Passive Control of Acoustic Potential Energy in a Rectangular Cavity by Means of Changing Boundary Condition

Abstract

Will eigenvalues and eigenfunctions be changed if the boundary surface is no longer rigid but has a specific acoustic admittance that may vary from point to point on surface? In this paper, the changes of eigenvalues and eigenfunctions are derived by using Kirchhoff-Helmholtz integral equation. Green’s function of which is composed by the sum of eigenfunctions is used in K-H integral equation. Acoustic potential energy is used to study the passive control performance that expresses an ability to make a quiet zone in the space of interest. Acoustic potential energy is found to have primary and secondary ones. Primary one is acoustic potential energy before changing boundary condition, and secondary one represents what can be gotten by changing boundary condition. Using these two terms, we attempt to see a control performance of each eigen mode when a boundary condition is changed. This index is defined by the ratio of acoustic potential energy after control to one before control in a quiet zone. Numerical simulations are carried out to illustrate and verify the proposed theory. One of highlights of this study is that it is possible to select or design a boundary condition if we do know what eigenfunctions we need, or vise versa.