LEADER 05119nam 22006735 450 001 9910299917603321 005 20200703080055.0 010 $a3-319-58826-5 024 7 $a10.1007/978-3-319-58826-1 035 $a(CKB)3710000001388772 035 $a(DE-He213)978-3-319-58826-1 035 $a(MiAaPQ)EBC4867472 035 $a(PPN)201472589 035 $a(EXLCZ)993710000001388772 100 $a20170529d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStrong Nonlinear Oscillators $eAnalytical Solutions /$fby Livija Cveticanin 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XII, 317 p. 93 illus., 21 illus. in color.) 225 1 $aMathematical Engineering,$x2192-4732 311 $a3-319-58825-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aPreface to Second Edition -- Introduction -- Nonlinear Oscillators -- Pure Nonlinear Oscillator -- Free Vibrations -- Oscillators with Time-Variable Parameters -- Forced Vibrations -- Harmonically Excited Pure Nonlinear Oscillator -- Two-Degree-of-Freedom Oscillator -- Chaos in Oscillators -- Vibration of the Axially Purely Nonlinear Rod. 330 $aThis textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author?s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations. . 410 0$aMathematical Engineering,$x2192-4732 606 $aVibration 606 $aDynamics 606 $aDynamics 606 $aPhysics 606 $aMathematical physics 606 $aStatistical physics 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 615 0$aVibration. 615 0$aDynamics. 615 0$aDynamics. 615 0$aPhysics. 615 0$aMathematical physics. 615 0$aStatistical physics. 615 14$aVibration, Dynamical Systems, Control. 615 24$aMathematical Methods in Physics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 676 $a621.381533 700 $aCveticanin$b Livija$4aut$4http://id.loc.gov/vocabulary/relators/aut$0788086 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299917603321 996 $aStrong Nonlinear Oscillators$92537963 997 $aUNINA