Advertisement

Acta Mechanica

, Volume 13, Issue 1–2, pp 11–20 | Cite as

Wave propagation in a micropolar elastic half-space

  • T. Ariman
Contributed Papers

Summary

Wave propagation in an infinite micropolar elastic half space and the reflection of plane longitudinal displacement waves from a fixed flat surface of a micropolar elastic half space are investigated. Reflection laws and amplitude ratios are presented for specific cases. New propagating and reflected waves are found in addition to the classical ones.

Keywords

Reflection Dynamical System Fluid Dynamics Wave Propagation Transport Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a1,a2,A3x,A4x

amplitudes

a, b

complex constants

A, B

complex constant vectors

fl

body force per unit mass

ik

unit cartesian base vectors

j

microinertia

k

wave number

l

wavelength

mkl

couple stress tensor

n

unit vector normal to the surface

r

position vector

t

time

tkl

stress tensor

U, Φ

vector potentials

v

phase velocity

vk

velocity vector =\(\dot u_k\)

lk

body couple per unit mass

xk

rectangular cartesian coordinates

L

surface of a body

V

volume element

α, β, γ, λ, μ, ϰ

elastic constants

σkl

Kronecker delta

vector operator =\(i_k \frac{\partial }{{\partial x_k }}\)

vr

microrotation velocity vector =φ r

ϕk

microrotation vector

ε

internal energy density

ϱ

mass density

ω

angular frequency

θi

reflection angles

Wellenausbreitung im mikropolaren elastischen Halbraum

Zusammenfassung

Die Wellenausbreitung in einem unendlichen mikropolaren elastischen Hellbraun und die Reflexion von ebenen Longitudinalwellen an der ruhenden ebenen Oberfläche dieses Halbraumes werden untersucht. Reflexionsgesetze und Amplitudenverhältnisse werden für Spezialfälle angegeben. Zusätzlich zu den klassischen werden neue sich ausbreitende bzw. reflektierte Wellen gefunden.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Eringen, A. C., andE. C. Suhubi: Nonlinear Theory of Simple Microelastic Solids I, Int. J. Engng. Sci.,2, 189–203 (1964).Google Scholar
  2. [2]
    Suhubi, E. S., andA. C. Eringen: Nonlinear Theory of Simple Microelastic Solids II. Int. J. Engng. Sci.,2, 389–404 (1964).Google Scholar
  3. [3]
    Eringen, A. C.: Mechanics of Micromorphic Materials. Proc. XI. Int. Congr. of Applied Mech., Munich, Germany, p. 131–138 (1966).Google Scholar
  4. [4]
    Eringen, A. C.: Linear Theory of Micropolar Elasticity. J. Math. and Mech.15, 909–924 (1966).Google Scholar
  5. [5]
    Eringen, A. C.: Linear Theory of Micropolar Viscoelasticity. Int. J. Engng. Sci.5, 191–204 (1967).Google Scholar
  6. [6]
    Eringen, A. C.: Theory of Micropolar Plates. J. Appl. Math. Phys. (ZAMP)18, 12–30 (1967).Google Scholar
  7. [7]
    Eringen, A. C.: Theory of Micropolar Elasticity. ONR Tech. Rep. No.1, Princeton University, June 1967.Google Scholar
  8. [8]
    Kaloni, P. N., andT. Ariman: Stress Concentrations in Micropolar Elasticity. J. Appl. Math. Phys. (ZAMP)18, 136–141 (1967).Google Scholar
  9. [9]
    Smith, A. C.: Deformations of Micropolar Elastic Solids. Int. J. Engng. Sci.5, 637–651 (1967).Google Scholar
  10. [10]
    Ariman, T.: On Stresses Around a Circular Hole in Micropolar Elasticity. Acta Mech.4 216–229 (1967).Google Scholar
  11. [11]
    Ariman, T.: On Circular Micropolar Plates. Ingenieur Archiv17, 156–160 (1968).Google Scholar
  12. [12]
    Ariman, T.: Some Problems in Bending of Micropolar Plates. Bulletin de l'Académie Polonaise des Sciences, séries des sciences techniques, Part I and Part II,16, 295–308 (1968).Google Scholar
  13. [13]
    Sandru, N.: On Some Problems of the Linear Theory of the Asymmetric Elasticity. Int. J. Engng. Sci.4, 81–94 (1967).Google Scholar
  14. [14]
    Claus, W. D., T. R. Tauchert, andT. Ariman: The Linear Theory of Micropolar Thermoelasticity. Int. J. Engng. Sci.6, 37–47 (1968).Google Scholar
  15. [15]
    Askar, A., A. S. Cakmak, andT. Ariman: Theory of Hereditary Micropolar Materials. Int. J. Engng. Sci.6, 283–293 (1968).Google Scholar
  16. [16]
    Hoffman, R. E., andT. Ariman: The Application of Micropolar Mechanics to Composites. Tech. Rep. THEMIS-UND-68-3, December, 1968. Also: Recent Advances in Engineering Science5, p. 385–404. (Eringen, A. C., ed.) Academic Press. 1970.Google Scholar
  17. [17]
    Parfitt, V. R., andA. C. Eringen: Reflection of Plane Waves from the Flat Boundary of a Micropolar Elastic Half-space. General Technology Corporation, NASW-1299, Tech. Rep. No. 8-3, July 1966.Google Scholar
  18. [18]
    Eringen, A. C.: Theory of Micropolar Elasticity. Fracture (Liebowitz, H., ed.)2, p. 621–729. Academic Press. 1962.Google Scholar
  19. [19]
    Roesler, F. C.: Glancing Angle Reflection of Elastic Waves from a Free Boundary. Phil. Mag.46, 517–526 (1955).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • T. Ariman
    • 1
  1. 1.Department of Aerospace and Mechanical Engng.University of Notre DameNotre DameUSA

Personalised recommendations