Abstract: The dynamics of parametrically excited systems are characterized by distinct types of resonances including parametric, combination, and internal. Existing resonance conditions for these instability phenomena involve natural ...

Abstract: A new technique for the analysis of dynamical equations with quasi-periodic coefficients (so-called quasi-periodic systems) is presented. The technique utilizes Lyapunov–Perron (L–P) transformation to reduce the linear ...

Abstract: In most parametrically excited systems, stability boundaries cross each other at several points to form closed unstable subregions commonly known as “instability pockets.” The first aspect of this study explores some general ...

Abstract: Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. ...