Weakly Nonlinear Harmonic Acoustic Waves In Classical Thermoviscous Fluids A Perturbation Analysis PDF Download
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Author | : |
Publisher | : |
Total Pages | : 5 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download Weakly Nonlinear Harmonic Acoustic Waves in Classical Thermoviscous Fluids: A Perturbation Analysis Book in PDF, ePub and Kindle
Using regular perturbation analysis, we investigate the propagation of a time-harmonic acoustic signal, generated by a sinusoidal boundary condition, in a half-space filled with a classical thermoviscous fluid. It is assumed that the flow is described by a recently introduced, weakly nonlinear partial differential equation (PDE) that, unlike earlier models, exhibits a Hamiltonian structure in the lossless limit.
Author | : Barbara Kaltenbacher |
Publisher | : Springer |
Total Pages | : 309 |
Release | : 2018-06-21 |
Genre | : Mathematics |
ISBN | : 3319927833 |
Download Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions Book in PDF, ePub and Kindle
This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.
Author | : Robert Thomas Beyer |
Publisher | : Van Nostrand Reinhold Company |
Total Pages | : 408 |
Release | : 1984 |
Genre | : Science |
ISBN | : |
Download Nonlinear Acoustics in Fluids Book in PDF, ePub and Kindle
New York : Van Nostrand Reinhold, c1984.
Author | : B.O. Enflo |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2006-04-11 |
Genre | : Science |
ISBN | : 0306484196 |
Download Theory of Nonlinear Acoustics in Fluids Book in PDF, ePub and Kindle
The aim of the present book is to present theoretical nonlinear aco- tics with equal stress on physical and mathematical foundations. We have attempted explicit and detailed accounting for the physical p- nomena treated in the book, as well as their modelling, and the f- mulation and solution of the mathematical models. The nonlinear acoustic phenomena described in the book are chosen to give phy- cally interesting illustrations of the mathematical theory. As active researchers in the mathematical theory of nonlinear acoustics we have found that there is a need for a coherent account of this theory from a unified point of view, covering both the phenomena studied and mathematical techniques developed in the last few decades. The most ambitious existing book on the subject of theoretical nonlinear acoustics is ”Theoretical Foundations of Nonlinear Aco- tics” by O. V. Rudenko and S. I. Soluyan (Plenum, New York, 1977). This book contains a variety of applications mainly described by Bu- ers’ equation or its generalizations. Still adhering to the subject - scribed in the title of the book of Rudenko and Soluyan, we attempt to include applications and techniques developed after the appearance of, or not included in, this book. Examples of such applications are resonators, shockwaves from supersonic projectiles and travelling of multifrequency waves. Examples of such techniques are derivation of exact solutions of Burgers’ equation, travelling wave solutions of Bu- ers’ equation in non-planar geometries and analytical techniques for the nonlinear acoustic beam (KZK) equation.
Author | : K. Naugolnykh |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 1998-05-28 |
Genre | : Mathematics |
ISBN | : 9780521399845 |
Download Nonlinear Wave Processes in Acoustics Book in PDF, ePub and Kindle
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.
Author | : Eduard Feireisl |
Publisher | : Springer Science & Business Media |
Total Pages | : 411 |
Release | : 2009-03-28 |
Genre | : Science |
ISBN | : 3764388439 |
Download Singular Limits in Thermodynamics of Viscous Fluids Book in PDF, ePub and Kindle
Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.
Author | : Richard Klinman |
Publisher | : |
Total Pages | : 222 |
Release | : 1971 |
Genre | : Fluid dynamics |
ISBN | : |
Download Propagation of Finite Amplitude Acoustic Waves in Nonlinear Relaxing Fluids Book in PDF, ePub and Kindle
The hydrodynamic equations for relaxing fluids are used to derive the evolutionary properties of longitudinal plane waves of finite amplitude in dispersive and dissipative media. The regimes of uniform and secular perturbation solutions, representing either shock free or possibly shock like solutions, are determined from the equations with no restriction on the dispersion number. Solutions are calculated to second order to demonstrate the main features of the progressive wave distortion in nonlinear relaxing media. Heuristic theories using an equivalent viscous model of relaxing media are evaluated through comparison with the correct relaxation results. A consistent consideration of the perturbation method leads to a representation of the thermal state functions containing many parameters of nonlinearity which include the well known B/A parameter. Finally, through recourse to the theory of characteristics it is demonstrated that, unlike thermoviscous media, relaxing media may sustain true discontinuities in the flow similar to those occurring in the nondissipative Riemann solution. (Author).
Author | : Steven L. Garrett |
Publisher | : Springer |
Total Pages | : 913 |
Release | : 2017-02-24 |
Genre | : Science |
ISBN | : 3319499785 |
Download Understanding Acoustics Book in PDF, ePub and Kindle
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.
Author | : David T. Blackstock |
Publisher | : |
Total Pages | : 47 |
Release | : 1963 |
Genre | : |
ISBN | : |
Download Approximate Equations Governing Finite-amplitude Sound in Thermoviscous Fluids Book in PDF, ePub and Kindle
The equations of motion for viscous, thermally conducting, inert fluids of arbitrary equation of state are approximated so as to account as simple as possible for effects of nonlinearity and dissipation. The purpose is to obtain a general improvement of the classical wave equation. The approximation method is basically the same as the one used by Lighthill (1956) to derive Burgers' equation for unbounded, progressive, plane waves in a perfect gas. Besider encompassing the case treated by Lighthill, the equations are applicable for nonplanar waves, for interacting waves, and for waves subject to boundary-layer effects. Moreover, the fluid need not be a perfect gas. Important simplifications arise when either boundary-layer or main-stream dissipation is negligible. When only mainstream losses are important, the assumption of plane progressive waves leads to Burgers' equation. Two forms of Burgers' equation are given. One is suitable for initial-value problems and the other is suitable for boundary-value problems. (Author).
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Publisher | : |
Total Pages | : |
Release | : 1690 |
Genre | : |
ISBN | : |
Download 'TLeven en bedryf van Jacobus de II. gewesen koning van Engeland Book in PDF, ePub and Kindle