Modification of the spectral response of a pipe resonator using a subordinate array of coupled Helmholtz resonators

Abstract

The dynamic response of a resonant system can be manipulated by attaching a set of substantially smaller resonators with a prescribed distribution of properties. These smaller resonators are collectively referred to as a subordinate array. This work describes an experimental demonstration of such a manipulation, in which we alter one resonant peak of the primary system to create a flat bandpass response, while leaving the other resonances unaffected. In this instance, the primary resonant system is a pipe with one end closed and the other open, and the subordinate array consists of a set of small Helmholtz resonators. We demonstrate the desired modification of the system response at the third resonant frequency without significant change in adjacent resonances. Specifically, a single system resonance of the primary resonator shows a peak response when no subordinates are attached and exhibits a band pass response when the subordinates are attached. Sensitivity of system response to errors in design parame...