Session: 01-06-01: New Advances in Acoustics and Vibration: AI and Machine Learning, New Methods and Materials

Paper Number: 150218

150218 - Decomposition Method for Helmholtz Resonators Using Origami-Inspired Deployable Cylinders 

This study aims to establish analytical method  to evaluate the Helmholtz resonators using the origami-inspired deployable cylinders. The resonance frequency of Helmholtz resonators is uniquely determined by its shape. Thus, Helmholtz resonators have the disadvantage of limiting the applicable frequency range. To overcome the limitation, the effectiveness of neck extension for covering a wide frequency range has been studied by various researchers.  In this study, the origami-inspired deployable cylinders were used as necks of Helmholtz resonators to change the lengths and extend the resonance frequencies.   
In the previous studies , Watanabe et al. numerically evaluated the effect of the resonator installed on a side wall of a square tube. They measured the sound pressure at the anti-node position of the standing wave (i.e., superposition of the incident and reflected waves) in the tube. However, for experiments, in a typical one-dimensional acoustic tube using the two-microphone method,  the measurement positions (i.e., the positions of two microphones) are fixed and not adjustable to anti-node positions according to variable sound frequency. In such cases that the measurement positions are close to node positions, the sound pressure in the tube is underestimated and the silencing effect of the resonator cannot be studied.  
To overcome the shortcoming, in this study, we investigated the decomposition method such that the combined waves measured at two positions in the acoustic tube were decomposed into the incident wave and the reflected wave, and the decomposed waves were used for evaluation of the resonator. The combined sound pressures were computed through acoustic frequency analysis in Ansys, a CAE software, and decomposed. The decomposed incident and reflected sound pressures were equivalent, because the end wall of the acoustic tube was rigid. In the acoustic tube, the incident and reflected sound pressures exhibited clear resonance peaks at the resonance frequencies according to the length of the acoustic tube, regardless the measurement positions were on nodes or anti-nodes of the combined wave. On the other hand, in the acoustic tube with the Helmholtz resonator using the origami-inspired deployable cylinder, the resonance peak was split into two peaks, whose phenomenon was also observed in the acoustic tube with the conventional Helmholtz resonator.  Moreover, as the deployable cylinder of the neck was contracted and deployed in length , the resonance frequency  of the resonator was adjusted in accordance with the change in sound frequency. 
In addition, to clarify the effect of the position of the Helmholtz resonator, two conditions were analyzed; one condition that the resonator was installed on the side wall of the acoustic tube and the other condition that the resonator was installed on the end wall of the tube. The silencing effect of the Helmholtz resonator was observed under both conditions, but  the decomposed sound pressure on the resonator installed on the end wall decreased at a slightly lower frequency than the intended resonance frequency, because the entire length of the acoustic tube was apparently increased by the length of the resonator on the end wall so that the resonance frequency decreased. 
The proposed decomposition method is applicable for acoustic experiments. In future, the experimental evaluation of the Helmholtz resonators using the origami-inspired deployable cylinders is required. The Helmholtz resonator on the end wall of the acoustic tube can be a potential experimental device, because installing the resonator on the flat end wall is relatively easier than installing on the cylindrical side wall in terms of design and prototyping.

Presenting Author: Atsuki Ito Meiji University

Presenting Author Biography: Atsuki Ito is a master’s student of mechanical engineering at Meiji University. He engages in research on the application of origami structures to engineering. In his studies, he particularly focuses on the use of origami structures to develop the technology for noise control. After completing his master’s degree, he intends to pursue a career as an engineer in an automobile company.

Authors:

Atsuki Ito Meiji University
Sachiko Ishida Meiji University