Envelope solitons in acoustically dispersive vitreous silica

Cantrell, John H.; Yost, William T.

doi:10.1088/0953-8984/24/21/215401

Cited by 2 publications

(2 citation statements)

References 19 publications

(44 reference statements)

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“…It is relevant to point out that for laterally constrained conditions, u 22 =u 33 =0 and = ( ) f f u . 11 Applying these conditions and following the derivation leading to equation (43) now results in the compatibility relation Equation (50) has been experimentally confirmed along the three, independent, pure mode propagation directions in monocrystalline silicon [45,55] and in isotropic vitreous silica [45,56]. The experimental confirmation attests the validity of the derivation leading to equations (48)- (50) and lends support to the analogous derivation leading to equation (46).…”

Section: Derivation Of Radiation Pressure Via Direct Application Of Fsupporting

confidence: 63%

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Acoustic radiation pressure in laterally unconfined plane wave beams

Cantrell

2019

J. Phys. Commun.

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The acoustic radiation pressure in laterally unconfined, plane wave beams in inviscid fluids is derived via the direct application of finite deformation theory for which an analytical accounting is made ab initio that the radiation pressure is established under static, laterally unconstrained conditions, while the acoustic wave that generates the radiation pressure propagates under dynamic (sinusoidal), laterally constrained conditions. The derivation reveals that the acoustic radiation pressure for laterally unconfined, plane waves along the propagation direction is equal to (3/4)〈2K〉, where á ñ K is the mean kinetic energy density of the wave, and zero in directions normal to the propagation direction. The results hold for both Lagrangian and Eulerian coordinates. The value á ñ ( ) / K 3 4 2 differs from the value á ñ K 2 ,traditionally used in the assessment of acoustic radiation pressure, obtained from the Langevin theory or from the momentum flux density in the Brillouin stress tensor. Errors in traditional derivations leading to the Brillouin stress tensor and the Langevin radiation pressure are pointed out and a long-standing misunderstanding of the relationship between Lagrangian and Eulerian quantities is corrected. The present theory predicts a power output from the transducer that is 4/3 times larger than that predicted from the Langevin theory. Tentative evidence for the validity of the present theory is provided from measurements previously reported in the literature, revealing the need for more accurate and precise measurements for experimental confirmation of the present theory.wave. This result differs considerably from the value á ñ K 2 for the radiation pressure obtained from the Langevin theory [29] or from the Brillouin stress tensor [26,27]. In the directions normal to the propagation direction, the radiation pressure is zero for both Lagrangian and Eulerian coordinates.The difference between the present assessment of radiation pressure and that obtained from the Langevin theory or from the Brillouin stress tensor is significant, since the assessment is used to link the radiation force on a target with the power generated by acoustic sources. As pointed out by Beissner [21], the 'measured radiation force must be converted to the ultrasonic power value and this is carried out with the help of theory.' It is generally assumed that for laterally unconfined, plane wave beams the relationship between the acoustic radiation pressure and the energy density for plane waves in the direction of wave propagation is that obtained from the Langevin theory [29] or from the Brillouin stress tensor [26,27]. The present model predicts a transducer output power 4/3 times larger than that predicted from the Langevin theory or from the Brillouin stress tensor. This has considerable implications regarding safety issues for medical transducers, calibrated using radiation pressure.Issenmann et al [52] point out that 'despite the long-lasting theoretical controversies K the Langevin radiation pressure K has been the...

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Section: Derivation Of Radiation Pressure Via Direct Application Of Fsupporting

confidence: 63%

“…where the last equality follows from equation (56). It is interesting to note from equation (57) that for nonlinear waves the total average energy density á ñ E is not exactly equal to á ñ K 2 .…”

Section: Acoustic Radiation Pressure and The Boltzmann-ehrenfest Adiamentioning

confidence: 99%

Acoustic radiation pressure in laterally unconfined plane wave beams

Cantrell

2019

J. Phys. Commun.

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Energy conservation and pulse propagation in an elastic medium with quadratic nonlinearity

Cantrell

Yost

2012

Journal of Applied Physics

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A sinusoidal acoustic tone-burst launched into an elastic medium with weak quadratic nonlinearity is shown to generate a right-triangular static displacement pulse, when conservation of energy is properly imposed on the model equations. The right-triangular displacement profile is shown to occur whether the tone-burst is modeled with displacement-prescribed or traction-prescribed boundary conditions. Definitive experimental evidence is presented confirming the model predictions. Theoretical arguments and experimental evidence are also presented showing that, contrary to the assertion of Qu et al. [J. Acoust. Soc. Am. 131, 1827 (2012)], the right-triangular shape is not in violation of causality.

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Envelope solitons in acoustically dispersive vitreous silica

Cited by 2 publications

References 19 publications

Acoustic radiation pressure in laterally unconfined plane wave beams

Acoustic radiation pressure in laterally unconfined plane wave beams

Energy conservation and pulse propagation in an elastic medium with quadratic nonlinearity

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