A Contribution on Forced Periodic Oscillations With Piecewise Linear and Constant Damping

[+] Author and Article Information
D. Karius

MTG Marinetechnik GmbH, Hamburg, Federal Republic of Germany

J. Vib., Acoust., Stress, and Reliab 107(4), 383-391 (Oct 01, 1985) (9 pages) doi:10.1115/1.3269277 History: Received June 03, 1985; Online November 23, 2009


In control system design and precision mechanics it is important to know the precise motion of excited or self-excited vibration under the influence of dry friction. In this paper, the motion of such a nonlinear oscillator is analyzed with the aid of pointmappings. As an example, a nonlinear function of damping dependent on the velocity can be approximated by piecewise linear functions. For this example, the stability of periodic solutions of the type q (t+T/2) = −q(t), (T = period, t = time), is discussed. The case of “critical stability” leads to potential points of bifurcation (branching-off solutions) which are investigated. Calculated examples are compared with experiments.

Copyright © 1985 by ASME
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