Bandgap prediction for a beam containing membrane-arch-mass resonators

This work aims to propose a promising locally resonating system consisting of a tensioned elastic membrane and two-arch masses attached on the membrane surface. Traditional membrane-type resonators, which usually create one obvious attenuation zone at low frequencies, might not be efficient in multi-frequency vibration suppression. The proposed structure can produce an extra clear flexural attenuation region and shift bandgap frequencies below 300 Hz. By adjusting geometric parameters (thickness, width, and location) of the arch mass, the bandgap region can be tuned. Introducing a feasible analytical model for accurately predicting the first and second initial frequencies of the bandgaps for a beam structure containing membrane-arch-mass resonators is another focus of this study. The proposed theoretical framework can be used to tune the bandgap to different target frequency ranges without knowing the actual width of the bandgap. Finite-element analysis and experiments are conducted to verify the theoretical predictions. A good agreement is seen among the theoretical, finite-element analysis, and experimental results. In addition, adjacent cells with different arch-mass distributions can generate two pairs of flexural bandgaps, increasing the practicality in engineering applications. The proposed structure might be used in low-frequency vibration isolation and filters.