Parametric Control of Nonlinear Longitudinal-Rotational Rod Oscillations and Phenomenon of Reverse Rotational Vibrations

TL;DR

This paper investigates nonlinear coupled longitudinal-torsional vibrations in a rotating rod, revealing a new reverse rotational vibration phenomenon driven by parametric interactions, with potential applications in precision mechanical control.

Contribution

It introduces a mathematical model for nonlinear coupled vibrations and uncovers a novel reverse rotational vibration mode caused by parametric effects.

Findings

Identification of resonance conditions for nonlinear oscillations

Discovery of a reverse torsional vibration phenomenon

Potential for controlling rotation direction in precision devices

Abstract

The article is devoted to the investigation of the nonlinear effects in a system of the coupled longitudinal-torsional parametric vibrations of a rotating rod. Constructed and investigated mathematical model, based on which we calculated the resonance conditions of the nonlinear oscillations and found the ratio of the parameters that require changing of the sign of the coefficient in front of the term defining the possible reverse of torsional vibrations. The latter is a new phenomenon, a special mode, where the parametric action in the form of longitudinal vibrations at one end of the rod (for example periodic strikes in the rod's end with a certain frequency) can lead to torsional vibrations due to the nonlinear parametric interaction of oscillations. In the context of this, the reverse leads to control not only the rotation parameters, but also the direction of rotation, and there are possible torsional oscillations, which can be used in precision mechanics devices.