Abstract
A two-degree-of-freedom oscillator excited by dry friction is considered. The system consists of two masses connected by a linear spring, one of which is connected to a fixed wall by another spring. The second mass is in contact with a driving belt moving at a constant velocity. Coulomb's friction force acts between the mass and the belt. Periodic orbits including stick phases and slip phases, during which the mass in contact with the belt moves faster than the belt, are found analytically. The stability of these “overshooting” orbits is also investigated.
Highlights
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Vibrating systems excited by dry friction are strongly nonlinear, and they are usually modeled as spring-mass oscillators
One of the most popular models of a stick-slip oscillator consists of several masses connected by linear springs, some of the masses are in contact with a driving belt moving at a constant velocity
Summary
The system (Fig. 1) consists of two masses m1 and m2 connected by a linear spring k2. The mass m1 is connected to a fixed wall by another spring k1. A friction force F acts between the mass m2 and the belt. This two-degree-of-freedom oscillator is governed by the following differential system. Where us is the dynamic friction force and ur is the static friction force (0 < us < ur). This model was investigated analytically in Ref.[7] and a more complex model, where both masses m1 and m2 are in contact with the belt, is considered in Refs 2 and 8
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