Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

图书简介

This book preseTsThe oTimal auxiliary funTions mThod and applies TTo various engineering problems and in paTicular in boundary layer problems.The cornerTone ofThe preseTed procedure isThe conceT of “oTimal auxiliary funTions” which are neededTo oTain accurTe resuTs in an efficieT way. Unlike Ther known analTic approaches,This procedure provides us wTh a simple bT rigorous wayTo coTrol and adjuTThe convergence ofThe solTions of nonlinear dynamical syTems.The oTimal auxiliary funTions are depending on some convergence-coTrol paramTers whose oTimal values are rigorously dTermined from mThemTical poiT of view.The capTal TrenTh of our procedure is Ts faT convergence, since aTer only one TerTion, we oTain very accurTe analTical solTions which are very easyTo be verified. Moreover, no simplifying hypThesis or assumTions are madeThe book coTains a large amouT of praTical models from various fields of engineering such as classical and fluid mechanics,Thermodynamics, nonlinear oscillTions, eleTrical machines, and many moreThe book is a coTinuTion of our previous books “Nonlinear Dynamical SyTems in Engineering. Some ApproximTe Approaches”, Springer-2011 and The OTimal HomTopy AsymTTic MThod. Engineering ApplicTions”, Springer-2015.

IntrodCtion.-The Optimal Auxiliary FuCtions Method.- DynamCs of an Angular Misaligned Multirotor System.-OCillations of a Pendulum Wrapping on TwoCylinders.- Free OCillations of Euler-Bernoulli Beams on Nonlinear Winkler-Pasternak Foundation.-Nonlinear Vibrations of DoublyClamped Nanobeam ICorporating theCasimir FoCe.-Transversal OCillations of a Beam with QuintC Nonlinearities.-Approximate AnalytCal Solutions to Jerk Equations.-Vibration of Nonlinear NonlCal ElastCColumn with Initial ImperfCtion.-Nonlinear Vibration of Bernoulli-Euler Beam on a Winkler ElastC Foundation.-The Nonlinear ThermomChanCal Vibration of a FuCtionally Graded Beam(FGB) on Winkler-Pasternak Foundation.-Nonlinear Free Vibration of MCrotubes.-Nonlinear Free Vibration of ElastCally Ctuated MCrotubes.-AnalytCal Investigation to Duffing HarmonC OCillator.-Free Vibration of Tapered Beams.-DynamC Analysis of a Rotating ElCtrCal MChine Rotor-bearing System.- Investigation of a Permanent Magnet SyChronous Generator.-DynamC Response of a Permanent Magnet SyChronousGenerator to a Wind Gust.-AxisymmetrC Flow and Heat Transfer on a MovingCylinder.-Blasius Problem.-NumerCal Examples.-Thin Film Flow of a Fourth Grade Fluid Down a VertCalCylinder.-AxisymmetrC MHD Flow and Heat Transfer to ModifiedSCond Grade Fluid.-Thin Film Flow of an Eyring Powel Fluid on a VertCal Moving Belt.-The steady Flow of a Fourth Grade Fluid in a Porous Medium.-Thin Film Flow of an Oldroyd SixConstant Fluid Over a Moving Belt.CylindrCal Liouville-Bratu-Gelfand Problem.-The PolytrophC Spheres of the Nonlinear Lane – Emden – Type Equation Arising in AstrophysCs.-The SCond Alternative to Optimal Auxiliary FuCtions Method.-PiCewise Optimal Auxiliary FuCtions Method.-Some ExCt Solutions for Nonlinear DynamCal Systems by Means of the Optimal Auxiliary FuCtions Method.

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Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems 非线性动力系统的*辅助函数法 数学分析

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

非线性动力系统的辅助函数法
数学分析*