Acoustic multi-stopband metamaterial plates design for broadband elastic wave absorption and vibration suppression

This paper presents the modeling technique, working mechanism and design guidelines for acoustic multi-stopband metamaterial plates for broadband elastic wave absorption and vibration suppression. The metamaterial plate is designed by integrating two-degree of freedom (DOF) mass-spring subsystems with art isotropic plate to act as vibration absorbers. For an infinite metamaterial plate without damping, a working unit is modeled using the extended Hamilton's principle, and two stopbands are observed through dispersion analysis on the averaged three-DOF model. For a finite metamaterial plate with boundary conditions and damping, shear-deformable conforming plate elements are used to model the whole plate, and stopbands are investigated by frequency response analysis and transient analysis. Influences of absorbers' resonant frequencies and damping ratios, plate's boundary conditions and dimensions, and effective plate-absorber vibration modes are thoroughly investigated. Results show that the metamaterial plate is essentially based on the concept of conventional vibration absorbers. The local resonance of the two-DOF subsystems generates two stopbands, and the inertial forces generated by the resonant vibrations of absorbers straighten the plate and attenuate/stop wave propagation. Each stopband's bandwidth can be increased by increasing the absorber mass and/or reducing the average mass of isotropic plate in each working unit. Moreover, while a low damping ratio for the primary absorber can guarantee absorbers' quick response to transient excitations, a high damping ratio for the secondary absorber can combine the two stopbands into a wide one. In the end, a sensitivity analysis on absorber resonant frequencies is conducted and relatively large sensitivity is found at the two stopband regions. (C) 2015 Elsevier Ltd. All rights reserved.