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

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.

arXiv commentImproved Theorem 2. Updated introduction and references. Added 1 figure. 11 pages

References in corpus (2)

• A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures
• Point interactions in acoustics: one dimensional models

Cited by in corpus (1)

• An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions