Nonlinear Wave Processes in Acoustics

Abstract

These reviews of books and other forms of information express the opinions of the individual reviewers and are not necessarily endorsed by the Editorial Board of this Journal. pp. Price: $74.95 hardback and $30.95 paperback.The area of acoustics concerned with nonlinear wave propagation is traditionally called nonlinear acoustics. Several books on this subject are available ͓Zarembo and Krasil'nikov ͑1966͒, Beyer ͑1974͒, Rudenko and Soluyan ͑1975͒, Hamilton and Blackstock ͑1998͔͒. The book by Naugolnykh and Ostrovsky provides yet another perspective on nonlinear acoustics, and it is written by two leading experts who have worked in this field for almost 40 years. Perhaps the more novel feature of their book, which is reflected in the title, is that nonlinear acoustics is considered as a branch of nonlinear wave physics. Such an approach appears to be very fruitful, as it permits the application to acoustics of many concepts and results obtained in other areas of nonlinear wave physics ͑e.g., nonlinear optics͒.The book consists of seven chapters. Chapter 1, entitled ''Nonlinearity, dissipation and dispersion in acoustics,'' describes several models illustrating the combined effects of these three phenomena on acoustic waves in various media. Westervelt, simple-wave, and Burgers equations are developed for nonlinear propagation in gases, liquids, and isotropic solids. Besides these results ͑which can be found in all books on nonlinear acoustics͒, the authors consider media with internal structure having dimensions small compared with a wavelength, such as liquids with gas bubbles and isotropic solids with empty spherical cavities. It is shown how these microinhomogeneities introduce not only additional losses, but also dispersion and a substantial increase in nonlinearity. The chapter concludes with discussion of ''anomalous'' nonlinearities in elastic solids, which are modeled with stress-strain relations not described by a simple power law. Such nonlinearities are associated with dislocations, grains, and microcracks in the medium. Recent developments in this area are very interesting, and it is unfortunate that only a brief survey of these results is presented.In Chapter 2, entitled ''Simple waves and shocks in acoustics,'' evolution of nonlinear plane waves is considered when effects of dissipation and dispersion are much weaker than that of nonlinearity. In this case, initially smooth acoustic perturbations transform eventually to weak shock waves. The chapter presents classical results for shock formation and describes the corresponding evolution of the frequency spectrum within the framework of the simple-wave and Burgers equations. Results for propagation of intense noise are also presented. In our opinion, the most interesting part of this chapter is Section 6, where propagation in media with anomalous nonlinearity is considered. Models are presented for media with two different stress-strain relations. The first, based on a modified Burgers equation, describes propagation in cubically nonlinear media. ...

Bright and gap solitons in membrane-type acoustic metamaterials

“…However, in acoustic metamaterials -and up to now-only few works have systematically consider the interplay between all the above phenomena [10][11][12][13][14] . Particularly, in some works, the combined effects of dissipation and dispersion were studied without considering the nonlinearity 2,[15][16][17][18] ; in this case, the relevance of dissipation was further exploited to the design of perfect absorbers 6,7 .…”

Nonlinear propagation and control of acoustic waves in phononic superlattices

“…However, the main nonlinear effects related to strong lattice dispersion still appreciated. An analogous effect has been also studied [13] where instead of dispersion, selective absorption at specific frequencies is used to modify and enhance harmonic generation.…”

“…The cumulative energy transfer from the interacting waves to the harmonics is dependent on the resonance conditions ω 1 ± ω 2 = ω 3 , k 1 ± k 2 = k 3 . Note these conditions express the laws of conservation of energy ( ω) and momentum ( k) in the quantum description for the disintegration and merging of quanta [13]. These conditions can be satisfied in a variety of situations.…”

“…It is worth noting here that as long 2k 1 k 2 , the forced and free waves in dispersive media have different phase speed, i. e. the forced and free waves are phase mismatched as can be seen in the argument of the sin function in Eq. (12)(13). Imposing the boundary condition, that the second harmonic must be absent at x = 0, the second harmonic field can be expressed as…”

“…Here, we use the equations of continuum mechanics for ideal fluids with space dependent parameters. These are the continuity equation for mass conservation [13]:…”