Premium
Effects of damping on mode‐coupling instability in friction induced oscillations
Author(s) -
Hoffmann N.,
Gaul L.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310022
Subject(s) - instability , physics , eigenvalues and eigenvectors , classical mechanics , mode coupling , mechanics , coupling (piping) , formalism (music) , control theory (sociology) , computer science , engineering , quantum mechanics , mechanical engineering , art , musical , control (management) , artificial intelligence , visual arts
The mode‐coupling instability has generally been acknowledged as one of the most prominent mechanisms leading to self‐excited oscillations in sliding friction systems. The influence of structural damping on this type of instability mechanism however has not yet been fully clarified. The objective of the present work therefore is to investigate qualitative and quantitative aspects of the mode‐coupling instability in the presence of structural damping, which will be assumed as linear viscous. For the sake of simplicity a two‐degree‐of‐freedom minimal model is set up and analyzed. It is shown that under specific conditions the mode‐coupling instability may be regarded as a viscous instability in the sense that an increase in structural damping may render a stable system unstable. An explanation for this behavior is given by two lines of argument: First a description and explanation is given in terms of eigenvalue‐analysis. Due to the mathematical formality of this approach, the insight gained remains phenomenological. Second, a feedback‐loop formalism is developed that allows a more detailed understanding of the underlying mechanical processes. Based on this formalism, necessary and in sum sufficient conditions for the onset of instability can be deduced and also the role of damping can be clarified.