Sources of Harmonic Force and Speed in Mechatronic Automatic Systems

Abstract

To study resonance and near-resonance phenomena, a symbolic (complex) method was used, which makes it possible to significantly increase productivity, simplify and formalize mathematical transformations. Parallel and sequential connections of elements of a mechanical system with a source of harmonic force or a source of harmonic speed as a source of external mechanical harmonic action are considered. The analytical descriptions of resonance in theoretical mechanics courses correspond to parallel connection. There are devices, in a satisfactory approximation, capable of performing the functions of sources of force and sources of speed. The source of harmonic speed can be a crank-yoke drive and a flywheel with a large moment of inertia. The source of the harmonic force can be the rod of the pneumatic cylinder, the cavity of which communicates with the cavity of another pneumatic cylinder, the diameter of which is immeasurably higher than that of the first, and the piston performs harmonic oscillations. The mechanical harmonic influences described in the courses of theoretical mechanics correspond to the source of the force. Four modes are described — resonances and antiresonances of forces and velocities. The use of the symbolic (complex) method has significantly simplified the study of resonance and near-resonance phenomena, in particular, it has made it possible to deeply unify and formalize the consideration of various mechanical systems. The cumbersome and time-consuming operations associated with the preparation and solution of differential equations have been replaced by simple algebraic transformations. Resonance and antiresonance of forces, resonance and antiresonance of velocities are determined.