Multi-resonant metamaterials based on self-sensing piezoelectric patches and digital circuits for broadband isolation of elastic wave transmission

This paper proposes a general method to design multi-resonant piezoelectric metamaterials. Such metamaterials contain periodically distributed piezoelectric patches bonded on the surfaces of a host structure. The patches are shunted with digital circuits and working on self-sensing mode. A transfer function to be implemented in the digital circiots is designed to realize multi-resonance. The transfer function is derived only using the parameters of the patches. Consequently, it can be used to realize any type of multi-resonant metamaterial structures, like beams, plates and shells. The mechanism of generating multi-bandgaps by the transfer function is explained by analytically studying the effective bending stiffness of a multi-resonant piezo-metamaterial plate. It is shown that the transfer function induces multiple frequency ranges in which the effective bending stiffness becomes negative, consequently results in multiple bandgaps. The characteristics of these bandgaps are investigated, coupling and merging phenomena between them are observed and analyzed. Isolation effects of vibration transmission (elastic wave) in the metamaterials at multiple line frequencies or within a broad frequency band are numerically verified in frequency domain. Further time domain simulations accounting for the full dynamics of the metamaterials with digital circuits are also performed, stability and functionality of the metamaterials are demonstrated. The proposed multi-resonant piezoelectric metamaterials may open new opportunities in vibration mitigation of transport vehicles and underwater equipment.