Elastic Waves at High Frequency by Harris J.G.

By Harris J.G.

John G. Harris meant to provide an explanation for during this ebook the targeted suggestions required to version the radiation and diffraction of elastic and floor waves. He unfortunately died ahead of he might fulfil this ambition, yet his plan has been delivered to fruition by means of a group of his uncommon collaborators. The ebook starts with the fundamental underlying equations for wave movement after which builds upon this beginning through fixing a couple of basic scattering difficulties. the remainder chapters supply a radical creation to trendy ideas that experience confirmed necessary to figuring out radiation and diffraction at excessive frequencies. Graduate scholars, researchers and execs in utilized arithmetic, physics and engineering will locate that the chapters bring up in complexity, starting with plane-wave propagation and spectral analyses. different themes contain elastic wave idea, the Wiener-Hopf procedure, the results of viscosity on acoustic diffraction, and the phenomenon of channelling of wave power alongside guided constructions.

Show description

Read Online or Download Elastic Waves at High Frequency PDF

Similar fluid dynamics books

Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering

Differential equations, specially nonlinear, current the simplest means for describing advanced actual techniques. equipment for developing detailed ideas of differential equations play a tremendous function in utilized arithmetic and mechanics. This booklet goals to supply scientists, engineers and scholars with an easy-to-follow, yet finished, description of the tools for developing particular options of differential equations.

Student Solutions Manual and Study Guide to accompany Fundamentals of Fluid Mechanics, 5th Edition

Paintings extra successfully and fee options as you associate with the textual content! This scholar options guide and examine advisor is designed to accompany Munson, younger and Okishi’s basics of Fluid Mechanics, fifth variation. This scholar complement comprises crucial issues of the textual content, “Cautions” to warn you to universal errors, 109 extra instance issues of options, and whole strategies for the evaluation difficulties.

Compressibility, Turbulence and High Speed Flow, Second Edition

Compressibility, Turbulence and excessive velocity circulation introduces the reader to the sphere of compressible turbulence and compressible turbulent flows throughout a huge pace variety, via a special complimentary remedy of either the theoretical foundations and the dimension and research instruments presently used.

Asymptotic Modelling of Fluid Flow Phenomena (Fluid Mechanics and Its Applications)

For the fluctuations round the skill yet fairly fluctuations, and showing within the following incompressible procedure of equations: on any wall; at preliminary time, and are assumed recognized. This contribution arose from dialogue with J. P. Guiraud on makes an attempt to push ahead our final co-signed paper (1986) and the most inspiration is to place a stochastic constitution on fluctuations and to spot the big eddies with part of the likelihood house.

Extra info for Elastic Waves at High Frequency

Sample text

8) When r > Fl the wavefield is in the far field. 9) where J0 is the Bessel function of order zero. 10) kρ ∗ϕ(kρ , x3 ))J0 (kρ ρ)dkρ . 9) appears as a spherical wave radiated by an anisotropic point source; the anisotropy is described by the Hankel transform of the distribution of particle velocity on the piston face. 3. 2 the wavefield in the neighborhood of the Fresnel length will be investigated, and there it will be found that it is well collimated and can be described as a beam. When microwave frequency sound is used to probe an environment, it is usual that one wants a beam rather than a spherical wave because when a beam strikes something one can more readily sort out where the echo is coming from.

4 That is, ϕ(x1 ) is a periodic function and can be represented by a Fourier series whose coefficients are cn . Therefore, u ¯1 (x1 ) becomes ∞ u ¯1 (x1 ) = cn eix1 (κ−2πn/L) . 20) −∞ The time-harmonic wavefield u ¯1 (x1 )e−iωt is thus a consequence of an infinite number of space harmonics. Note that shifting κL by ±2mπ would not change this expression. More importantly, it is clear that it is κ, through the term ei(κx1 −ωt) , that is the wavenumber. 16) indicates that ω is a function of κ, or κ a function of ω.

Diffraction from edges, and by extension wedges, still remains an important mathematical challenge; Osipov and Norris (1999) review the important work of Malyuzhinets, which echoes Sommerfeld’s original work on edge diffraction. Sommerfeld’s original work has recently been translated and combined with various historical and mathematical notes in Sommerfeld (2004); briefer descriptions of his work are given in Baker and Copson (1987, pp. 124–152) and Sommerfeld (1967, pp. 247–272). There are now several books that deal with various aspects of radiation and edge diffraction: Achenbach et al.

Download PDF sample

Rated 4.46 of 5 – based on 20 votes