Vibration bandgap of immersed periodic plates with fluid surface sloshing effect

Abstract

This study extends our previous work by implementing a unit cell-based symmetric fluid–structure formulation to predict vibration bandgaps in immersed periodic composite plates, with the account for fluid surface sloshing effects. The novelty lies in integrating Bloch periodic boundary conditions into a symmetric hydro-elastic $(u,\eta ,\phi )$ unit cell model with fluid–structure interaction (FSI). The unit cell comprises three subdomains: the immersed composite plate, the fluid, and the fluid free surface. Bloch periodic conditions are applied across all subdomains, enabling bandgap predictions that incorporate the combined effects of fluid inertia and surface sloshing. Hence, the approach accounts for full-range immersion depths ranging from deep submersion to near-surface scenarios. The numerical cases investigate an immersed periodic plate with square inclusions, revealing a competition between fluid inertia and surface sloshing in influencing the structure’s vibration dynamics. Specifically, fluid inertia dominates in deeply immersed conditions, whereas surface sloshing prevails in shallow immersion. The observation is validated by comparing with frequency response analysis performed under equivalent FSI conditions. Additionally, the method is applied to explore dispersive bandgaps in microstructures with anisotropic wave propagation. The results underline the effectiveness of the proposed model in designing immersed meta-structures for vibration mitigation.