# Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

## TL;DR

This paper introduces a novel vibration isolation mechanism in periodic pendulum chains that mimics phononic band gaps, enabling targeted vibration suppression without traditional wave dispersion analysis.

## Contribution

It develops a method to identify pseudo-unit cells in pendulum chains for phononic band gap analysis, expanding vibration control techniques beyond conventional wave dispersion methods.

## Key findings

- Demonstrates forbidden wave propagation in specific frequency ranges.
- Shows potential for vibration reduction in payload delivery systems.
- Introduces a new approach to analyze chain dynamics without traditional phononic crystal methods.

## Abstract

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.