Fluid-structural coupling in metamaterial plates for vibration and noise mitigation in acoustic cavities

Locally resonant metamaterials exhibit sub-wavelength tunable bandgaps that can be exploited for vibroacoustic mitigation. The present work investigates the use of metamaterial plates for the simultaneous control of structural vibration and acoustic sound radiation in an adjacent acoustic cavity. We adopt a coupled fluid-structure finite element model based on a variational mathematical framework in terms of structural displacement and fluid pressure to capture the vibroacoustic characteristics of the coupled system and shed light onto the spatial average pressure levels inside the cavity. The model is used to predict and distinguish between structural and fluid modes within frequency ranges of interest. Furthermore, differences between the metamaterial's structural response in the presence and lack of fluid coupling are explained. The pressure changes inside the cavity are discussed in relation to the frequency bandgap range predicted theoretically via a dispersion analysis for a couple of different metamaterial designs. Results obtained from the numerical analysis can be used to set design guidelines to optimally tune locally resonant metamaterials to achieve prescribed acoustic properties in the fluid component of such coupled systems.