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Wave propagation in a micropolar elastic half-space

Wellenausbreitung im mikropolaren elastischen Halbraum

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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.

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.

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Abbreviations

a 1,a 2,A 3x ,A 4x :

amplitudes

a, b :

complex constants

A, B :

complex constant vectors

f l :

body force per unit mass

i k :

unit cartesian base vectors

j :

microinertia

k :

wave number

l :

wavelength

m kl :

couple stress tensor

n :

unit vector normal to the surface

r :

position vector

t :

time

t kl :

stress tensor

U, Φ:

vector potentials

v :

phase velocity

v k :

velocity vector =\(\dot u_k\)

l k :

body couple per unit mass

x k :

rectangular cartesian coordinates

L :

surface of a body

V :

volume element

α, β, γ, λ, μ, ϰ:

elastic constants

σ kl :

Kronecker delta

∇:

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

v r :

microrotation velocity vector =φ r

ϕk :

microrotation vector

ε:

internal energy density

ϱ:

mass density

ω:

angular frequency

θ i :

reflection angles

References

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engng., University of Notre Dame, Notre Dame, Ind., USA

    T. Ariman

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  1. T. Ariman
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Ariman, T. Wave propagation in a micropolar elastic half-space. Acta Mechanica 13, 11–20 (1972). https://doi.org/10.1007/BF01179655

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  • DOI: https://doi.org/10.1007/BF01179655

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