Effective equation for a system of mechanical oscillators in an acoustic field

TL;DR

This paper develops an effective equation to model the dynamics of a one-dimensional acoustic field coupled with a continuous distribution of mechanical oscillators, analyzing the system's behavior through PDEs and boundary conditions.

Contribution

It introduces a new effective equation for the coupled acoustic-oscillator system in the continuum limit, advancing understanding of such interactions.

Findings

Derivation of an effective equation for the coupled system

Analysis of solutions with time-dependent boundary conditions

Insights into the continuum limit behavior of oscillators

Abstract

We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent boundary conditions describing the evolution in the limit of a continuous distribution of oscillators.