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| Titel |
The quasi-static approximation of the spring-slider motion |
| VerfasserIn |
M. E. Belardinelli, E. Belardinelli |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 3, no. 3 ; Nr. 3, no. 3, S.143-149 |
| Datensatznummer |
250001019
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| Publikation (Nr.) |
 copernicus.org/npg-3-143-1996.pdf |
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| Zusammenfassung |
| The spring-slider is a simple
dynamical system
consisting in a massive block sliding with friction and
pulled
through a spring at a given velocity. Understanding
the block
motion is fundamental for studying more complex
phenomena of
frictional sliding, such as the seismogenic fault
motion. We
analyze the dynamical properties of the system,
subject to
rate- and state-dependent friction laws and forced
at a
constant load velocity. In particular we study the
limits
within which the quasi-static model can be used. The
latter
model approximates the complete model of the system
without
taking into account the inertia effects. The
system parameters are here found to be grouped into three characteristic times of the three dynamics present in the
complete
model. A necessary condition for the
quasi-static
approximation to hold is that the characteristic time
of the
inertial equation is much smaller than the
other two
characteristic times. We have studied a modification
of one
of the classical forms of the rate- and state-dependent
friction laws. Subsequently we have developed a
linear
analysis in the neighbourhood of the equilibrium point
of the
system. For the quasi-static model we rigorously
found, by
means of a nonlinear analysis, a supercritical
Hopf
bifurcation, a dynamical property of the complete
model. The
classical form of the friction laws can be obtained
as a
particular case of the one we considered, but
fails to
preserve the Hopf bifurcation in the
quasi-static
approximation. We conclude that to have a good
quasi-static
approximation of the system, even in nonlinear
conditions, the
form of the friction laws considered is a critical
factor. |
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