Optimal bounds for attenuation of elastic waves in porous fluid-saturated media
Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Glubokovskikh, Stanislav [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: © Acoustical Society of America |
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| Systematik: |
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| Übergeordnetes Werk: |
Enthalten in: The journal of the Acoustical Society of America - Melville, NY : AIP, 1929, 142(2017), 5, Seite 3321-3329 |
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| Übergeordnetes Werk: |
volume:142 ; year:2017 ; number:5 ; pages:3321-3329 |
| Links: |
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| DOI / URN: |
10.1121/1.5011748 |
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OLC1999239741 |
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| 520 | |a Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. | ||
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10.1121/1.5011748 doi PQ20171228 (DE-627)OLC1999239741 (DE-599)GBVOLC1999239741 (PRQ)s716-9215d5ae7433091a5ce9d8944663f12e5540ea5b611fff4316bea4657cdfe6de0 (KEY)0112299120170000142000503321optimalboundsforattenuationofelasticwavesinporousf DE-627 ger DE-627 rakwb eng 530 DE-600 LING fid EQ 1000: AVZ rvk 33.12 bkl 50.36 bkl Glubokovskikh, Stanislav verfasserin aut Optimal bounds for attenuation of elastic waves in porous fluid-saturated media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. Nutzungsrecht: © Acoustical Society of America Gurevich, Boris oth Enthalten in The journal of the Acoustical Society of America Melville, NY : AIP, 1929 142(2017), 5, Seite 3321-3329 (DE-627)129550264 (DE-600)219231-7 (DE-576)015003663 0001-4966 nnns volume:142 year:2017 number:5 pages:3321-3329 http://dx.doi.org/10.1121/1.5011748 Volltext http://dx.doi.org/10.1121/1.5011748 GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-PHY SSG-OLC-MUS GBV_ILN_59 GBV_ILN_60 GBV_ILN_70 GBV_ILN_120 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2006 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2192 GBV_ILN_2256 GBV_ILN_4219 GBV_ILN_4315 GBV_ILN_4319 GBV_ILN_4700 EQ 1000: 33.12 AVZ 50.36 AVZ AR 142 2017 5 3321-3329 |
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10.1121/1.5011748 doi PQ20171228 (DE-627)OLC1999239741 (DE-599)GBVOLC1999239741 (PRQ)s716-9215d5ae7433091a5ce9d8944663f12e5540ea5b611fff4316bea4657cdfe6de0 (KEY)0112299120170000142000503321optimalboundsforattenuationofelasticwavesinporousf DE-627 ger DE-627 rakwb eng 530 DE-600 LING fid EQ 1000: AVZ rvk 33.12 bkl 50.36 bkl Glubokovskikh, Stanislav verfasserin aut Optimal bounds for attenuation of elastic waves in porous fluid-saturated media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. Nutzungsrecht: © Acoustical Society of America Gurevich, Boris oth Enthalten in The journal of the Acoustical Society of America Melville, NY : AIP, 1929 142(2017), 5, Seite 3321-3329 (DE-627)129550264 (DE-600)219231-7 (DE-576)015003663 0001-4966 nnns volume:142 year:2017 number:5 pages:3321-3329 http://dx.doi.org/10.1121/1.5011748 Volltext http://dx.doi.org/10.1121/1.5011748 GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-PHY SSG-OLC-MUS GBV_ILN_59 GBV_ILN_60 GBV_ILN_70 GBV_ILN_120 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2006 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2192 GBV_ILN_2256 GBV_ILN_4219 GBV_ILN_4315 GBV_ILN_4319 GBV_ILN_4700 EQ 1000: 33.12 AVZ 50.36 AVZ AR 142 2017 5 3321-3329 |
