  We reveal the unique and fundamental advantage of inerter-based elastic
metamaterials by a comparative study among different configurations. When the
embedded inerter is connected to the matrix material on both ends, the
metamaterial shows definite superiority in forming a band gap in the ultra-low
frequency -- equivalently the ultra-long wavelength -- regime, where the unit
cell size can be four or more orders of magnitude smaller than the operating
wavelength. In addition, our parametric studies in both one and two dimensions
pave the way towards designing next-generation metamaterials for structural
vibration mitigation.
