Nonlinear Dynamics And Acoustics

This research monograph provides a brief overview of the authors' research in the area of ordered granular media over the last decade. The exposition covers one-dimensional homogeneous and dimer chains in great detail incorporating novel analytical tools and experimental results supporting the analytical and numerical studies. The proposed analytical tools have since been successfully implemented in studying two-dimensional dimers, granular dimers on on-site perturbations, solitary waves in Toda lattices to name a few. The second part of the monograph dwells on weakly coupled homogeneous granular chains from analytical, numerical and experimental perspective exploring the interesting phenomenon of Landau-Zener tunneling in granular media. The final part of the monograph provides a brief introduction to locally resonant acoustic metamaterials incorporating internal rotators and the resulting energy channeling mechanism in unit-cells and in one- and two-dimensional lattices. The monograph provides a comprehensive overview of the research in this interesting domain. However, this exposition is not all exhaustive with regard to equally exciting research by other researchers across the globe, but we provide an exhaustive list of references for the interested readers to further explore in this direction.

This text considers models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. It also considers the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams.

Contents: Parametric sound sources and receivers; Methods of calculation of nonlinear interactions in sound beams; Nonlinear interaction of plane waves; Method of the parabolic equation and basic results of linear diffraction theory; Parametric sound radiators with nondiffracting beams of pump waves; Calculation of different regimes of operation of the parametric radiator; Parametric receiving arrays; Operation of parametric radiators at high intensities of the pump waves; Thermal opto acoustic arrays; Construction features of parametric underwater devices; Experimental investigations and testing of parametric arrays; Parametric apparatus and the regions of their use, and Use of nomograms for calculation of the characteristics of a parametric radiator.

"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is the Full member of Russian Academy of Sciences, the head of Department at Moscow University and Professor at BTH (Sweden). Dr. Saichev A.I. is the Professor at the Faculty of Radiophysics of Nizhny Novgorod State University, Professor of ETH Zürich.

This textbook provides a unified approach to acoustics and vibration suitable for use in advanced undergraduate and first-year graduate courses on vibration and fluids. The book includes thorough treatment of vibration of harmonic oscillators, coupled oscillators, isotropic elasticity, and waves in solids including the use of resonance techniques for determination of elastic moduli. Drawing on 35 years of experience teaching introductory graduate acoustics at the Naval Postgraduate School and Penn State, the author presents a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation that can incorporate attenuation mechanisms and complex media. This view provides a consistent and reliable approach that can be extended with confidence to more complex fluids and future applications. Understanding Acoustics opens with a mathematical introduction that includes graphing and statistical uncertainty, followed by five chapters on vibration and elastic waves that provide important results and highlight modern applications while introducing analytical techniques that are revisited in the study of waves in fluids covered in Part II. A unified approach to waves in fluids (i.e., liquids and gases) is based on a mastery of the hydrodynamic equations. Part III demonstrates extensions of this view to nonlinear acoustics. Engaging and practical, this book is a must-read for graduate students in acoustics and vibration as well as active researchers interested in a novel approach to the material.

This book covers recent trends and applications of nonlinear dynamics in various branches of society, science, and engineering. The selected peer-reviewed contributions were presented at the International Conference on Nonlinear Dynamics and Applications (ICNDA 2022) at Sikkim Manipal Institute of Technology (SMIT) and cover a broad swath of topics ranging from chaos theory and fractals to quantum systems and the dynamics of the COVID-19 pandemic. Organized by the SMIT Department of Mathematics, this international conference offers an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in all possible areas of nonlinear dynamics.

Market: Acousticians, research scientists, instructors, and graduate and advanced undergraduate students in nonlinear acoustics. This book contains a collection of papers by authors of the Former Soviet Union. The topics covered are media with "structural" nonlinearities, optical generation of sound, acoustic beat-wave interactions, acoustic shock waves, thermal self-focusing of acoustic waves, solitons, statistical nonlinear acoustics, media with relaxation and oscillatory degrees of freedom, parametric arrays, and fluid cavitation.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.