NASA LogoNTRSNTRS - NASA Technical Reports ServerSearchmore_vertCollectionsAboutNewsHelpLogin Back to ResultsAcoustic Radiation PressureThe theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.Document ID20180002538Acquisition SourceLangley Research CenterDocument TypeTechnical Memorandum (TM)AuthorsCantrell, John H.*(NASA Langley Research Center Hampton, VA, United States)*Date AcquiredApril 24, 2018Publication DateApril 1, 2018Subject CategoryFluid Mechanics And ThermodynamicsAcousticsReport/Patent NumberNASA/TM-2018-219806L-20907NF1676L-29332Funding Number(s)WBS: WBS 826611.04.07.02Distribution LimitsPublicCopyrightWork of the US Gov. Public Use Permitted.KeywordsFinite deformation theoryAdiabatic invarianceLaterally confined and unconfined wavesAcoustic radiation pressureAvailable DownloadsNameType20180002538.pdfSTIcloud_downloadcontent_copyvisibilityRelated RecordsThere are no records associated with this record.visibility_offNo Preview Available
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