A new strategy for vibration suppression in locally resonant metamaterials based on autoparametric resonance

Locally resonant metamaterials can achieve vibration suppression within a certain bandgap range. However, even a slight deviation between the excitation frequency and the bandgap range can cause large amplitude response due to the resonant peaks near the linear bandgap region. To overcome this issue, nonlinear locally resonant metamaterials shift the resonance peaks through hardening or softening stiffness, effectively weakening the intensity of the resonance and broadening the vibration attenuation range. Different from such conventional nonlinear locally resonant metamaterials, this paper integrates the concepts of dynamic vibration absorbers and autoparametric vibration absorbers, proposing a novel nonlinear locally resonant metamaterial based on autoparametric resonance. This paper begins by deriving the system’s governing equations through the extended Hamilton’s principle while considering the effects of geometric nonlinearity. Then, the nonlinear vibration suppression characteristics of the unit cell and metamaterial are investigated. It is found that the autoparametric resonance-based metamaterial not only preserves the original linear bandgap but also suppresses the resonant peaks near the bandgap, generating a new adjustable nonlinear vibration attenuation region at the lower frequency. Besides, the effect of damping is also examined, demonstrating that reducing damping can further enhance the vibration suppression within the nonlinear range. Finally, by employing the gradient design of the absorbers’ natural frequency, the nonlinear attenuation regions and linear bandgap are merged, effectively broadening the range of vibration suppression. The study shows that metamaterials based on the autoparametric resonance mechanism can overcome the limitations of the existing locally resonant metamaterials, providing a new strategy and insights for resonance suppression in periodic structures.