Abstract
The secular equation is obtained for small amplitude waves propagated in an arbitrary direction in a body of incompressible isotropic elastic material subjected to a pure homogeneous deformation. Conditions are obtained that the wave speeds be real.
Zusammenfassung
Es wird die Säkulargleichung für Wellen kleiner Amplitude gewonnen, welche sich in beliebiger Richtung in einem inkompressiblen isotropen elastischen Material fortpflanzen, das einer reinen homogenen Deformation unterworfen ist. Es werden Bedingungen dafür aufgestellt, dass die Fortpflanzungsgeschwindigkeiten reell sind.
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References
K. N. Sawyers andR. S. Rivlin, Int. J. Solids Structures9, 607 (1973).
M. Baker andJ. L. Ericksen, J. Washington Acad. Sciences44, 33 (1954).
K. N. Sawyers andR. S. Rivlin, Int. J. Solids Structures10, 483 (1974).
J. L. Ericksen, J. Rational Mech. Anal.2, 141 (1953).
D. V. Widder,Advanced Calculus, Prentice Hall, New York (1947).
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Sawyers, K.N., Rivlin, R.S. On the speed of propagation of waves in a deformed elastic material. Journal of Applied Mathematics and Physics (ZAMP) 28, 1045–1057 (1977). https://doi.org/10.1007/BF01601672
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DOI: https://doi.org/10.1007/BF01601672