Multi-Frequency Broadband Vibration Mitigation of a Beam Under Tensile Load

The vibration characterization is directly associated with the system’s physical properties, such as mass, damping, and stiffness. For over a century, vibration resonator or dynamic absorber has been used for vibration control and mitigation in many sectors of engineering. A limitation of this device is that it acts as a notch filter, which is only effective over a narrow band of frequencies. Therefore, researchers have designed the call metamaterial, which in this case, targets the improvement of vibration attenuation and induces locally resonant bandgaps. This work investigates the broadband vibration mitigation of a beam under tensile load with periodically attached dynamic absorbers. The study uses the modal analysis approach, a simple formulation that only depends on the resonator target frequency and total mass ratio to investigate single and multiple-frequency bandgap formation. Metamaterial and rainbow metamaterial beam under tensile load are employed to widen the gap. In practical designs, a finite number of resonators is required for the open bandgap, and this ideal number is explored in the paper. Additionally, a tensiled beam (cable) virtual twin is built from a physical system to forecast its broadband vibration mitigation with the metamaterial approach. Numerical investigations are conducted regarding the effects of mass ratio and the ideal mass ratio on the open and on the gap convergence, as well as resonators in single and multiple arrangements inducing multiple gaps.

Multi-resonant piezoelectric metamaterials 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 assumed to be shunted with digital circuits. A transfer function 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. The proposed multi-resonant piezoelectric metamaterials may open new opportunities in vibration mitigation of transport vehicles and underwater equipment.