Optimal auxiliary functions method for nonlinear dynamical systems / Vasile Marinca, Nicolae Herisanu, Bogdan Marinca.

Format:

Book

Author/Creator:

Marinca, Vasile, author.

Herisanu, Nicolae, author.

Marinca, Bogdan, author.

Language:

English

Subjects (All):

Nonlinear systems--Mathematical models.

Nonlinear systems.

Dynamics--Mathematical models.

Dynamics.

Genre:

Electronic books.

Physical Description:

1 online resource : illustrations (chiefly color)

Place of Publication:

Cham : Springer, [2021]

System Details:

text file PDF

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.

Contents:

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.

Notes:

Includes bibliographical references.

Online resource; title from PDF title page (SpringerLink, viewed August 3, 2021).

ISBN:

9783030756536

303075653X

OCLC:

1260341071

Access Restriction:

Restricted for use by site license.