VARIETY OF RESONANCES IN MECHANICS

Author(s):  I.P. Popov, Kurgan state university, Kurgan, Russia, ip.popow@yandex.ru

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  The definitions of mechanical resonances of forces and speeds are given. Definition 1. Mechanical resonance of forces is a mechanical resonance that occurs at a frequency in a mechanical system, including an inert body and an elastic element, at which the reactive forces developed by them are maximal and opposite. Definition 2. Mechanical speed resonance is a mechanical resonance that occurs at a frequency in a mechanical system, including an inert body and an elastic element, at which the speeds developed by them are maximum and opposite. Two theorems are proved. Theorem 1. When the condition is fulfilled in a mechanical system consisting of a parallel-connected inert body, an elastic element and a damper, a mechanical resonance of forces occurs. Theorem 2. When the condition is fulfilled in a mechanical system consisting of a series-connected inert body, an elastic element and a damper, a mechanical velocity resonance occurs. Classic mechanical resonance is a resonance of forces. It corresponds to a parallel connection of an inert body, an elastic element and a damper. When these elements are connected in series, a mechanical velocity resonance occurs. The resonance speeds mistaken for "antiresonance".

Keywords:  resonance of forces, velocities, parallel connection, series, source of force, speed

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