Innovative design of metamaterial structures for elastic wave absorption and structural vibration suppression

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation presents the design procedures, the modeling techniques and the working mechanism of metamaterial structures for wide-band elastic wave absorption and structure vibration suppression. The metamaterial structures are designed by attaching discrete mass-spring subsystems to elastic homogeneous bars, beams or plates. Dispersion analysis is used to find the band gap for infinite metamaterial structures without damping. Frequency response analysis (FRA) and transient analysis are conducted for metamaterial structures with boundary conditions and damping. The work explains the concept of negative effective mass and spring constants as well as acoustic and optical modes. The work also shows that metamaterial structures are essentially based on the concept of conventional vibration absorbers. The local resonance between the subsystems and external excitation generates concentrated forces to resist the longitudinal deformation of bars and straighten the curvature of beams and plates so that the propagation of elastic waves can be prohibited. Numerical simulation shows that boundary conditions have a significant effect on the propagation of elastic waves especially in low-frequency band, band gap can be expanded by damping, and the damping in vibration absorber is much more efficient than modal damping in homogeneous structures. Besides, a multi-frequency acoustic metamaterial plate for broadband wave absorption is designed. The metamaterial plate is designed by attaching 2-DOF (degree of freedom) mass-spring subsystems to an isotropic elastic plate as vibration absorbers. The work shows that two stopbands are created by the multi-frequency absorber and the stopbands can be expanded by increasing the absorbers' mass or reducing the edge length of the working unit. A high damping ratio for the secondary absorbers helps to combine the two stopbands into a broad one while a low damping ratio for the primary absorber still guarantee a quick response in transient period. In the end, nonlinear vibration absorb