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Polarization of the longitudinal Pochhammer-Chree waves

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The exact solutions of the linear Pochhammer-Chree equation for propagating harmonicwaves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersionequation for longitudinal axially symmetric modes is performed. Analytical expressionsfor displacement fields are obtained. Variation of wave polarization on the free surfacedue to variation of Poisson's ratio and circular frequency is analyzed. It is observed thatat the phase speed coinciding with the bulk shear wave speed all the components of thedisplacement eld vanish, meaning that no longitudinal axisymmetric Pochhammer-Chree wave can propagate at this phase speed.
Rocznik
Strony
1329--1336
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Moscow State University of Civil Engineering, 26 Yaroslavscoe sh., Moscow, 117526, Russia
  • Institute for Problems in Mechanics, 101 Prosp. Verndskogo, Moscow, 129526, Russia
Bibliografia
  • [1] Bakhvalov, N. S.: Homogenized characteristics of bodies with periodic structure (in Russian), Dokl. AN USSR, 218, 1046–1048, 1974.
  • [2] Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic analysis for periodic structures, North-Holland Publ., Amsterdam, 1978.
  • [3] Sanchez-Palencia, E.: Homogenization method for the study of composite media, Asymptotic Analysis, II, 192–214, 1983.
  • [4] Nemat-Nasser, S., Iwakuma, T. & Hejazi, M.: On composite with periodic microstructure, Mech. Mater., 1, 239–267, 1982.
  • [5] Nemat-Nasser, S., Taya, M.: On effective moduli of an elastic body containing periodically distributed voids, Quart. Appl. Math., 39, 43–59, 1981.
  • [6] Nemat-Nasser, S., Taya, M.: On effective moduli of an elastic body containing periodically distributed voids: comments and corrections, Quart. Appl. Math., 43, 187–188, 1985.
  • [7] Sangani, S., Acrivos, A.: Slow flow through a periodic array of spheres, Int. J. Mul- tiphase Flow, 8, 343–360, 1982.
  • [8] Sangani, S., Lu, W.: Elastic coefficients of composites containing spherical inclusions in a periodic array, J. Mech. Phys. Solids, 35, 1–21, 1987.
  • [9] Hasimoto, H.: On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech., 5, 317–328, 1959.
  • [10] Nunan, K. C., Keller, J. B.: Effective elasticity tensor of a periodic composite, J. Mech. Phys. Solids, 32, 259–280, 1984.
  • [11] Kuznetsov, S. V.: Periodic fundamental solutions for anisotropic media (in Russian), Izv. RAN. MTT., 4, 99–104, 1991.
  • [12] Kuznetsov, S. V.: Effective elasticity tensors for dispersed composites (in Russian), Prikl. Matem. Mech., 57, 103–109, 1993.
  • [13] Kuznetsov, S. V.: Porous media with internal pressure (in Russian), Izv. RAN. MTT., 6, 22–28, 1993.
  • [14] Kuznetsov, S. V.: Microstructural stresses in porous media (in Russian), Prikl. Mech., 27, 23–28, 1991.
  • [15] Kuznetsov, S. V.: Wave scattering in porous media (in Russian), Izv. RAN. MTT., 3, 81–86, 1995.
  • [16] Bose, S. K., Mal, A. K.: Longitudinal shear waves in a fiber-reinforced composite, Int. J. Solids Struct., 9, 1075–1085, 1979.
  • [17] Datta, S. K.: Diffraction of plane elastic waves by ellipsoidal inclusions, J. Acoust. Soc. Am., 61, 1432–1437, 1977.
  • [18] Sadina, F. J., Willis, J. R.: A simple self-consistent analysis of wave propagation in particulate composites, Wave Motion, 10, 127–142, 1988.
  • [19] Piau, M. Attenuation of a plane compressional wave by a random distribution in thin circular cracks, Int. J. Eng. Sci., 17, 151–167, 1979.
  • [20] Willis, J. R.: A polarization approach to the scattering of elastic waves – II. Multiple scattering from inclusions, J. Mech. Phys. Solids, 28, 307–327, 1980.
  • [21] Gubernatis, J. E.: Long-wave approximations for the scattering of elastic waves from flaws with applications to ellipsoidal voids and inclusions, J. Appl. Phys., 50, 4046–4058, 1979.
  • [22] Gubernatis, J. E., Domani, E. & Krumhasl, J. A.: Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials, J. Appl. Phys., 48, 2804–2811, 1977.
  • [23] Berdichevskij, V. L.: Spatial homogeneous of periodic structures (in Russian), Dokl. AN SSSR, 222, 1975, 565–567.
  • [24] Waterman, P. C.: Matrix theory of elastic wave scattering, J. Acoust. Soc. Am., 60, 567–580, 1976.
  • [25] Ruschitskij, J. J., Ostrakov, I. A.: Distortion of plane harmonic wave in a composite material (in Russian), Dokl. AN USSR, 11, 51–54, 1991.
  • [26] Kuznetsov, S. V.: Direct boundary integral equation method in the theory of elasticity, Quart. Appl. Math., 53, 1–8, 1995.
  • [27] Liu F., Liu, Z.: Elastic waves scattering without conversion in metamaterials with simultaneous zero Indices for longitudinal and transverse waves, Phys. Rev. Lett., 115, 1–12, 2015.
  • [28] Liu, F. et al.: Scattering of waves by three-dimensional obstacles in elastic metamaterials with zero index, Phys. Rev., B 94, 1–10, 2016.
  • [29] Caspani, L. et al.: Enhanced nonlinear refractive index in ε-near-zero materials, Phys. Rev. Lett., 116, 1–5, 2016.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7f3ea0ab-e261-44e7-8266-468d8517301b
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