Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems
Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

Author: Vasile Marinca

Publisher: Springer Nature

Published: 2021-07-14

Total Pages: 479

ISBN-13: 303075653X

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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.

Acoustics and Vibration of Mechanical Structures – AVMS-2021
Acoustics and Vibration of Mechanical Structures – AVMS-2021

Author: Nicolae Herisanu

Publisher: Springer Nature

Published: 2022-08-10

Total Pages: 381

ISBN-13: 3030967875

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This book is a collection of contributions presented at the 16th Conference on Acoustic and Vibration of Mechanical Structure held in Timişoara, Romania, May 28, 2021. The conference focused on a broad range of topics related to acoustics and vibration, such as noise and vibration control, noise and vibration generation and propagation, effects of noise and vibration, condition monitoring and vibration testing, modelling, prediction and simulation of noise and vibration, environmental and occupational noise and vibration, noise and vibration attenuators, biomechanics and bioacoustics. The book also discusses analytical, numerical and experimental techniques applicable to analyze linear and non-linear noise and vibration problems (including strong nonlinearity) and it is primarily intended to emphasize the actual trends and state-of-the-art developments in the above mentioned topics. The primary audience of this book consist of academics, researchers and professionals, as well as PhD students concerned with various fields of acoustics and vibration of mechanical structures.

Nonlinear Dynamical Systems in Engineering
Nonlinear Dynamical Systems in Engineering

Author: Vasile Marinca

Publisher: Springer Science & Business Media

Published: 2012-01-05

Total Pages: 403

ISBN-13: 364222735X

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This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Dynamical Systems in Applications
Dynamical Systems in Applications

Author: Jan Awrejcewicz

Publisher: Springer

Published: 2018-09-01

Total Pages: 507

ISBN-13: 3319966014

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The book is intended for all those who are interested in application problems related to dynamical systems. It provides an overview of recent findings on dynamical systems in the broadest sense. Divided into 46 contributed chapters, it addresses a diverse range of problems. The issues discussed include: Finite Element Analysis of optomechatronic choppers with rotational shafts; computational based constrained dynamics generation for a model of a crane with compliant support; model of a kinetic energy recuperation system for city buses; energy accumulation in mechanical resonance; hysteretic properties of shell dampers; modeling a water hammer with quasi-steady and unsteady friction in viscoelastic conduits; application of time-frequency methods for the assessment of gas metal arc welding conditions; non-linear modeling of the human body’s dynamic load; experimental evaluation of mathematical and artificial neural network modeling for energy storage systems; interaction of bridge cables and wake in vortex-induced vibrations; and the Sommerfeld effect in a single DOF spring-mass-damper system with non-ideal excitation.

The Optimal Homotopy Asymptotic Method
The Optimal Homotopy Asymptotic Method

Author: Vasile Marinca

Publisher: Springer

Published: 2015-04-02

Total Pages: 476

ISBN-13: 3319153749

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This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

Dynamical Systems: Theoretical and Experimental Analysis
Dynamical Systems: Theoretical and Experimental Analysis

Author: Jan Awrejcewicz

Publisher: Springer

Published: 2016-09-17

Total Pages: 424

ISBN-13: 3319424084

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The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Łódź, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

Acoustics and Vibration of Mechanical Structures—AVMS-2017
Acoustics and Vibration of Mechanical Structures—AVMS-2017

Author: Nicolae Herisanu

Publisher: Springer

Published: 2017-12-21

Total Pages: 404

ISBN-13: 3319698230

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This book is a collection of papers presented at Acoustics and Vibration of Mechanical Structures 2017 – AVMS 2017 – highlighting the current trends and state-of-the-art developments in the field. It covers a broad range of topics, such as noise and vibration control, noise and vibration generation and propagation, the effects of noise and vibration, condition monitoring and vibration testing, modeling, prediction and simulation of noise and vibration, environmental and occupational noise and vibration, noise and vibration attenuators, as well as biomechanics and bioacoustics. The book also presents analytical, numerical and experimental techniques for evaluating linear and non-linear noise and vibration problems (including strong nonlinearity). It is primarily intended for academics, researchers and professionals, as well as PhD students in various fields of the acoustics and vibration of mechanical structures.

Current Trends in Dynamical Systems in Biology and Natural Sciences
Current Trends in Dynamical Systems in Biology and Natural Sciences

Author: Maira Aguiar

Publisher: Springer Nature

Published: 2020-05-06

Total Pages: 250

ISBN-13: 3030411206

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This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop “Dynamical Systems Applied to Biology and Natural Sciences – DSABNS”, held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.

Optimization and Related Topics
Optimization and Related Topics

Author: Alexander M. Rubinov

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 466

ISBN-13: 147576099X

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This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: • optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. • emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. • gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. • auxiliary function, generalized penalty function, modified Lagrange func tion. • convexity, quasiconvexity, abstract convexity.