Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

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.

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 -- …