About the Book
This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.
Table of Contents:
Chapter I: Introduction.- Why Nonlinear Oscillations?.- Brief Review of Nonlinear Oscillations History.- Overview of the Book.- Nonlinear Dynamical Systems.- Conservative Oscillatory Systems.- Non-Conservative Oscillatory Systems.- Parametrically Excited Vibration.- Resonance in Nonlinear Systems.- Chapter II: Classical Methods.- Nonlinear Differential Equations.- Perturbation Methods.- Parametric Excitation and Hill’s Equation.- Practice Problems.- Chapter III: Energy Balance Methods.- Part I Approach.- Fundamentals of the Energy Balance Method.- Modified Energy Balance Method: Galerkin Approach.- Modified Energy Balance Method: Least Square Method.- Hamiltonian Approach.- Modified Hamiltonian Approach.- Rational Energy Balance Method.- Part II Applications.- Generalized Duffing Equation.- Nonlinear Dynamic Buckling of an Elastic Column.- Vibrations of Cracked Rectangular Plate.- Relativistic Oscillator.- Plasma Physics Equation.- Nonlinear Oscillator with Discontinuity.- NonlinearOscillator with Fractional-Power Restoring Force.- Generalized Conservative Oscillatory Systems (Type 1).- Generalized Conservative Oscillatory Systems (Type 2).- Duffing Harmonic Oscillator.- Helmholtz Duffing Oscillator.- Autonomous Conservative Oscillatory System.- Nonlinear Oscillation of Rigid Bar on Semi-Circular Surface.- Nonlinear Oscillations of Centrifugal Governor Systems.- Nonlinear Lateral Sloshing in Partially-Filled Elliptical Tankers.- Nonlinear Oscillations of Elevator Cable in in a Drum Drive Elevator.- Chapter IV: Residual Methods.- Part I Approach.- Basic Idea.- Frequency Amplitude Formulation.- Max-Min Approach.- Part II Applications.- Generalized Duffing Equation.- Generalized Conservative Oscillatory Systems (Type 1).- Generalized Conservative Oscillatory Systems (Type 2).- Nonlinear Oscillator with Fractional Power.- Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire.- Nonlinear Schrödinger Equation.- A Rigid Frame Rotates at a Fixed Rate.- Conservative Lienard Type Equation.- Part III Practice Problems.- Chapter V: Semi-Inverse and Variational Methods.- Semi-Inverse and Variational Approaches.- Part I Approach.- Variational Principle.-Semi-Inverse Method.- Variational Approach.-Hamiltonian Approach.- Relationship between Hamiltonian and Variational Approaches.- Part II Applications.- Generalized Duffing Equation.- Elastic Force with Rational Characteristic Equation.- Elastic Force with Non-integer Fractional Characteristic Equation.- Higher-Order Hamiltonian Approach to Duffing Equations.- Hamiltonian Approach to Rational and Irrational Oscillator.- Hamiltonian Approach to Nonlinear Oscillator with Discontinuity.- Nonlinear Oscillator with Quintic Nonlinearity.- Nonlinear Schrodinger’s Equation.- Thomas-Fermi Equation.- Heat Conduction Equation.- Lane-Edmen Type Equation.- Dynamic Analysis of Centrifugal Governor System.- Duffing Harmonic Equation.- Part III Practice Problems.- Chapter VI: Ingegral Based Methods.- Part I Approaches.- Adomian Decomposition Method.- Variational Iteration Method.- Homotopy Analysis Method.- Part II Applications.- Volterra-Integro Differential Equations.- Nonlinear Schrödinger Equations.- Van der Pol Equation.- Korteweg-de Vries Equation.- Part III Practice Problems.- Chapter VII:Nonlinearities in Nano and Micro Systems.- Duffing Equation in NEMS and MEMS.- Parametric and Self-Excited Oscillations.- Nonlinear Coupled Oscillators.- Other Types of Nonlinearities.- Part III Practice Problems.
