Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression

This article presents the design and modeling techniques and design guidelines, and reveals the actual working mechanism of acoustic metamaterial plates for elastic wave absorption and structural vibration suppression. Each of the studied metamaterial plates is designed by integrating two (or one) isotropic plates with distributed discrete mass-spring-damper subsystems that act as local vibration absorbers. For an infinite metamaterial plate, its stopband is obtained by dispersion analysis on an analytical unit cell. For a finite metamaterial plate with specific boundary conditions, frequency response analysis of its full-size finite-element model is performed to show its stopband behavior, and the stopband behavior is further confirmed by transient analysis based on direct numerical integration of the finite-element equations. Influences of the vibration absorbers׳ local resonant frequencies and damping ratios and the plate׳s damping, boundary conditions, and natural frequencies and mode shapes are thoroughly examined. The concepts of negative effective mass and spring and acoustic and optical wave modes are explained in detail. The working mechanism of acoustic metamaterial plates is revealed to be based on the concept of conventional vibration absorbers. An absorber׳s resonant vibration excited by the incoming elastic wave generates a concentrated inertial force to work against the plate׳s internal shear force, straighten the plate, and attenuate/stop the wave propagation. Numerical results show that the stopband׳s location is determined by the local resonant frequency of absorbers, the stopband׳s width increases with the (absorber mass)/(unit cell mass) ratio, and increase of absorbers׳ damping significantly increases the stopband׳s width and reduces low-frequency vibration amplitudes. However, too much damping may deactivate the stopband effect, and the plate׳s material damping is not as efficient as absorbers׳ damping for suppression of low-frequency vibrations. •We model metamaterial plates with mass-spring-damper subsystems.•A bandgap is observed right above the natural frequency of the subsystems.•Local resonance of the subsystems absorbs energy and creates stopband.•The stopband׳s width is determined by absorber-mass/unit-plate-cell-mass ratio.•Proper damping in absorbers suppresses low-frequency vibration and expands stopband.