Summary
A study of small amplitude, plane, longitudinal waves in a nonlinear, viscoelastic material is presented. The mechanical behavior of the material is described by the use of state variables and the associated differential equations. In particular, we examine the response of a half-space of viscoelastic material which is subjected to a small constant velocityu(0,t)=ε, ε≪1 at the surface of the halfspace for timet>0. This behavior is analyzed by the use of matched asymptotic expansions in the plane of characteristic coordinates. With the use of these matched asymptotic expansions, the nature of the waves in the near and far fields are discussed. A particular advantage of this method is that wave velocities in the far field can be corrected to second and higher orders. We show that the far field wave is a steady state wave to first order, but that its higher order behavior is transient.
Zusammenfassung
Eine Untersuchung der im Titel genannten Wellen wird angegeben. Das mechanische Verhalten des Werkstoffes wird unter Verwendung innerer Zustandsvariablen durch Differentialgleichungen beschrieben. Insbesondere untersucht wird das Verhalten eines Halbraumes aus viskoelastischem Material, dessen Oberfläche sich für Zeitent>0 mit einer kleinen konstanten Geschwindigkeitu(0,t)=ε, ε≪1, bewegt. Das Verhalten wird untersucht unter Verwendung von asymptotischen Entwicklungen in der Ebene der charakteristischen Koordinaten. Dadurch wird die Art der Wellen im Nah- und Fernfeld erläutert. Eine besonderer Vorteil dieser Methode ist die Möglichkeit von Korrekturen zweiter und höherer Ordnung beim Fernfeld. Gezeigt wird, daß die Fernfeldwelle erster Ordnung stationär ist, nicht jedoch die höherer Ordnung.
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Blake, T.R. Plane longitudinal waves of small amplitude in a nonlinear viscoelastic material. Acta Mechanica 17, 211–226 (1973). https://doi.org/10.1007/BF01183756
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DOI: https://doi.org/10.1007/BF01183756