Lectures on Nonlinear Dynamics

This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, nonlinear modal analysis and model reduction, synchronization, and strongly nonlinear dynamics. Interwoven seamlessly, these groups cover a wide range of topics, from fundamental concepts to practical applications, catering to both introductory and advanced readers. The first group, consisting of chapters 1 and 2, serves as an introduction to the theory of parametric resonance and the dynamics of parametrically excited slender structures. Chapters 3, 4, and 5 form the second group, offering insights into normal forms, nonlinear normal modes, and nonlinear system identification. Chapters 6 and 7 delve into asynchronous modes of structural vibration and master-slave topologies for time signal distribution within synchronous systems, respectively, representing the third group. Finally, the last four chapters tackle the fourth group, exploring nonlinear dynamics of variable mass oscillators, advanced analytical methods for strong nonlinear vibration problems, chaos theory, and dynamic integrity from the perspectives of safety and design. This book harmoniously combines theoretical depth and practical relevance to provide a comprehensive understanding of nonlinear dynamics.

José Roberto Castilho Piqueira has a doctorate in Electric Engineering from Universidade de São Paulo (1987). Since 1999 he is a full-professor at Escola Politécnia da Universidade de São Paulo and was the school Dean between 2014-2018. Nowadays, he is a member of Brazilian Engineering Academy (ANE). His experience is in Electric Engineering, focusing on General Theory of Electric Circuits and acting on the following subjects: dynamics, bifurcation, PLL systems, synchronism and stability. 

Carlos Mazzilli holds a Ph.D. in Structural Engineering from the University of London (1982) and a Habilitation in Mechanics of Deformable Solids from the University of São Paulo (1988). He joined the University of São Paulo in 1976, where he has held a Full Professorship since 1992. He has scientific experience in the areas of Mechanics of Structures, acting mainly on the following research themes: static and nonlinear dynamic analysis, finite element method, vibration control in structures, nonlinear modes of vibration and reduced-order models. 

Celso Pesce has a Doctorate in Ocean Engineering (1988) from the University of São Paulo. Associate Professor in Mechanics (Livre Docente) (1997-98) and Professor of Mechanical Sciences (1998 on) at the Department of Mechanical Engineering; Visiting Professor (1999) at the Naval Architecture and Marine Engineering Department, the University of Michigan, Ann Arbor; Invited Lecturer at CISM—International Centre for Mechanical Sciences, Italy, 2012; Editor in Chief at Marine Systems & Ocean Technology (2004-2013) and Associate Editor at Journal of Offshore Mechanics and Arctic Engineering, ASME (2007-10; 2013-16; 2016-19); Member of the Executive Committee, OOAE-ASME, 2019-2026; Head of the Mechanical Engineering Department (2007-2011); Head of the Naval and Ocean Engineering Department (2022-2024); Founder (1994) and Head (ever since) of the Offshore Mechanics Laboratory—LMO. 

Guilherme Rosa Franzini has a doctorate in Naval Engineering from University of Sao Paulo (2012) and a Habilitation in Theory of Structures. He is Associate Professor at the Department of Structural and Geotechnical Engineering, Escola Politécnica, University of São Paulo. He has experience in themes related to linear and nonlinear dynamics, including flow-induced vibration, passive suppression of oscillations, energy harvesting, reduced-order models and experimental analysis.