Bandgap Characteristics and Seismic Applications of Inerter-in-Lattice Metamaterials

Longitudinal elastic wave propagation characteristics of a proposed inerter-in-lattice metamaterial (ILM) were investigated. Its local resonance emerges from the additional degree of freedom induced by a series combination of a spring element and an inerter in the lattice. The presence of inerters provides a means to reduce expenses in terms of the associated mass compared with locally resonant metamaterials (LRMs). Parametric studies of the number of cells, mass ratios, and damping ratios of finite ILM lattices were conducted. Those parameters affect not only widths and depths of attenuation zones but also resonant responses in nonattenuation zones, which is important for seismic applications. Wave propagations in finite lattices were investigated in perspective of energy, and it was found that both quantities of input energy and energy spatial distributions are different when excitation frequencies fall in passbands and stopbands, respectively. A conceptual configuration of the unit cell for ILMs applied as a seismic barrier was proposed. Numerical simulations of the barrier under excitations of three seismic records revealed its feasibility for the attenuation of ground motions.