LEADER 03702nam 2200553 450 001 9910254338203321 005 20210311145132.0 010 $a3-662-53094-5 024 7 $a10.1007/978-3-662-53094-8 035 $a(CKB)3710000000872795 035 $a(DE-He213)978-3-662-53094-8 035 $a(MiAaPQ)EBC5577227 035 $a(MiAaPQ)EBC6381392 035 $a(Au-PeEL)EBL5577227 035 $a(OCoLC)1066180830 035 $a(PPN)195508092 035 $a(EXLCZ)993710000000872795 100 $a20210311d2017 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA smooth and discontinuous oscillator $etheory, methodology and applications /$fQingjie Cao; Alain Le?ger 205 $a1st ed. 2017. 210 1$aBerlin, Germany :$cSpringer,$d[2017] 210 4$dİ2017 215 $a1 online resource (XIX, 262 p. 131 illus., 54 illus. in color.) 225 1 $aSpringer Tracts in Mechanical Engineering,$x2195-9862 300 $aIncludes index. 311 $a3-662-53092-9 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aBackground: 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. 330 $aThis is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and th e perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences. 410 0$aSpringer Tracts in Mechanical Engineering,$x2195-9862 606 $aChaotic behavior in systems 606 $aNonlinear theories 615 0$aChaotic behavior in systems. 615 0$aNonlinear theories. 676 $a003.857 700 $aCao$b Qingjie$0996187 702 $aLe?ger$b A$g(Alain),$f1943- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254338203321 996 $aA smooth and discontinuous oscillator$92283018 997 $aUNINA