner workings of the real world through this simple actual mechanical model without any truncationOffers an opportunity to broaden our conventional nonlinear understanding to the unconventional nonlinear systems with applications in engineering and interdisciplinary areasIncludes supplementary material: sn.pub/extras

Verkaufsargumente

Clearly illustrates the nature of nonlinear phenomena by introducing a real mechanical model, the SD oscillator, which offers an effectives model for describing geometrical nonlinearitiesOpens a new perspective on the inner workings of the real world through this simple actual mechanical model without any truncationOffers an opportunity to broaden our conventional nonlinear understanding to the unconventional nonlinear systems with applications in engineering and interdisciplinary areas