Flexural Wave Band-Gap Characteristics of Metamaterial Beams with Membrane-Type Resonators: A Finite Element Investigation

Abstract

Membrane-type locally resonant metamaterials (MAMs) offer a potential approach for controlling structural vibration through frequency-selective modification of elastic-wave propagation. This study numerically investigates the flexural-wave dispersion and dynamic response of a metamaterial beam incorporating membrane-type resonators. Three-dimensional finite element models were developed in COMSOL Multiphysics V5.2 and analyzed using complementary eigenfrequency and frequency-domain approaches. A representative periodic unit cell was employed to determine the dispersion characteristics, while a finite four-cell structure was used to examine the frequency-dependent structural response. Aluminum 3003-H18 and AISI 4340 steel were used as constituent materials. Periodic boundary conditions and a parametric wave-number sweep were applied in the unit-cell analysis. The calculated dispersion relation exhibited flexural-wave band-gap behavior within the investigated frequency range extending to approximately 28 kHz, with the first reported band-gap feature occurring at approximately 4 kHz. Representative eigenmodes showed substantial changes in deformation pattern with frequency, supporting the interpretation that the observed dispersion characteristics are associated with the dynamic interaction between the host structure and local resonators. Frequency-domain analysis of the finite four-cell beam revealed pronounced frequency-dependent variations in displacement amplitude and deformation pattern. A notable response feature was observed in the approximately 20–25 kHz range and was qualitatively consistent with the unit-cell dispersion characteristics. Overall, the numerical results demonstrate that periodically distributed membrane-type resonators can substantially modify the flexural-wave characteristics of a supporting beam. The study provides a numerical basis for further investigation of membrane-resonator structures for frequency-selective vibration control, including future studies incorporating mesh convergence, damping, experimentally characterized membrane properties, quantitative transmission metrics, and experimental validation.