Engelbrecht, Jüri; Braun, Manfred:
Nonlinear wave phenomena and nonlocality
1997
In: Proceedings of the Estonian Academy of Sciences, Physics - Mathematics, Jg. 46 (1997), Heft 1/2, S. 41 - 47
Artikel/Aufsatz in Zeitschrift / Fach: Maschinenbau
Titel:
Nonlinear wave phenomena and nonlocality
Autor(in):
Engelbrecht, Jüri; Braun, Manfred im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen
Erscheinungsjahr
1997
Erschienen in:
Proceedings of the Estonian Academy of Sciences, Physics - Mathematics, Jg. 46 (1997), Heft 1/2, S. 41 - 47
ISSN

Abstract:

The paper gives a brief overview of nonlocal theories in solid mechanics from the viewpoint of wave motion. The influence of two essential qualities of solids - nonlocality and nonlinearity - is discussed. The effects of microstructure are analysed in order to understand their role in nonlocal theories. Various models are specified on the level of one-dimensional unidirectional motion in order to achieve mathematical clarity of interpreting physical phenomena. Three main types of evolution equations are shown to govern deformation waves under such assumptions. Based on the dispersion analysis, weak, true, and strong nonlocality are distinguished.