Wave propagation in heterogeneous materials

著者

    • Kanaun, S. K.
    • Levin, V. M.

書誌事項

Wave propagation in heterogeneous materials

by S.K. Kanaun and V.M. Levin

（Solid mechanics and its applications, v. 150 . Self-consistent methods for composites ; v. 2）

Springer, c2008

大学図書館所蔵 件 / 全2件

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This unique book is dedicated to the application of self-consistent methods to the solution of static and dynamic problems of the mechanics and physics of composite materials. The effective elastic, electric, dielectric, thermo-conductive and other properties of composite materials reinforced by ellipsoidal, spherical multi-layered inclusions, thin hard and soft inclusions, short fibers and unidirected multi-layered fibers are considered. The book contains many concrete results.

目次

  • 1. Introduction
  • Self-consistent methods for scalar waves in composites
  • 2.1 Integral equations for scalar waves in a medium with isolated inclusions
  • 2.2 The effective field method
  • 2.3 The effective medium method
  • 2.3.1 Version I of the EMM
  • 2.3.2 Version I1 of the EMM
  • 2.3.3 Version I11 and nT of the EMM
  • 2.4 Notes
  • Electromagnetic waves in composites and polycrystals
  • 3.1 Integral equations for electromagnetic waves
  • 3.2 Version I of EMM for matrix composites
  • 3.3 One-particle EMM problems for spherical inclusions
  • 3.4 Asymptotic solutions of the EMM dispersion equation
  • 3.5 Numerical solution of the EMM dispersion equation
  • 3.6 Versions I1 and I11 of the EMM
  • 3.7 The effective field method
  • 3.8 One-particle EFM problems for spherical inclusions
  • 3.9 Asymptotic solutions of the EFM dispersion equation
  • 3.9.1 Long-wave asymptotics
  • 3.9.2 Short-wave asymptotics
  • 3.10 Numerical solution
  • 3.11 Comparison of version I of the EMM and the EFM
  • 3.12 Versions I, 11, and I11 of EMM
  • 3.13 Approximate solutions of one-particle problems
  • 3.13.1 Variational formulation of the diffraction problem for an isolated inclusion
  • 3.13.2 Plane wave approximation
  • 3.14 The EFM for composites with regular lattices of spherical inclusions
  • 3.15 Versions I and IV of EMM for polycrystals and granular materials
  • 3.16 Conclusion
  • 3.17 Notes
  • 4. Axial elastic shear waves in fiber reinforced composites
  • 4.1 Integral equations of the problem
  • 4.2 The effective medium method
  • 4.3 The effective field method
  • 4.3.1 Integral equations for the local exciting fields
  • 4.3.2 The hypotheses of the EFM
  • 4.3.3 The dispersion equation of the EFM
  • 4.4 One-particle problems of EMM and EFM
  • 4.4.1 The one-particle problem of the EMM
  • 4.4.2 The one-particle problem of the EFM
  • 4.4.3 The scattering cross-section of a cylindrical fiber
  • 4.4.4 Approximate solution of the one-particle problem in the long-wave region
  • 4.5 Solutions of the dispersion equations in the long-wave region
  • 4.5.1 Long-wave asymptotic solution for EMM
  • 4.5.2 Long-wave asymptotic solution for EFM
  • 4.6 Short-wave asymptotics
  • 4.7 Numerical solutions of the dispersion equations
  • 4.8 Composites with regular lattices of cylindrical fibers
  • 4.9 Conclusion
  • 4.10 Notes
  • 5. Diffraction of long elastic waves by an isolated inclusion in a homogeneous medium
  • 5.1 The dynamic Green tensor for a homogeneous anisotropic medium
  • 5.2 Integral equations for elastic wave diffraction by an isolated inclusion
  • 5.3 Diffraction of long elastic waves by an isolated inclusion
  • 5.4 Diffraction of long elastic waves by a thin inclusion
  • 5.4.1 Thin soft inclusion
  • 5.4.2 Thin hard inclusion
  • 5.5 Diffraction of long elastic waves by a short axisymmetric fiber
  • 5.6 Total scattering cross-sections of inclusions
  • 5.6.1 An isolated inclusion
  • 5.6.2 Long range scattering cross-sections
  • 5.7 Notes
  • 6. Effective wave operator for a medium with random isolated inclusions
  • 6.1 Diffraction of elastic waves by a random set of ellipsoidal inclusions
  • 6.2 The Green function of the effective wave operator
  • 6.3 Velocities and attenuations of long elastic waves in matrix composites
  • 6.4 Long elastic waves in composites with random thin inclusions
  • 6.4.1 Isotropic elastic medium with random crack-like inclusions
  • 6.4.2 Isotropic elastic medium with a random set of hard disks
  • 6.5 Long elastic waves in composites with short hard fibers
  • 6.5.1 Random sets of fibers homogeneously distributed over orientations
  • 6.5.2 Random set of fibers of the same orientation
  • 6.6 Notes
  • 7. Elastic waves in a medium with spherical inclusions
  • 7.1 Version I of the EMM for elastic waves
  • 7.2 The one-particle problems of EMM
  • 7.2.1 Diffraction of a plane monochromatic wave by an isolated spherical inclusion
  • 7.2.2 An approximate solution of the one-particle problems in the long-wave region
  • 7.3 The dispersion equations of the EMM
  • 7.3.1 The EMM dispersion equation for longitudinal waves
  • 7.3.2 The EMM dispersion equation for transverse waves

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