0000000001206095
AUTHOR
M. A. Kiseleva
Drilling Systems: Stability and Hidden Oscillations
There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis, which may lead to unreliable results. Nowadays, advances in computer engineering allow for simulations of complex dynamical systems in order to obtain information on the behavior of their trajectories. However, this simple approach based on construction of trajectories using numerical integration of differential equations describing dynamical systems turned out to be quite limited for investigation of stability and oscillations of these s…
Hidden Oscillations in Electromechanical Systems
In this paper an electromechanical system with two different types of motor is considered. It is shown that during the spin-up, the system with DC motor may experience unwanted vibration—the Sommerfeld effect. This is a well-known effect when the motor of electromechanical system gets stuck near the resonance zone instead of reaching its nominal power. The absence of this effect is demonstrated in the system with synchronous motor. Nowadays, there are many works devoted to the study of this effect in various systems. Here we discuss the Sommerfeld effect from the point of view of localization of the so-called hidden oscillations.
Theory of Differential Inclusions and Its Application in Mechanics
The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work, three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torqu…