  In this manuscript we report on adiabatic pumping in quasiperiodic stiffness
modulated beams. We show that distinct topological states populating nontrivial
gaps can nucleate avoided crossings characterized by edge-to-edge transitions.
Such states are inherently coupled when a smooth variation of the modulation
phase is induced along a synthetic dimension, resulting in topological
edge-to-edge transport stemming from distinct polarizations of the crossing
states. We first present a general framework to estimate the required
modulation speed for a given transition probability in time. Then, this
analysis tool is exploited to tailor topological pumping in a stiffness
modulated beam.
