Nonlinear Mechanical Metamaterial: A Novel Approach Towards Wideband Sound and Vibration Attenuation

Abstract

Metamaterials have become very popular in the field of noise and vibration suppression, cloaking, wave guide, wave shield, wave absorber owing to its frequency dependent material properties. However, due to the dependency on the linear resonance, the performance of a linear metamaterial is restricted to a narrow bandwidth, which limits its application. The main objective of this thesis is to investigate the various possibilities towards the wideband metamaterial. Resonating metamaterials can be mathematically modelled as a periodic chain of mass-in-mass structures. As a first step towards the wideband metamaterial, an aperiodic or graded variation of frequencies of each building block is investigated, instead of a periodic repetition of the mass-in-mass units. Furthermore, keeping the periodic pattern of a metamaterial intact, the possibility of bandwidth increment is evaluated by assigning nonlinearity to the resonating unit of the metamaterial. The effects of the cubic nonlinearity and discontinuity on the vibration transmission through metamaterials are investigated in this thesis. Semi-analytical and numerical solution algorithms are developed to solve the wave propagation through these various nonlinear and graded linear metamaterials and the associated dynamics are identified and validated experimentally. Implementing 3D printing technology, initially curved beams are fabricated as a representative model of the bistable metamaterial unit. Attaching this unit with an electro-dynamic shaker, it is experimentally shown that the nonlinear metamaterial can be used for wideband vibration isolation. Impacting metamaterials are tested on the impedance tube and found that it can improve the acoustical performance of the light weight partition wall for a wide range of frequencies. A properly tuned graded metamaterial can extend the attenuation bandwidth almost 40% more in the lower frequency side and by attenuating the second transmission band it can infinitely widen the higher side of the attenuation band. Computationally and experimentally it is illustrated that performance of nonlinear metamaterials depends on excitation amplitude. To achieve the desired nonlinear behaviour, higher amplitudes are required. In low excitation level, the response is close to the linear response and for medium levels it is mostly chaotic. The attenuation band increases to infinity for the high nonlinearity. Impacting metamaterial can attenuate both the transmittance peak and can widen the attenuation bandwidth simultaneously in the lower and higher frequency side.