Elastic Waves at High Frequencies: Techniques for Radiation by John G. Harris

By John G. Harris

John G. Harris meant to provide an explanation for during this publication the designated concepts required to version the radiation and diffraction of elastic and floor waves. He unfortunately died ahead of he may possibly fulfil this ambition, yet his plan has been delivered to fruition by means of a workforce of his uncommon collaborators. The e-book starts off with the elemental underlying equations for wave movement after which builds upon this beginning through fixing a few basic scattering difficulties. the remainder chapters supply a radical advent to fashionable options that experience confirmed necessary to figuring out radiation and diffraction at excessive frequencies. Graduate scholars, researchers and pros in utilized arithmetic, physics and engineering will locate that the chapters raise in complexity, starting with plane-wave propagation and spectral analyses. different subject matters contain elastic wave concept, the Wiener-Hopf method, the consequences of viscosity on acoustic diffraction, and the phenomenon of channelling of wave power alongside guided buildings.

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Extra resources for Elastic Waves at High Frequencies: Techniques for Radiation and Diffraction of Elastic and Surface Waves (Cambridge Monographs on Mechanics)

Example text

24) that contains no length; it could be calculated by solving a radiation problem formed by the boundary condition ∂3 ϕ = ikA H(1 − x1 /a), x3 = 0. 26) The geometrical ray is expected from geometrical optics, but geometrical optics does not include diffracted rays. The notions that diffracted rays originating on an edge satisfy Fermat’s principle, and that the diffracted amplitudes can be determined by a geometrical spreading factor and a diffraction coefficient, are the essence of the geometrical theory of diffraction, at least as applied to problems such as the piston radiator.

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 ] . kFl x ¯23 1 Gathering the various pieces, it is readily shown that ˆρ ∇1 r · e a =1+x ¯1 cos φ + O[(kFl )−1 ] ˆ3 )2 r 1 − (∇1 r · e and 2 eikr = eik Fl x¯3 eiπ(¯x1 −2¯x1 cos φ+1)/¯x3 + O[(kFl )−1 ]. 21), gives, after removing the scaling, 2 2 ϕ(x) = ϕg (x) − A eikx3 eik(x1 +a )/(2x3 ) J0 kax1 2x3 −i x1 J1 a + O[(kFl ]−1 ) . 28) Noting that x1 = r sin θ, this expression can be written for an arbitrary observation point.

18) now lie in ∂Ss and in its reflection in the plane ∂R, respectively. The distances from these points to the observation point x are given by s∓ = (x1 − x1 )2 + (x2 − x2 )2 + (x3 ∓ x3 )2 1/2 . 18) where ˆρ . cos χ∓ = (∇2 s∓ ) · e The subscript 2 indicates that the derivative is taken with respect to x (the −) or x (the +). Note that ∇2 s∓ = −∇1 s∓ , where the subscript 1 indicates that the derivative is taken with respect to x. ˆρ |, from a point on the boundary of ∂Sa to The distance r = |x − a e the observation point x (see Fig.

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