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

A dynamical system whose damping of oscillation or vibration is directly controlled may manifest a periodically varying damping ratio. In this letter, such a phenomenon is discovered to arise from a new type of parametric resonance, named the “zero-th order parametric resonance,” which is different from the conventional principal parametric resonance. This letter proposes an approach using the method of multiple scales to find approximate, analytical solutions of the system and thus providing an interpretation on damping variations.