  In this work, we investigate theoretically and demonstrate experimentally the
existence of valley-Hall edge states in the in-plane dynamics of honeycomb
lattices with bi-valued strut thickness. We exploit these states to achieve
non-trivial waveguiding of optical modes that is immune to backscattering from
sharp corners. We also present how different types of interfaces can be
combined into multi-branch junctions to form complex waveguide paths and
realize a variety of structural logic designs with unconventional wave
transport capabilities. We illustrate this potential with two applications. The
first is a direction-selective energy-splitting waveguide tree featuring a
pronounced asymmetric wave transport behavior. The second is an internal
waveguide loop along which the energy can be temporarily trapped and
periodically released, effectively working as a signal delayer. The modal
complexity of in-plane elasticity has important consequences on the regime of
manifestation of the edge states, as the availability of viable total bandgaps
is shifted to higher frequencies compared to the out-of-plane counterpart
problem. It also poses additional experimental challenges, associated with
proper acquisition and deciphering of the in-plane modes, the solution of which
requires a systematic use of in-plane laser vibrometry.
