# Sources of force and velocity, resonances and anti-resonances

DOI: 10.34759/trd-2021-117-01

### Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

### Abstract

The article considers parallel and series connections of a mechanical system’s elements with a source of harmonic force, or a source of harmonic velocity as a source of the external mechanical harmonic impact. A crank-and-yoke drive and a flywheel with a large moment of inertia can be the source of harmonic velocity. The source of the harmonic force can be represented by the rod of the pneumatic cylinder, which cavity can be in communication with the cavity of another pneumatic cylinder, which diameter is immeasurably higher than that of the first one, and which piston performs harmonic oscillations. The mechanical harmonic impacts, described in the courses of theoretical mechanics, correspond to the source of harmonic force. The article describes the four modes, namely resonances and anti-resonances of forces and velocities. The symbolic (complex) method implementation has significantly simplified the study of resonance and near-resonance phenomena, particularly, it allowed deeply unify and formalize 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cumbersome and time-consuming operations associated with the preparation and solution of differential equations have been replaced by simple algebraic transformations. This method is based on the mechanical analogue of Ohm’s law in a complex representation and the concept of mechanical reactance, resistance, impedance, susceptance, conductance and admittance. The classical consideration delivers one amplitude-frequency characteristic, while the symbolic (complex) method delivers eight ones with a significantly larger number of characteristic points and characteristic ratios. Resonance and anti-resonance of forces, resonance and anti-resonance of velocities were determined. Resonances stem from the combinations of parallel connection of elements and a source of harmonic force, or a series connection of elements and a source of harmonic speed. Anti-resonances occur due to the combination of parallel connection of elements and a harmonic velocity source, or their series connection and a harmonic force source.

### Keywords:

source of force, source of velocity, series connection, parallel connection, resonance, anti-resonance

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