Phase dependent nonlinear parametrically excited systems

Nonlinear parametrically excited (NPE) systems govern the dynamics of many engineering applications, from cable-stayed bridges where vibrations need to be suppressed, to energy harvesters, transducers and acoustic amplifiers where vibrations need to be amplified. This work investigates the effect of different system parameters on the dynamics of a prototype NPE system. The NPE system in this work is a cantilever beam with an electromagnetic subsystem excited at its base. This system allows cubic stiffness, parametric stiffness, cubic parametric stiffness, and the phase difference between different sources of excitation to be varied independently to achieve different dynamic behaviors. A mathematical model is also derived, which provides theoretical understanding of the effects of these parameters and allows the analysis to be extended to other applications.