Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

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.

Wave control of a flexible space tether based on elastic metamaterials

“…However, the lack of passive vibration absorbers for space tether systems highlights the significance of the research in this area. The vibration absorber consisting of periodic structures proposed by Al Ba'ba'a et al 6 provides a promising approach for passive vibration control of space tether systems.…”

“…The vibration absorber consisting of periodic structures proposed by Al Ba'ba'a et al 6 provides a promising approach for passive vibration control of space tether systems.…”

Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures

“…If a synthetic substance has either negative ρ or negative K, then waves within that substance have an imaginary-valued velocity, so they attenuate rather than propagate or reflect. These novel characteristics of EMTMs lead to various applications such as passive vibration attenuation systems [18][19][20][21][22][23][24][25], active vibration attenuation systems [26][27][28][29], energy harvesters [30][31][32], energy dissipation systems [33,34], seismic barriers [35][36][37][38][39][40][41][42], viscoelastic systems [43,44], non-reciprocal elastic wave propagation systems [45][46][47], gyroscopic metamaterials [48,49] and elastic topological phononic crystals [50,51].…”