About the Author :
Ebrahim Esmailzadeh studied in England and received his B.Sc. (Honors), M.Phil., and Ph.D. all in Mechanical Engineering from the University of London, UK. His research and teaching span over four decades and his expertise and leadership in the fields of vibrations, nonlinear systems, control, vehicle dynamics, and active control of vibration are widely known in the community. He is an active researcher, passionate and dedicated teacher and has received numerous awards and recognitions for excellence in teaching and research. He has published over 300 papers in prestigious journals and international conference proceedings and throughout his distinguished career he has played a major role within the professional societies and facilitated international collaborations between industry and academia. He serves at the Editorial Boards of several international and national journals. Prior to his appointment as Professor and Founding Director of Engineering Programs at the University of Ontario Institute of Technology, Oshawa, he was a Distinguished Professor at Sharif University of Technology, Tehran and an Exemplar Professor of the Universities in Iran. His excellence in teaching and research has been recognized through several prestigious national and international awards and honors. Dr. Esmailzadeh received the prestigious awards of Fellow of the Canadian Academy of Engineering, Fellow of the American Society of Mechanical Engineers, Fellow of the British Institution of Mechanical Engineers, Fellow of the Canadian Society for Mechanical Engineering, and Fellow of the Engineering Institute of Canada, the attainment of which recognizes exceptional engineering achievements in education, research, and contributions to the engineering profession.
Davood Younesian received BSc degree from K.N.T. University, Tehran, Iran in 1998 and MSc and PhD degrees from Sharif University of Technology, Tehran in 2000 and 2004, respectively, all in Mechanical Engineering. He was awarded two post-doctoral fellowships in nonlinear and random vibration of flexible structures at the Institute of Sound and Vibration Research, Southampton, UK and at the University of Ontario Institute of Technology, Oshawa, Canada from 2004 to 2005. Dr. Younesian joined the School of Railway Engineering of Iran University of Science and Technology, Tehran where he is currently a professor. In 2016 he spent one- year sabbatical leave at the Mechanical Engineering Department, University of California at Berkeley, USA. Since 2012 he is an Honorary Member of the International Research Center for Mathematics & Mechanics of Complex Systems, L’Aquila in Italy, Head of the Center of Excellence in Railway Engineering and Vice-President of the Iranian Society of Acoustics and Vibrations. He has authored more than 200 refereed journal and conference papers in the areas of dynamics, vibration and control. He serves at the Editorial Boards of several international and national journals. Professor Younesian has received many prestigious awards and recognition certificates. In 2005, he was selected as one of the key scientists in Computational Science and Engineering, by Saxe-Coburg Institute, UK. He was awarded Medal for the Chair of the Young Scientists in Engineering Science by the Iran Academy of Sciences in 2015. Recently he received the 2017 Agnew/Goodall prize from the Institution of Mechanical Engineers, London, UK.
Hassan Askari was born in Rasht, Iran and received his engineering degrees from Iran University of Science and Technology, Tehran, Iran, and the University of Ontario Institute of Technology, Oshawa, Canada in 2011 and 2014, respectively. He is currently a PhD candidate in the Mechanical and Mechatronic Engineering Department at the University of Waterloo, Canada working in the areas of nano-resonators, nano-generators and self-powered sensors. He published more than 60 journal and conference papers in the areas of nonlinear vibrations, applied mathematics, and nano and self-powered sensors. He is an active reviewer and editorial board member of several scientific and international journals. He has received several prestigious awards including, Outstanding Researcher at the Iran University of Science and Technology, Fellowship of the Waterloo Institute of Nanotechnology, NSERC Graduate Scholarship, Ontario Graduate Scholarship, and the University of Waterloo President Award. He was nominated for the Governor General's Academic Gold Medal at the University of Ontario Institute of Technology in 2014.
Review :
“The basic aim of this book is to present very recent analytical methods in nonlinear systems, which mainly have been developed during the past few decades. It can be useful for researchers and graduate students, who are pursuing research studies on nonlinear differential equations and systems as well as on nonlinear oscillations, analytical dynamics and applied mathematics. It may also be considered as a broad reference source for those seeking advanced knowledge in the area of nonlinear differential equations and systems.” (V. A. Pron’ko, zbMATH 1439.34002, 2020)
