# Exploitation of Modal Superposition Toward Forced Vibration Localization in a Coupled Symmetric Oscillator Array

## TL;DR

This paper explores how vibrations can be localized in symmetric transducer arrays by adjusting coupling and natural frequencies.

## Contribution

The study introduces a novel understanding of forced vibration localization through modal superposition in symmetric oscillator arrays.

## Key findings

- Forced vibration localization is inversely related to coupling strength between oscillators.
- Breaking symmetry leads to normal mode localization affecting vibration response.
- Resonance frequency variation is attributed to curve veering effects.

## Abstract

In transducer arrays, symmetric grouping of identical elements is often employed to achieve uniform array performance. Such arrays can possess high coupling, preventing localized operation of individual transducers. This paper provides insight into how forced vibration localizes in a symmetric system of coupled oscillators. We use a simple lumped-parameter model of highly coupled oscillators derived from ultrasound transducer arrays. Forced vibration localization can be shown to be inversely related to the coupling strength between the oscillators. The results demonstrate how forced vibration in a coupled symmetric system may localize through modal superposition and how it may be tuned via the spacing of natural frequencies. Breaking the system’s symmetry leads to normal mode localization, which can be shown to affect the forced vibration response. The results reveal a variation in the system’s resonance frequency, attributed to curve veering effects.