On Periodical Damping Ratio of a Controlled Dynamical System with Parametric Resonances

TL;DR

This paper investigates the periodic variation of damping ratios in controlled dynamical systems, analyzing principal and novel zero-th order parametric resonances using multiple scales to derive analytical solutions.

Contribution

It introduces a new type of parametric resonance and provides analytical insights into damping variations in controlled systems.

Findings

Identification of zero-th order parametric resonance

Analytical solutions for damping ratio variations

Interpretation of resonance effects on damping

Abstract

This report provides an interpretation on the periodically varying damping ratio of a dynamical system with direct control of oscillation or vibration damping. The principal parametric resonance of the system and a new type of parametric resonance, named "zero-th order" parametric resonance, are investigated by using the method of multiple scales to find approximate, analytical solutions of the system, which provide an interpretation on such damping variations.