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10.1121/1.5011748 doi PQ20171228 (DE-627)OLC1999239741 (DE-599)GBVOLC1999239741 (PRQ)s716-9215d5ae7433091a5ce9d8944663f12e5540ea5b611fff4316bea4657cdfe6de0 (KEY)0112299120170000142000503321optimalboundsforattenuationofelasticwavesinporousf DE-627 ger DE-627 rakwb eng 530 DE-600 LING fid EQ 1000: AVZ rvk 33.12 bkl 50.36 bkl Glubokovskikh, Stanislav verfasserin aut Optimal bounds for attenuation of elastic waves in porous fluid-saturated media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. Nutzungsrecht: © Acoustical Society of America Gurevich, Boris oth Enthalten in The journal of the Acoustical Society of America Melville, NY : AIP, 1929 142(2017), 5, Seite 3321-3329 (DE-627)129550264 (DE-600)219231-7 (DE-576)015003663 0001-4966 nnns volume:142 year:2017 number:5 pages:3321-3329 http://dx.doi.org/10.1121/1.5011748 Volltext http://dx.doi.org/10.1121/1.5011748 GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-PHY SSG-OLC-MUS GBV_ILN_59 GBV_ILN_60 GBV_ILN_70 GBV_ILN_120 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2006 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2192 GBV_ILN_2256 GBV_ILN_4219 GBV_ILN_4315 GBV_ILN_4319 GBV_ILN_4700 EQ 1000: 33.12 AVZ 50.36 AVZ AR 142 2017 5 3321-3329 |
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10.1121/1.5011748 doi PQ20171228 (DE-627)OLC1999239741 (DE-599)GBVOLC1999239741 (PRQ)s716-9215d5ae7433091a5ce9d8944663f12e5540ea5b611fff4316bea4657cdfe6de0 (KEY)0112299120170000142000503321optimalboundsforattenuationofelasticwavesinporousf DE-627 ger DE-627 rakwb eng 530 DE-600 LING fid EQ 1000: AVZ rvk 33.12 bkl 50.36 bkl Glubokovskikh, Stanislav verfasserin aut Optimal bounds for attenuation of elastic waves in porous fluid-saturated media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. Nutzungsrecht: © Acoustical Society of America Gurevich, Boris oth Enthalten in The journal of the Acoustical Society of America Melville, NY : AIP, 1929 142(2017), 5, Seite 3321-3329 (DE-627)129550264 (DE-600)219231-7 (DE-576)015003663 0001-4966 nnns volume:142 year:2017 number:5 pages:3321-3329 http://dx.doi.org/10.1121/1.5011748 Volltext http://dx.doi.org/10.1121/1.5011748 GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-PHY SSG-OLC-MUS GBV_ILN_59 GBV_ILN_60 GBV_ILN_70 GBV_ILN_120 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2006 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2192 GBV_ILN_2256 GBV_ILN_4219 GBV_ILN_4315 GBV_ILN_4319 GBV_ILN_4700 EQ 1000: 33.12 AVZ 50.36 AVZ AR 142 2017 5 3321-3329 |
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10.1121/1.5011748 doi PQ20171228 (DE-627)OLC1999239741 (DE-599)GBVOLC1999239741 (PRQ)s716-9215d5ae7433091a5ce9d8944663f12e5540ea5b611fff4316bea4657cdfe6de0 (KEY)0112299120170000142000503321optimalboundsforattenuationofelasticwavesinporousf DE-627 ger DE-627 rakwb eng 530 DE-600 LING fid EQ 1000: AVZ rvk 33.12 bkl 50.36 bkl Glubokovskikh, Stanislav verfasserin aut Optimal bounds for attenuation of elastic waves in porous fluid-saturated media 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. Nutzungsrecht: © Acoustical Society of America Gurevich, Boris oth Enthalten in The journal of the Acoustical Society of America Melville, NY : AIP, 1929 142(2017), 5, Seite 3321-3329 (DE-627)129550264 (DE-600)219231-7 (DE-576)015003663 0001-4966 nnns volume:142 year:2017 number:5 pages:3321-3329 http://dx.doi.org/10.1121/1.5011748 Volltext http://dx.doi.org/10.1121/1.5011748 GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-LING SSG-OLC-PHY SSG-OLC-MUS GBV_ILN_59 GBV_ILN_60 GBV_ILN_70 GBV_ILN_120 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2006 GBV_ILN_2011 GBV_ILN_2027 GBV_ILN_2045 GBV_ILN_2192 GBV_ILN_2256 GBV_ILN_4219 GBV_ILN_4315 GBV_ILN_4319 GBV_ILN_4700 EQ 1000: 33.12 AVZ 50.36 AVZ AR 142 2017 5 3321-3329 |
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optimal bounds for attenuation of elastic waves in porous fluid-saturated media |
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Optimal bounds for attenuation of elastic waves in porous fluid-saturated media |
| abstract |
Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. |
| abstractGer |
Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. |
| abstract_unstemmed |
Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions. |
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