Anti-Resonance — Velocity Resonance

Abstract

The task of the study is to establish the nature of mechanical resonance, namely, it is a resonance of forces or speeds. Two definitions are introduced. Definition 1. Resonance of forces is a resonance arising at a frequency ω = (k/m)0,5 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. The velocity resonance is a resonance arising at a frequency ω = (k/m)0,5 in a mechanical system, including an inert body and an elastic element, at which the speeds developed by them are maximum and opposite. The equation of forced mechanical oscillations corresponds to a parallel connection scheme, in which the inert body and changes in the dimensions of the elastic element and damper have a uniform speed, and their reactive forces are added. The sum of the reactive forces of the consumers of mechanical power is equal to the force developed by the source of mechanical power, which, like a voltage source in electrical engineering, can be called a source of power. Theorem 1 holds. If the condition ω = (k/m)0,5 is satisfied in a mechanical system consisting of parallel-connected inert bodies, an elastic element and a damper, a resonance of forces occurs. The inert body, the elastic element and the damper can be connected not only in parallel but also in series. With a series connection, a single force is applied to the elements of the system, and the velocities of the inert body and the changes in the dimensions of the elastic element and damper are added. The sum of the speeds of consumers of mechanical power is equal to the speed developed by the source of mechanical power, which, like a current source in electrical engineering, can be called a source of speed. Theorem 2 is valid. Under the condition ω = (k/m)0,5 in a mechanical system consisting of a series-connected inert body, an elastic element and a damper, a velocity resonance occurs. The mechanical resonance described in the courses of theoretical mechanics is the 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 velocity resonance occurs.