A meta-plate with radial rainbow reflection effect for broadband suppression of vibration and sound radiation

The suppression of vibration and sound radiation of thin plates has always been a concern in engineering fields such as aerospace, transportation, etc. The rainbow effect refers to that the waves with different frequencies can be stopped in different positions, where the wave energy is also enhanced, as the result of the spatial slowing-down of wave velocities. This effect exhibits great potential in suppressing structural vibration and sound radiation, but corresponding studies have not been reported yet. In this paper, a meta-plate composed of ring-type unit-cells with gradient heights is proposed to generate the radial rainbow reflection effect. Upon analyzing the dispersion relationship of unit-cells and revealing the rainbow reflection mechanism, the broadband vibration and sound radiation performances of a square meta-plate with free boundaries are studied. Numerical and experimental results demonstrate that the proposed meta-plate can suppress the vibration and sound radiation in broadband only with the extreme-low structural inherent loss. The wavenumber spectra of vibration velocity and supersonic intensity at typical frequencies including local and global resonant ones are analyzed to reveal the suppression mechanism of sound radiation, which is the vibration redistribution and systematic vibration reduction resulting from the rainbow reflection effect. Our design enhances the stiffness of plate structures and requires no additional damping, providing a novel approach for structural vibration and sound radiation suppression.