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Determination of the Filippov solutions of the nonlinear oscillator with dry friction

In previous papers by Awrejcewicz in 1986 and Narayanan and Jayaraman in
1991, it was claimed that the nonlinear oscillator with dry friction exhibited chaos
for several forcing frequencies. The chaos determination was achieved using the
characteristic exponent of Lyapunov which requires the right-hand side of the differential
equation to be differentiable. With the addition of the dry friction term,
the right-hand side of the equation of motion is not continuous and therefore not
differentiable. Thus this approach cannot be used. The Filippov definition must
be employed to handle the discontinuity in the spatial variable. The behavior of the
nonlinear oscillator with dry friction is studied using a numerical solver which produces
the Filippov solution. The results show that the system is not chaotic; rather
it has a stable periodic limit cycle for at least one forcing frequency. Other forcing
frequencies produce results that do not clearly indicate the presence of chaotic
motion. / Graduation date: 2002
Date04 September 2001
CreatorsMoreland, Heather L.
ContributorsGuenther, Ronald B.
Source SetsOregon State University
Detected LanguageEnglish

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