Optimal auxiliary functions method for nonlinear dynamical systems / Vasile Marinca, Nicolae Herisanu, Bogdan Marinca.
Marinca, Vasile, author.; Herisanu, Nicolae, author.; Marinca, Bogdan, author.
2021
QA402 .M37 2021
Available Online

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Title Optimal auxiliary functions method for nonlinear dynamical systems / Vasile Marinca, Nicolae Herisanu, Bogdan Marinca.
Author Marinca, Vasile, author.
ISBN 9783030756536 (electronic bk.)
303075653X (electronic bk.)
9783030756529
3030756521
DOI https://doi.org/10.1007/978-3-030-75653-6
Published Cham : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource : illustrations (chiefly color)
Other Standard Identifiers 10.1007/978-3-030-75653-6 doi
Call Number QA402 .M37 2021
Dewey Decimal Classification 629.8/36015118
Summary This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of "optimal auxiliary functions" which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches, Springer-2011 and The Optimal Homotopy Asymptotic Method. Engineering Applications, Springer-2015
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed August 3, 2021).
Added Author Herisanu, Nicolae, author.
Marinca, Bogdan, author.
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Introduction
The Optimal Auxiliary Functions Method
Dynamics of an Angular Misaligned Multirotor System
Oscillations of a Pendulum Wrapping on Two Cylinders
Free Oscillations of Euler-Bernoulli Beams on Nonlinear Winkler-Pasternak Foundation
Nonlinear Vibrations of Doubly Clamped Nanobeam Incorporating the Casimir Force
Transversal Oscillations of a Beam with Quintic Nonlinearities
Approximate Analytical Solutions to Jerk Equations
Vibration of Nonlinear Nonlocal Elastic Column with Initial Imperfection
Nonlinear Vibration of Bernoulli-Euler Beam on a Winkler Elastic Foundation
The Nonlinear Thermomechanical Vibration of a Functionally Graded Beam(FGB) on Winkler-Pasternak Foundation
Nonlinear Free Vibration of Microtubes
Nonlinear Free Vibration of Elastically Actuated Microtubes
Analytical Investigation to Duffing Harmonic Oscillator
Free Vibration of Tapered Beams
Dynamic Analysis of a Rotating Electrical Machine Rotor-bearing System
Investigation of a Permanent Magnet Synchronous Generator
Dynamic Response of a Permanent Magnet Synchronous Generator to a Wind Gust
Axisymmetric Flow and Heat Transfer on a Moving Cylinder
Blasius Problem
Numerical Examples
Thin Film Flow of a Fourth Grade Fluid Down a Vertical Cylinder
Axisymmetric MHD Flow and Heat Transfer to Modified Second Grade Fluid
Thin Film Flow of an Eyring Powel Fluid on a Vertical Moving Belt
The steady Flow of a Fourth Grade Fluid in a Porous Medium
Thin Film Flow of an Oldroyd Six-constant Fluid Over a Moving Belt
Cylindrical Liouville-Bratu-Gelfand Problem
The Polytrophic Spheres of the Nonlinear Lane-Emden-Type Equation Arising in Astrophysics
The Second Alternative to Optimal Auxiliary Functions Method
Piecewise Optimal Auxiliary Functions Method
Some Exact Solutions for Nonlinear Dynamical Systems by Means of the Optimal Auxiliary Functions Method.

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