  Topological metamaterials unlock confined and robust elastic wave control in
mechanical structures. Recent breakthroughs have precipitated the development
of 3D topological mechanical metamaterials, which extend beyond the
conventional 1D and 2D metamaterials to facilitate extraordinary wave
manipulation along 2D planar and layer-dependent elastic waveguides. While
promising, significant research gaps exist that impede the practical
implementation of 3D topological metamaterials. The 3D topological
metamaterials studied thus far are constrained to function in single frequency
bandwidths that are typically in a high-frequency regime, and a comprehensive
experimental investigation remains elusive. In this paper, we address these
research gaps and advance the state of the art through the synthesis and
experimental realization of a 3D topological metamaterial that exploits
multimodal local resonance to enable low-frequency elastic wave control over
multiple distinct frequency bands. The proposed metamaterial is geometrically
configured to create multimodal local resonators whose frequency
characteristics govern the emergence of four unique low-frequency topological
states. Numerical simulations uncover how these topological states can be
employed to achieve polarization-, frequency-, and layer-dependent wave
manipulation in 3D structures. An experimental study results in the attainment
of complete wave fields that unambiguously illustrate 2D topological waveguides
and multi-polarized wave control in a physical testbed. The outcomes from this
work open the door for future research with 3D topological mechanical
metamaterials and reveal the applicability of the proposed metamaterial for
various wave control applications.
