By John G. Harris
ISBN-10: 0521875307
ISBN-13: 9780521875301
John G. Harris meant to provide an explanation for during this e-book the detailed thoughts required to version the radiation and diffraction of elastic and floor waves. He unfortunately died sooner than he may perhaps fulfil this ambition, yet his plan has been dropped at fruition by means of a crew of his individual collaborators. The publication starts off with the fundamental underlying equations for wave movement after which builds upon this origin through fixing a few basic scattering difficulties. the remainder chapters supply an intensive creation to trendy concepts that experience confirmed necessary to realizing radiation and diffraction at excessive frequencies. Graduate scholars, researchers and execs in utilized arithmetic, physics and engineering will locate that the chapters elevate in complexity, starting with plane-wave propagation and spectral analyses. different themes comprise elastic wave thought, the Wiener-Hopf procedure, the consequences of viscosity on acoustic diffraction, and the phenomenon of channelling of wave strength alongside guided constructions.
Read Online or Download Elastic Waves at High Frequencies: Techniques for Radiation and Diffraction of Elastic and Surface Waves (Cambridge Monographs on Mechanics) PDF
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Additional resources for Elastic Waves at High Frequencies: Techniques for Radiation and Diffraction of Elastic and Surface Waves (Cambridge Monographs on Mechanics)
Example text
1982), Babi˘c and Buldyrev (1991), Borovikov and Kinber (1994), and James (1980), that provide comprehensive treatments. Moreover, while there are numerous references to the geometrical theory of diffraction from apertures, Keller (1957) is arguably the best reference to begin studying. This reference can be found in the collections by Hansen (1981) and Oughstun (1991). 25) is not an accurate representation in many regions of R: the representation fails along the central axis x3 and along the shadow boundaries at α∓ = π/2.
14) gives a 2 × 2 system of algebraic equations that has a non-trivial solution if and only if det TP − eiκL I = 0. 15) Recalling our previous definition of tan θ = kM/2ρ, this equation can be written compactly as cos κL = cos(kL + θ)/ cos θ. 16) This is a non-linear relationship between the angular frequency ω = cb k and the effective wavenumber κ, though it may not be apparent, as yet, that κ (and not k) is the wavenumber of interest. Note that if κL ∈ [−π, π] is a solution, then κL±2nπ, for n = 1, 2, .
Continuing to leave the observation point in the x2 = 0 plane, the scaled coordinates x ¯1 = x1 /a, x ¯3 = x3 /Fl are introduced. 21) in the neighborhood x ¯1 < 1, x (kFl )1/2 . The resulting wavefield will be a beam in the sense just defined. Note that kx1 x ¯1 = , (2π)1/2 (k Fl )1/2 so that for kx1 ≤ 1 (equivalently ka > 1), x ¯1 = O[(kFl )−1/2 ]. Referring back to Fig. 2, with a bit of work, it is readily shown that ˆρ = (−∇1 r ) · e a(1 − x ¯1 cos φ) ; r ˆ3 = ∇1 r · e Fl x ¯3 . 22), is rewritten as x1 , x ¯3 ; φ) = (a2 x¯1 2 + Fl2 x¯3 2 − 2a2 x ¯1 cos φ + a2 )1/2 r (¯ = Fl x ¯3 1 + π (¯ x2 − 2¯ x1 cos φ + 1) + O[(kFl )−2 ] .
Elastic Waves at High Frequencies: Techniques for Radiation and Diffraction of Elastic and Surface Waves (Cambridge Monographs on Mechanics) by John G. Harris
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