A metamaterial plate with magnetorheological elastomers and gradient resonators for tuneable, low-frequency and broadband flexural wave manipulation

Incorporating magnetorheological elastomers and multiple gradient resonators (MRE–MGRs), a novel metamaterial plate is proposed, which entails low-frequency, broadband and tuneable bandgap features. The proposed MRE-MGR design embeds an adaptive magnetic field adjustment mechanism to alter the elastic modulus of the MRE to modulate the local resonance bandgap frequency and bandwidth. A bandgap prediction model of the metamaterial plate is developed using the plane wave expansion (PWE) method. Integrated into the model through equivalent stiffness terms, the magneto-controlled modulus of the MRE can be estimated using the energy method and magnetic dipole theory. The established model allows for revealing the dispersion relation of the proposed metamaterial plate under various magnetic fields. The predicted tuneable bandgaps, vibration transmission loss and flexural wave modulation of the metamaterial plate are validated through comparisons with finite element simulations. Numerical analyses show the benefit of the gradient resonator design, which alongside the effective MRE tuning, entails broadening low frequency bandgaps at 92 Hz (relative band of 79.3% for the exponential gradient) and 72.7 Hz (relative band of 65.9% for the linear gradient). The mechanisms underpinning the observed bandgap widening phenomenon are analysed and attributed to the combined effects arising from the gradient design of the distributed resonators and the effective tuning of the MRE elastic modulus under magnetic field modulation. The proposed metamaterial plate functionally achieves simultaneous magnetron adjustment of the bandgap frequency and its width, thus holding great promise for applications such as flexural wave guiding as well as vibration and sound radiation control in planar structures.