{"product_id":"9789814719711","title":"Deterministic Chaos In One Dimensional Continuous Systems","description":"\u003cp\u003eThis book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.\u003c\/p\u003e\u003cp\u003eBeginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.\u003c\/p\u003e\u003cp\u003eThe book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eBifurcational  and Chaotic Dynamics of Simple Structural Members:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eBeams\u003c\/li\u003e\n\u003cli\u003ePlates\u003c\/li\u003e\n\u003cli\u003ePanels\u003c\/li\u003e\n\u003cli\u003eShells\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eIntroduction to Fractal Dynamics:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eCantor Set and Cantor Dust\u003c\/li\u003e\n\u003cli\u003eKoch Snowflake\u003c\/li\u003e\n\u003cli\u003e1D Maps\u003c\/li\u003e\n\u003cli\u003eSharkovsky's Theorem\u003c\/li\u003e\n\u003cli\u003eJulia Set\u003c\/li\u003e\n\u003cli\u003eMandelbrot's Set\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eIntroduction to Chaos and Wavelets:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eRoutes to Chaos\u003c\/li\u003e\n\u003cli\u003eQuantifying Chaotic Dynamics\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eSimple Chaotic Models:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eAutonomous Systems\u003c\/li\u003e\n\u003cli\u003eNon-Autonomous Systems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eDiscrete and Continuous Dissipative Systems:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eLinear Friction\u003c\/li\u003e\n\u003cli\u003eNonlinear Friction\u003c\/li\u003e\n\u003cli\u003eHysteretic Friction\u003c\/li\u003e\n\u003cli\u003eImpact Damping\u003c\/li\u003e\n\u003cli\u003eDamping in Continuous 1D Systems\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eEuler-Bernoulli Beams:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003ePlanar Beams\u003c\/li\u003e\n\u003cli\u003eLinear Planar Beams and Stationary Temperature Fields\u003c\/li\u003e\n\u003cli\u003eCurvilinear Planar Beams and Stationary Temperature and Electrical Fields\u003c\/li\u003e\n\u003cli\u003eBeams with Elasto-Plastic Deformations\u003c\/li\u003e\n\u003cli\u003eMulti-Layer Beams\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eTimoshenko and Sheremetev-Pelekh Beams:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThe Timoshenko Beams\u003c\/li\u003e\n\u003cli\u003eThe Sheremetev-Pelekh Beams\u003c\/li\u003e\n\u003cli\u003eConcluding Remarks\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003ePanels:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eInfinite Length Panels\u003c\/li\u003e\n\u003cli\u003eCylindrical Panels of Infinite Length\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003ePlates and Shells:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003ePlates with Initial Imperfections\u003c\/li\u003e\n\u003cli\u003eFlexible Axially-Symmetric Shells\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers.\u003cbr\u003eBifurcation;Chaos;Structural Members;PDEs and ODEs;Lyapunov Exponents;Wavelets\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIncludes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicists\u003c\/li\u003e\n\u003cli\u003eCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation  of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scales\u003c\/li\u003e\n\u003cli\u003eContains originally discovered, illustrated and discussed novel and\/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185351475440,"sku":"9789814719711","price":83.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814719711_p0.jpg?v=1763691444","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814719711","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}