  Topological lattices have recently generated a great deal of interest based
on the unique mechanical properties rooted in their topological polarization,
including the ability to support localized modes at certain floppy edges. The
study of these systems has been predominantly restricted to the realm of
in-plane mechanics, to which many topological effects are germane. In this
study, we stretch this paradigm by exploring the possibility to export certain
topological attributes to the flexural wave behavior of thin lattice sheets. To
couple the topological modes to the out-of-plane response, we assemble a
bilayer lattice by stacking a thick topological kagome layer onto a thin
twisted kagome lattice. The band diagram reveals the existence of modes whose
out-of-plane character is controlled by the edge modes of the topological
layer, a behavior elucidated via simulations and confirmed via laser vibrometer
experiments on a bilayer prototype specimen. These results open an alternative
direction for topological mechanics whereby flexural waves are controlled by
the in-plane topology, leading to potential applications for flexural wave
devices with engineered polarized response.
