Study of the Impact of Boundary Conditions on Acoustical Behavior of Granular Materials and their Implementation in the Finite Difference Method

Authors

Zhuang Mo, Purdue UniversityFollow
Guochenhao Song, Purdue UniversityFollow
Tongyang Shi, Institute of Acoustics, Chinese Academy of SciencesFollow
J Stuart Bolton, Purdue UniversityFollow

Comments

Zhuang Mo, Guochenhao Song, Tongyang Shi and J. Stuart Bolton, “Study of the impact of boundary conditions on acoustical behavior of granular materials and their implementation in the finite difference method,”184^th meeting of the Acoustical Society of America, Chicago, Il, May 2023. Paper 3pCA1, Session: Boundary Conditions Across Acoustics (Invited by Jennifer Cooper and Michelle Swearingen). Abstract published in the Journal of the Acoustical Society of America 153(3) Pt. 2, p. A227. DOI: https://doi.org/10.1121/10.0018730

Abstract

Granular materials display significant differences in their acoustical response when tested in a standing wave tube, compared with the behavior of more traditional sound absorbing materials such as fibrous webs and foams. The latter materials can often be modeled as an equivalent fluid with the further assumption that the material properties do not depend on the input signal level. In contrast, the level dependence of the acoustical behavior of granular materials has been observed in measurements of glass bubbles, as reported in previous studies, for example. When the input level is low, the absorption coefficient of the glass bubble stack shows solid-like behavior with multiple peaks associated with modal response of the stack. On the other hand, when the input level is high, glass bubble stacks show fluid-like behavior, with the quarter wavelength resonance in the direction of the tube axis dominating the response. In the current work, the boundary conditions at the air/granule interface and the granule/tube wall boundary are studied, as is the mechanism causing the variation of the apparent stiffness of the granule stack. The proposed model is implemented with a finite difference approach, and the model predictions are compared with acoustic measurements of granule stacks.

Keywords

Granular materials, Activated carbon, Glass bubbles, Finite Difference method, Sound absorption, Boundary conditions, Biot model, Poro-elastic

Subject

Acoustics and Noise Control

Date of this Version

5-10-2023