- PII
- 10.31857/S0032823524050069-1
- DOI
- 10.31857/S0032823524050069
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 88 / Issue number 5
- Pages
- 738-744
- Abstract
- Body waves in an isotropic elastic space propagating along the line of action of a concentrated force singularity are analyzed. It is shown that along the line of action of the force singularity, in addition to the P-wave, the S-wave also propagates. The erroneous statements found in a number of publications about the absence of S-waves on the line of action of the force singularity are noted.
- Keywords
- объемная волна изотропия силовая особенность представление Гельмгольца девиатор деформаций
- Date of publication
- 01.05.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 28
References
- 1. Nakano H. On Rayleigh waves // Japan J. Astron.&Geophys. 1925. V. 2. P. 233–326.
- 2. Nakano H. Some problems concerning the propagations of the disturbances in and on semi-infinite elastic solid // Geophys. Mag. 1930. V. 2. P. 189–348.
- 3. Fuchs K., Müller G. Computation of synthetic seismograms with the reflectivity method and comparison with observations // Geophys. J.R. Astr. Soc. 1971. V. 23. P. 417–433.
- 4. Kennett B.L.N., Kerry N.J., Woodhouse J.H. Symmetries in the reflection and transmission of elastic waves // Geophys. J.R. Astr. Soc. 1978. V. 52. P. 215–230.
- 5. Wang, D. et al. Ground surface response induced by shallow buried explosions // Earthquake Eng.&Eng. Vib. 2014. V. 13. P. 163–169.
- 6. Cagniard L. Reflexion et Refraction des Ondes Seismiques Progressives. Paris: Gauthier-Villard, 1939.
- 7. Lapwood E.R. The disturbance due to a line source in a semiinfinite elastic medium // Phil. Trans. R. Soc. London, Ser. A. 1949. V. 242. P. 63–100.
- 8. Pekeris C.L. The seismic buried pulse // Proc. Nat. Acad. Sci. 1955. V. 41. P. 629–639.
- 9. Garvin W.W. Exact transient solution of the buried line source problem // Proc. Roy. Soc. A. 1956. V. 234. P. 528–541.
- 10. Pekeris C.L., Lifson H. Motion of the surface of a uniform elastic half-space produced by a burried pulse // J. Acoust. Soc. Am. 1957. V. 29. P. 1233–1238.
- 11. Ewing W.M., Jardetzky W.S., Press F. Elastic Waves in Layered Media. New York: McGraw-Hill, 1957.
- 12. Payton R.G. Epicenter motion of an elastic half-space due to buried stationary and moving line sources // Int. J. Solids Struct. 1968. V. 4. P. 287–300.
- 13. Norwood F.R. Similarity solutions in plane elastodynamics // Int. J. Solids Struct. 1973. V. 9(7). P. 789–803.
- 14. Johnson L.R. Green’s function for Lamb’s problem // Geophys. J.R. Astron. Soc. 1974. V. 37. P. 99–131.
- 15. Payton R.G. Epicenter motion of a transversely isotropic elastic half-space due to a suddenly applied buried point source // Int. J. Engng. Sci. 1979. V. 17. P. 879–887.
- 16. Poruchikov V.B. Methods of the Classical Theory of Elastodynamics. Berlin: Springer. 1993.
- 17. Willams D.P., Craster R.V. Cagniard-de Hoop path perturbations with applications to nongeometric wave arrivals // J. Eng. Math. 2000. V. 37. P. 253–272.
- 18. Sanchez-Sesma F, Iturraran-Viveros U. The classic Garvin’s problem revisited // Bull. Seismol. Soc. Am. 2006. V. 96(4A). P. 1344–1351.
- 19. Sanchez-Sesma F, Iturraran-Viveros U., Kausel E. Garvin’s generalized problem revisited // Soil Dyn. Earthquake Eng. 2013. V. 47. P. 4–15.
- 20. Feng X., Zhang H. Exact closed-form solutions for Lamb’s problem // Geophys. J. Int. 2018. V. 214. P. 444–459.
- 21. Lamb H. On the propagation of tremors over the surface of an elastic solid // Philos. Trans. Roy. Soc. London A. 1904. V. 203. P. 1–42.
- 22. Kuznetsov S.V. “Forbidden” planes for Rayleigh waves // Quart. Appl. Math. 2002. V. 60. P. 87–97.
- 23. Kravtsov A.V. et al. Finite element models in Lamb’s problem // Mech. Solids. 2011. V. 46. P. 952–959.
- 24. Kuznetsov S.V. Seismic waves and seismic barriers // Acoust. Phys. 2011. V. 57. P. 420–426.
- 25. Terentjeva E.O. et al. Planar internal Lamb problem: Waves in the epicentral zone of a vertical power source // Acoust. Phys. 2015. V. 61. P. 356–367.
- 26. Il’yasov K.K. et al. Exterior 3D Lamb problem: Harmonic load distributed over a surface // Mech. of Solids. 2016. V. 51. P. 39–45.
- 27. Li S. et al. Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers // Comp. Geotech. 2021. V. 131. Paper 103808.
- 28. Dai Y., Yan S., Zhang B. Acoustic field excited by single force with arbitrary direction in semi-infinite elastic space // Acoust. Phys. 2019. V. 65. P. 235–245.
- 29. Dai Y., Yan S., Zhang B. Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid // Chinese Phys. B. 2020. V. 29. Paper 034304.
- 30. Dai Y., Yan S., Zhang B. Research on ultrasonic multi-wave focusing and imaging method for linear phased arrays // Chinese Phys. B. 2021. V. 30, Paper 074301.
- 31. Auld B.A. Acoustic Fields and Waves in Solids. Malabar (Florida): Krieger Pub., 1990.
- 32. Gurtin M.E. The linear theory of elasticity // in: Linear Theories of Elasticity and Thermoelasticity / Ed. by Truesdell C. Berlin;Heidelberg: Springer., 1973.
- 33. Goldstein R.V. et al. The modified Cam-Clay (MCC) model: cyclic kinematic deviatoric loading // Arch. APl. Mech. 2016. V. 86. P. 2021–2031.
- 34. Pao Y.-H., Gajewski R.R. The generalized ray theory and transient responses of layered elastic solids // Phys. Acoust. 1977. V. 13. P. 183–265.
- 35. Kupradze V.D. The Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. Amsterdam: North-Holland, 1979.
- 36. Ilyashenko A.V. et al. Theoretical aspects of applying Lamb waves in nondestructive testing of anisotropic media // Russ. J. Nondestruct. Test. 2017. V. 53. P. 243–259.
- 37. Kuznetsov S.V. Love waves in stratified monoclinic media // Quart. Appl. Math. 2004. V. 62. P. 749–766.
- 38. Kuznetsov S.V. Love waves in layered anisotropic media // JAMM. 2006. V. 70. P. 116–127.