This handbook aims to provide a comprehensive view of the state of the art in nonlinear dynamics, vibrations, and acoustics, offering hands-on introductions and perspectives on future developments in the decades to come. These fields are widely recognized as well-established and mature scientific disciplines with rich histories and a legacy of remarkable developments that have profoundly influenced the exact sciences, natural sciences, and even the social sciences.The Handbook consists of five independent volumes, comprising a total of 61 papers. Volume I (eds. Professors Alexander Vakakis and Oleg Gendelman) is devoted to fundamental concepts and basic methods. Volume II (ed. Professor Vincent Acary) focuses on numerical methods. Volume III (ed. Professor Kathryn Matlack) addresses the relatively new but rapidly developing field of nonlinear acoustics of solids and structures. Volume IV (ed. Professor Norbert Hoffmann) presents several examples of applications of nonlinear dynamics across diverse scientific disciplines. Volume V (ed. Professor Giuseppe Rega) offers a broad overview of the many applications of nonlinear dynamics in engineering.Volume I: Fundamental Concepts and Basic Methods (Alexander F Vakakis and Oleg V Gendelman):The subject of nonlinear dynamics has relatively long history and well-established set of fundamental concepts and basic notions. Current Volume is primarily devoted to these topics. After relatively brief historical introduction, the book presents basic notions, including bifurcations, chaos, nonlinear normal modes, synchronization and entrainment, stability, localization and some others. Besides, it reviews basic analytic approaches widely used in the nonlinear dynamics: a variety of asymptotic and approximate methods used for systems with weak and strong nonlinearity, reduced-order modeling, invariant manifolds and Hamiltonian perturbations theory. These methods are presented in connection with steady-state and transient responses. The models presented in this volume range from simple low-DFO systems with lumped masses to extended lattices and continuous structures.Volume II: Numeric Methods (Vincent Acary):This volume is devoted to numerical methods for nonlinear dynamics, with a particular focus on robust, structure-aware methods capable of addressing modern modelling challenges. It brings together contributions from leading experts who have shaped the development of numerical analysis, dynamical systems theory and computational mechanics. The chapters cover a wide range of methodologies, including advanced time-integration techniques; continuation and bifurcation methods for ordinary and partial differential equations; reduced-order modelling strategies; and data-driven and probabilistic approaches for identification and uncertainty quantification. Rather than aiming to present a single unifying algorithmic framework, this handbook acknowledges the diversity of numerical tools required by nonlinear dynamics. Each contribution highlights the mathematical foundations of the methods and their practical implications, providing illustrative examples from mechanics, physics and engineering. Particular attention is paid to geometric integration, invariant structures, stability and bifurcation phenomena, model reduction, and the reliable computation of complex behavior patterns, such as chaos, wave patterns and localized nonlinear responses.Volume III: Nonlinear Acoustics of Solids and Structures (Kathryn Matlack):The intent of this volume is to survey the current state-of-the-art research in nonlinear acoustics of solids and structures, through the introduction of currently relevant topics grounded in foundational concepts. The chapters provide a snapshot of current research in this still-growing area. The volume is organized thematically, beginning with foundational concepts in more classical configurations such as guided waves, bulk nonlinear media, and single nonlinear interfaces, while remaining at the forefront of state-of the-art research. The volume then shifts toward more "architected" configurations such as granular media, periodic lattices, and phononic materials. This volume is intended as both a reference and a catalyst, supporting the learning of graduate students and new researchers in the area, as well as spawning new research directions for the more advanced researcher.Volume IV: Applications of Nonlinear Dynamics in Sciences (Norbert Hoffmann):This volume presents a snapshot on applications of nonlinear dynamics in various branches of science. Historically, the sciences have always served as a fruitful test bed and even powerhouse for the discovery of new phenomena in nonlinear dynamics, and for the development of new corresponding methods to deal with them. In gravity waves and vibrations nonlinearity has probably made its appearance in the 19th century. Groundbreaking work on spatially or temporally localized dynamics have followed soon. The study of weather and climate phenomena contributed significantly to the understanding of deterministic chaos and turbulence. And the wide field of emergence and pattern formation, which had started out in chemistry, biology and thermodynamics, substantially widened the present view about dynamical systems, and the world. Today, natural and social systems are usually and naturally understood as nonlinear. And in consequence, nature, including humans, animals and plants, keeps demonstrating novel, intricate and fascinating phenomena, which are deeply and fundamentally nonlinear. The contributions serve to demonstrate this and hopefully will give interested readers an accessible overview about some of the respective fields, and perhaps even good starting points to become actively involved themselves.Volume V: Nonlinear Dynamics and Vibrations: Applications in Engineering (Giuseppe Rega):The present volume of the Handbook on Nonlinear Dynamics, Vibrations and Acoustics is specifically dedicated to engineering applications in nonlinear dynamics and vibrations, By virtue of the substantial widening of perspectives of mechanical and, even more, engineering sciences, occurred in connection with the hybridization of disciplines, topics of interest in applied nonlinear dynamics at the quarter of the 21st century pertain to a large number of subject areas, of both technological and societal relevance. Any volume of a reasonable size can only report on some of them. The proposed selection has been made in the background of ongoing advanced developments in the field and of those expected in the near years to come. Overall, the seventeen chapters of this volume are deemed to provide a fairly articulated picture of the important transition that nonlinear dynamics is currently facing as regards modeling, methods and phenomena. It essentially consists in moving from the fundamentals aspects of the discipline — as established over 40+ years of in-depth analysis of local and global phenomena in low-dimensional models, accomplished through systematic use of a variety of 'classical', analytical, numerical and/or experimental, techniques — to a basket full of important challenges and a wide range of new interesting topics in various branches of engineering.
