Widening of Anti-resonances by Increasing the Amplitude of Parametric Excitation

Anti-resonance is a feature of parametrically excited systems, which introduces a stabilizing effect to the system dynamics. To be applicable in real systems, it must be robust against parameter variation. One way to increase robustness is to widen the frequency range in which the anti-resonance can be utilized for vibration mitigation. In this work, a two-dimensional system is investigated. Lyapunov characteristic exponents (LCEs) serve as an indicator for the damping behavior of the system. An analytical approximation of the LCEs in the vicinity of the anti-resonance is derived using the method of normal forms. It is found that an increase in the amplitude of the parametric excitation leads to a widening of the anti-resonance with respect to the excitation frequency.