×

Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. (English) Zbl 1305.74047

The authors consider reflection and transmission of compression and shear waves at elastic interfaces having material properties in an infinite second gradient material. They use variational principle to deduce general balance equations and jump conditions at the elastic interface. These equations include effect of surface inertial and elastic properties. The results are applied to a simplified one-dimensional model in axial symmetric case.

MSC:

74J20 Wave scattering in solid mechanics
74E99 Material properties given special treatment
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/0020-7683(65)90006-5
[2] Nicolson MM, Proc R Soc London Ser A 228 pp 490– (1955) · Zbl 0064.23603
[3] Gouin H, C R Acad Sci Ser II 306 pp 755– (1988)
[4] Gurtin ME, Int J Solids Struct 14 pp 431– (1975) · Zbl 0377.73001
[5] Gurtin ME, Arch Ration Mech Anal 57 pp 291– (1979)
[6] Steigmann DJ, Proc R Soc London Ser A 453 pp 853– (1997) · Zbl 0938.74014
[7] Ogden RW, J Mech Phys Solids 50 pp 1869– (2002) · Zbl 1062.74021
[8] dell’Isola F, Ric Mater 35 pp 325– (1986)
[9] dell’Isola F, Arch Mech 45 pp 333– (1993)
[10] dell’Isola F, Int J Eng Sci 25 pp 1469– (1987) · Zbl 0629.73006
[11] de Gennes PG, J Phys Lett 42 pp 377– (1981)
[12] de Gennes PG, Capillarity and wetting phenomena: drops, bubbles, pearls, waves (2004) · Zbl 1139.76004
[13] Cahn JW, J Chem Phys 28 pp 258– (1958)
[14] Cahn JW, J Chem Phys 31 pp 688– (1959)
[15] Rowlinson JS, Molecular theory of capillarity (1982)
[16] Bongiorno V, J Colloid Interface Sci 57 pp 462– (1976)
[17] DOI: 10.1177/1081286503008001658 · Zbl 1039.74028
[18] Gatignol R, J Mec Theor Appl pp 225– (1986)
[19] Seppecher P, Ann Phys 13 pp 13– (1988)
[20] Seppecher P, Etude d’une modelisation des zones capillaires fluides: interfaces et lignes de contact (1987)
[21] dell’Erba R, Continuum Mech Thermodyn 11 pp 89– (1999) · Zbl 0946.76101
[22] DOI: 10.1016/0020-7225(87)90023-1 · Zbl 0624.73001
[23] dell’Isola F, Int J Eng Sci 27 pp 1069– (1989) · Zbl 0693.76106
[24] dell’Isola F, C R Acad Sci Ser IIb 321 pp 303– (1995)
[25] dell’Isola F, Meccanica 32 pp 33– (1997) · Zbl 0877.73055
[26] dell’Isola F, Int J Solids Struct 46 pp 3150– (2009) · Zbl 1167.74393
[27] dell’Isola F, Z Angew Math Phys 63 pp 1119– (2012) · Zbl 1330.76016
[28] Casal P, Cahier du groupe Français de rhéologie. CNRS VI 3 pp 31– (1961)
[29] Casal P, C R Acad Sci Ser II 300 pp 231– (1985)
[30] Casal P, Int J Eng Sci 32 pp 1553– (1994) · Zbl 0899.76357
[31] Casal P, C R Seances Acad Sci Ser A 274 pp 1571– (1972)
[32] Casal P, J Mec Theor Appl 7 (6) pp 689– (1988)
[33] Casal P, C R Acad Sci Ser II 306 pp 99– (1988)
[34] Gouin H, C R Acad Sci Ser II 305 pp 833– (1987)
[35] Gouin H, Physicochem Hydrodyn 174 pp 667– (1986)
[36] Gouin H, Meccanica 30 pp 305– (1995) · Zbl 0837.76030
[37] Germain P, J Mec 12 pp 235– (1973)
[38] DOI: 10.1137/0125053 · Zbl 0273.73061
[39] Korteweg DJ, Arch Neerl Sci Exactes Ser II 6 pp 1– (1901)
[40] DOI: 10.1016/0093-6413(95)00052-S · Zbl 0845.76006
[41] Casal P, Ann Phys 13 pp 3– (1988)
[42] Daher N, Acta Mech 60 pp 217– (1986) · Zbl 0594.73004
[43] Seppecher P, Les Fluides de Cahn–Hilliard (1996)
[44] Seppecher P, Continuum thermomechanics: The art and science of modeling matter’s behaviour pp 43– (2000)
[45] Seppecher P, C R Acad Sci Ser II 309 pp 497– (1989)
[46] DOI: 10.1007/s004190050192 · Zbl 0920.73111
[47] dell’Isola F, Arch Appl Mech 68 pp 1– (1998) · Zbl 0908.73067
[48] Rosi G, J Vib Control 19 (5) pp 658– (2013) · Zbl 06647692
[49] Rosi G, Eur J Mech A-Solids 29 (5) pp 859– (2010)
[50] Sciarra G, Int J Solids Struct 44 pp 6607– (2007) · Zbl 1166.74341
[51] Sciarra G, Continuum Mech Thermodyn 13 pp 287– (2001) · Zbl 1134.74365
[52] Sciarra G, Int J Geomech 5 pp 233– (2005)
[53] Sciarra G, J Mech Math Struct 3 pp 507– (2008)
[54] Madeo A, Continuum Mech Therm 25 (1) pp 173– (2013) · Zbl 1343.76068
[55] Placidi L, Eur J Mech, A/Solids 2008 (27) pp 582– (2008) · Zbl 1146.74012
[56] dell’Isola F, C R Acad Sci Ser IIb 320 pp 211– (1995)
[57] dell’Isola F, Int J Eng Sci 27 pp 1053– (1989) · Zbl 0695.76048
[58] Seppecher P, Int J Eng Sci 34 pp 977– (1996) · Zbl 0899.76042
[59] Seppecher P, Eur J Mech B 12 pp 69– (1993)
[60] DOI: 10.1002/zamm.201100022 · Zbl 1247.74031
[61] Carcaterra A, J Acoust Soc Am 121 pp 1971– (2007)
[62] Carcaterra A, Phys Rev E 84 pp 011121– (2011)
[63] DOI: 10.1098/rspa.2008.0530 · Zbl 1186.74019
[64] Madeo A, C R Mec 340 pp 575– (2012)
[65] van Kampen NG, Phys Rev 135 pp A362– (1964)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.