  Mechanical resonator networks are currently discussed in the context of model
systems giving insight into problems of condensed matter physics including
effects in topological phases. Here, we discuss networks based on three
high-quality factor nanomechanical string resonators (nanostrings) made from
highly tensile-stressed Si$_{3}$N$_{4}$. The strings are strongly coupled via a
shared support and thus can form a fully mechanical, classical multi-level
system. Moreover, the individual strings are tunable in frequency, which allows
one to explore their coupling behaviour using continuous wave spectroscopy and
time domain techniques. In particular, such systems allow for the experimental
exploration of quantum phenomena such as Landau-Zener transition dynamics by
studying their classical analogues. Here, we extend the previous work performed
on two coupled strings to three coupled resonators and discuss the additional
features of the inter-string dynamics, such as the classical analog of
Landau-Zener transition dynamics in a three-mode system. classical analog of
Landau-Zener transition dynamics in a three-mode system.
