By J. D. Achenbach
ISBN-10: 0511550480
ISBN-13: 9780511550485
ISBN-10: 052181734X
ISBN-13: 9780521817349
The reciprocity theorem has been used for over a hundred years to set up attention-grabbing and precious relationships and to formulate difficulties. across the world wonderful for his contributions to mechanics, Jan Achenbach provides a unique approach to fixing wave fields. the cloth offered here's proper to purposes in engineering and utilized physics similar to ultrasonics for scientific imaging and non-destructive review, acoustic microscopy, seismology, exploratory geophysics, and structural acoustics.
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Extra info for Reciprocity in elastodynamics
Sample text
The equation of state for an acoustic medium defines the pressure as a function of the mass density, p = p(ρ). A wave motion in an acoustic medium is a dynamic perturbation of a static equilibrium state defined by p0 and ρ0 . The perturbations are denoted by p (x, t), ρ (x, t) and v(x, t), where v(x, t) is the particle velocity. The derivation of the linearized equations that relate p (x, t), ρ (x, t) and v(x, t) can 26 Some elastodynamic theory be found in books on acoustics; see for example Pierce (1981) and Dowling and Ffowcs Williams (1983).
6) as κ= 2 (1 − υ) 1 − 2υ 1/2 . Since κ > 1 and θ2 ≤ π/2, it is apparent that θ2 < θ1 . The wavenumber k = k0 sin θ0 refers to the wave propagating along the surface x2 = 0. The phase velocity along the surface x2 = 0 is then obtained as c= cL ω . 10) the algebraic equations for A1 /A0 and A2 /A0 can now be simplified to (λ + 2µ cos2 θ0 )(A1 /A0 ) − κµ sin 2θ2 (A2 /A0 ) = −(λ + 2µ cos2 θ0 ), −µ sin 2θ0 (A1 /A0 ) − κµ cos 2θ2 (A2 /A0 ) = −µ sin 2θ0 . 11) RTL = A2 2κ sin 2θ0 cos 2θ2 = . 12) Here R LL and RTL are the reflection coefficients; the superscript defines the incident wave and the subscript the reflected wave.
4) we note that for a given frequency and amplitude the time-averaged rate of energy transmission is larger for an L wave than for a T wave. 1 Reflection of an L wave at a free surface. 4 Reflection of time-harmonic plane waves at a free surface Incident longitudinal wave Let us investigate the reflection of plane longitudinal waves whose displacement vectors and propagation vectors are situated in the x1 x2 -plane. 1) where different values of the index n serve to label the various types of wave that occur when a longitudinal wave is reflected, and where ηn follows from Eq.
Reciprocity in elastodynamics by J. D. Achenbach
by Charles
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