  We demonstrate that modulations of the stiffness properties of an elastic
plate along a spatial dimension induce edge states spanning non-trivial gaps
characterized by integer valued Chern numbers. We also show that topological
pumping is induced by smooth variations of the phase of the modulation profile
along one spatial dimension, which results in adiabatic edge-to-edge
transitions of the edge states. The concept is first illustrated numerically
for sinusoidal stiffness modulations, and then experimentally demonstrated in a
plate with square-wave thickness profile. The presented numerical and
experimental results show how continuous modulations of properties may be
exploited in the quest for topological phases of matter. This opens new
possibilities for topology-based waveguiding through slow modulations along a
second dimension, spatial or temporal.
