Summary
Longitudianal wave propagation in a semi-infinite rod is considered, where the medium is nonlinear viscoelastic and under constant initial axial stress, i.e., the rod is undergoing axial creep deformation. The deformation gradient is assumed to be infinitesimal, but the deformation itself may be finite. The constitutive law is taken with stress power functions in the elastic, transient creep and steady creep terms. A wave is generated by a step input in velocity or stress at one end of the rod. It is assumed that the initial stress is much greater than the increment of stress generated by the impact and a perturbation technique is employed. Closed form perturbation stress solutions are obtained for five nonlinear viscoelastic models. Numerical examples are given and discussed.
Zusammenfassung
Es wird die Ausbreitung von Longitudinalwellen in einem halbunendlichen Stab betrachtet. Das Material ist nichtlinear viskoelastisch und befindet sich unter konstanter axialer Anfangsspannung, d. h., der Stab erleidet eine axiale Kriechdeformation. Der Deformationsgradient wird infinitesimal klein angenommen, die Deformation selbst kann aber endlich sein. Die Materialgleichung enthält eine Spannungs-Potenzfunktion im elastischen Teil sowie instationäre und stationäre Kriechanteile. Die Welle wird durch eine Stufenfunktion in der Geschwindigkeit oder Spannung an einem Ende des Stabes erzeugt. Die Anfangsspannung wird groß gegenüber der stoßartig aufgebrachten Spannung angenommen. Zur Lösung wird eine Störungsmethode verwendet. Für fünf nichtlinear viskoelastische Modelle werden geschlossene Lösungen für die Störspannungen erhalten. Numerische Beispiele werden angegeben und diskutiert.
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This research was supported in part (at Buffalo) by the Office of Naval Research under Contract No. Nonr. 4449 (00).
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Cozzarelli, F.A., Tang, S. Longitudinal waves in nonlinear viscoelastic rods under initial axial stress. Acta Mechanica 10, 277–300 (1970). https://doi.org/10.1007/BF01175884
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DOI: https://doi.org/10.1007/BF01175884