Unravel the Effects of Locally Resonant Metamaterials on Hydroelastic Membranes for Wave Energy Modulation

Abstract

This study investigates the integration of local resonant metamaterials (LRMM) into floating membrane systems to enhance their wave energy interaction performance. The primary objective is to numerically examine how LRMM influence the dynamic response and energy characteristics of a coupled fluid–structure system, with a particular focus on wave reflection, transmission, and absorption under different configurations and excitation frequencies.

Floating membranes have gained attention as novel candidates for wave energy converters (WECs) and floating breakwaters due to their lightweight, flexible properties and adaptability to marine environments. However, they are less effective at lower frequencies and near their structural natural frequencies, where wave transmission becomes dominant and energy absorption is low. Insights from previous studies in acoustic and elastic metamaterials suggest that local resonators may introduce bandgaps that block wave propagation in certain frequency ranges. Motivated by this, the current work explores whether similar principles can be applied to enhance hydrodynamic control in floating membrane systems.

The numerical model is built upon a monolithic finite element framework that handles strong fluid–structure coupling in a unified variational formulation. The fluid is governed by a linear free-surface potential flow model, while the membrane is treated as a pre-tensioned one-dimensional structure. Alinear single-degree-of-freedom (SDOF) viscoelastic model is used to describe the dynamics of the LRMM. This setup enables consistent coupling and modal analysis across mixed-dimensional domains, and serves as the foundation for all simulations performed in this study.

A comprehensive set of dry and wet modal analyses reveal that LRMM introduce new resonant modes that are strongly frequency-selective and spatially localized. The presence of LRMM also alters membrane-dominated modes, with effects depending on resonator frequency, mass, and placement relative to modes. Frequency domain simulations further demonstrate that LRMM can significantly reduce wave transmission and amplify reflection when resonance occurs, even suppressing the structural resonance of the membrane itself. These results confirm the potential of LRMM to induce bandgaps in water wave systems and to function as passive wave control devices.

Extensive parametric studies were conducted to systematically examine how key resonator properties—including natural frequency, spatial placement, mass, and damping—affect the system’s energy behavior. The results provide clear design insights, such as optimal placements aligned with antinodes and damping-tuning to maximize absorption. Finally, a realistic sea-state scenario based on a scaled JONSWAP spectrum was simulated to assess the effectiveness of the system in practical conditions. The findings demonstrate that LRMM can meaningfully reduce the downstream wave loading and increase wave energy absorption over a target frequency band, highlighting its application potential in floating structures.

In summary, this work provides a systematic numerical investigation into LRMM-enhanced floating membrane systems, establishes a rigorous modeling and simulation framework, and offers key insights into their wave energy control capabilities. The results form a theoretical basis for future design and experimental implementation of metamaterial-based wave-interacting structures.