Vibrational resonance in a parametric oscillator without a power nonlinear term

Abstract Since vibrational resonance was first reported, this nonlinear phenomenon has been extensively investigated in a wide range of nonlinear systems. It is generally believed that a power nonlinearity is a necessary prerequisite for the occurrence of vibrational resonance. In this work, however, vibrational resonance is demonstrated for the first time in a parametric oscillator without a power nonlinear term. The existence of vibrational resonance in this kind of system is confirmed through analytical derivations and numerical simulations. Although both the power nonlinear term and the parametric excitation can cause vibrational resonance, their dynamical properties also has many differences in nature. The parametric excitation modulates the natural frequency of the system in response to the external excitation, thereby enabling vibrational resonance to occur at higher characteristic frequencies, an important advantage of this configuration for generating vibrational resonance. Furthermore, the proposed system exhibits good performance in processing noisy signals. Noise reduction is validated using both simulated signals and experimental radio-frequency identification signals. This work extends the class of models capable of generating vibrational resonance from system with power nonlinearity to system with periodic coefficient, with significant implications for both future theoretical developments and practical applications.