000 03619nam a22005055i 4500
001 978-3-642-12799-1
003 DE-He213
005 20140220084536.0
007 cr nn 008mamaa
008 100509s2010 gw | s |||| 0|eng d
020 _a9783642127991
_9978-3-642-12799-1
024 7 _a10.1007/978-3-642-12799-1
_2doi
050 4 _aTA355
050 4 _aTA352-356
072 7 _aTGMD4
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI018000
_2bisacsh
082 0 4 _a620
_223
100 1 _aPilipchuk, Valery N.
_eauthor.
245 1 0 _aNonlinear Dynamics
_h[electronic resource] :
_bBetween Linear and Impact Limits /
_cby Valery N. Pilipchuk.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _a360p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Applied and Computational Mechanics,
_x1613-7736 ;
_v52
505 0 _aSmooth 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.
520 _aNonlinear 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.
650 0 _aEngineering.
650 0 _aPhysics.
650 0 _aMechanics.
650 0 _aVibration.
650 1 4 _aEngineering.
650 2 4 _aVibration, Dynamical Systems, Control.
650 2 4 _aComplexity.
650 2 4 _aMechanics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642127984
830 0 _aLecture Notes in Applied and Computational Mechanics,
_x1613-7736 ;
_v52
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-12799-1
912 _aZDB-2-ENG
999 _c112139
_d112139