  In this paper, we incorporate the effect of nonlinear damping with the
concept of locally resonant metamaterials to enable vibration attenuation
beyond the conventional bandgap range. The proposed design combines a linear
host cantilever beam and periodically distributed inertia amplifiers as
nonlinear local resonators. The geometric nonlinearity induced by the inertia
amplifiers causes an amplitude-dependent nonlinear damping effect. Through the
implementation of both modal superposition and numerical harmonic methods the
finite nonlinear metamaterial is accurately modelled. The resulting nonlinear
frequency response reveals the bandgap is both amplitude-dependent and
broadened. Furthermore, the modal frequencies are also attenuated due to the
nonlinear damping effect. The theoretical results are validated experimentally.
By embedding the nonlinear damping effect into locally resonant metamaterials,
wideband attenuation of the proposed metamaterial is achieved, which opens new
possibilities for versatile metamaterials beyond the limit of their linear
counterparts.
