Self frequency-locking of a chain of oscillators

TL;DR

This paper investigates how damping at a specific node in a chain of coupled oscillators can induce the entire system to lock into a particular vibrational frequency, demonstrating a form of self-synchronization.

Contribution

It introduces the concept of self frequency-locking in a chain of oscillators through damping at a node, revealing a natural synchronization mechanism.

Findings

Damping at a node constrains the system to a specific frequency.

The damped mass acts as a node, dividing the chain into synchronized subchains.

Self-locking occurs at certain chain lengths and configurations.

Abstract

The paper studies the vibrational modes of a slightly damped uniform chain, with n masses coupled by elastic forces. It will be shown that, for certain lengths of the chain, that is for certain values of n, the damping of one of the masses at a specific position in the chain is able to constrain the vibration of the system to oscillate at a specific frequency. The damped mass turns out to be a node of the chain, subdividing it in two parts. This node can be considered as the synchronization element of the two subchains. As a consequence the oscillating system of n-masses is self-locking to the synchronized frequency of its subchains.