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Strongly nonlinear oscillators = ana...

Cveticanin, Livija.

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Strongly nonlinear oscillators = analytical solutions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Strongly nonlinear oscillators/ by Livija Cveticanin.
Reminder of title:	analytical solutions /
Author:	Cveticanin, Livija.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xii, 317 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface 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.
Contained By:	Springer eBooks
Subject:	Nonlinear oscillators. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-58826-1
ISBN:	9783319588261

Strongly nonlinear oscillators = analytical solutions /
Cveticanin, Livija.

Strongly nonlinear oscillatorsanalytical solutions /[electronic resource] :by Livija Cveticanin. - 2nd ed. - Cham :Springer International Publishing :2018. - xii, 317 p. :ill., digital ;24 cm. - Mathematical engineering,2192-4732. - Mathematical engineering..

Preface 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.

This 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.

ISBN: 9783319588261

Standard No.: 10.1007/978-3-319-58826-1doiSubjects--Topical Terms:

705350
Nonlinear oscillators.

LC Class. No.: TK7872.O7

Dewey Class. No.: 621.381533

Strongly nonlinear oscillators = analytical solutions /
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100 1 $a Cveticanin, Livija. $3 2068733
245 1 0 $a Strongly nonlinear oscillators $h [electronic resource] : $b analytical solutions / $c by Livija Cveticanin.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xii, 317 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematical engineering, $x 2192-4732
505 0 $a Preface 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.
520 $a This 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.
650 0 $a Nonlinear oscillators. $3 705350
650 0 $a Chaotic behavior in systems. $3 524350
650 1 4 $a Engineering. $3 586835
650 2 4 $a Vibration, Dynamical Systems, Control. $3 893843
650 2 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 3134772
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Mathematical engineering. $3 2055144
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-58826-1
950 $a Engineering (Springer-11647)