  Rejection of unmitigated vibrational disturbances represents an ongoing
dilemma in complex linkage systems. In this work, we present an inherent and
self-reliant vibration isolation mechanism in architected periodic chains of
serially pivoted pendulums. Absorption of external excitations is achieved by
virtue of Bragg-type band gaps which stem from the emergent chain dynamics.
Owing to its coupled dynamics, the self-repeating cell of a Phononic Crystal
(PC) is not trivial and cannot be readily identified from the periodic
arrangement by inspection. As such, this work entails the extraction of a
"pseudo" unit cell of an equivalent PC lattice from the derived motion
equations of a finite chain, which departs from traditional wave dispersion
methods. The model presented herein comprises a chain of linked pendulums with
periodic variations of inertial/geometrical properties, carrying a payload at
one end. We ultimately show evidence of forbidden wave propagation in
prescribed frequency regimes, reminiscent of band gaps in PC lattices. The
presented framework can be invaluable in applications that require vibration
reduction in the delivery of payloads including gantry cranes, robotic arms and
space tethers.
