[Paper Review] Acoustic metamaterial with negative modulus and a double negative structure

Bhisham Sharma, Chin-Teh Sun|arXiv (Cornell University)|Jan 7, 2015

Acoustic Wave Phenomena Research1 references3 citations

TL;DR

This paper proposes an acoustic metamaterial with negative bulk modulus using a modified expansion chamber with neck regions, enhancing low-frequency transmission loss. By combining it with membrane-based structures exhibiting negative effective density, the design achieves double negative behavior—simultaneously negative modulus and density—demonstrated via finite element modeling (FEM).

ABSTRACT

An acoustic negative bulk modulus metamaterial based on the concept of expansion chambers is proposed. It is shown that addition of a neck region to an ordinary expansion chamber improves its transmission loss characteristics at low frequencies and the resulting structure displays a negative bulk modulus behavior. Additionally, membrane based metamaterials are analyzed. Using FEM, the negative density behavior of a membrane carrying a center mass and of a tensioned membrane array is analyzed and the inherent similarity of the two designs is discussed. Further, the modified expansion chamber is combined with an array of stretched membranes and the resulting structure is analyzed for double negative behavior.

Motivation & Objective

• To design an acoustic metamaterial with negative bulk modulus using expansion chamber geometry.
• To analyze membrane-based structures for achieving negative effective density.
• To combine negative modulus and negative density components into a single double negative acoustic metamaterial.
• To validate the double negative behavior through finite element method (FEM) simulations.
• To explore the inherent similarity between center-mass-loaded membranes and tensioned membrane arrays.

Proposed method

• Design a modified expansion chamber with a neck region to enhance low-frequency transmission loss.
• Model the modified expansion chamber to demonstrate negative bulk modulus behavior via FEM.
• Analyze a membrane with a central mass to achieve negative effective density using FEM.
• Investigate an array of pre-tensioned membranes for negative density behavior and compare with the center-mass design.
• Integrate the modified expansion chamber with a membrane array to create a double negative structure.
• Perform finite element simulations to evaluate the effective medium parameters and confirm double negative behavior.

Experimental results

Research questions

• RQ1 Can a modified expansion chamber with a neck region exhibit negative bulk modulus at low frequencies?
• RQ2 How does adding a central mass to a membrane affect its effective density in acoustic metamaterials?
• RQ3 What is the similarity between a membrane with a center mass and an array of pre-tensioned membranes in terms of effective density response?
• RQ4 Can the combination of a negative modulus chamber and a negative density membrane array yield a double negative acoustic metamaterial?
• RQ5 What is the frequency range and magnitude of double negative behavior in the proposed hybrid structure?

Key findings

• The modified expansion chamber with a neck region exhibits negative bulk modulus at low frequencies, significantly improving transmission loss.
• The membrane with a central mass demonstrates negative effective density due to resonant behavior, confirmed via FEM simulations.
• The tensioned membrane array shows equivalent negative density behavior to the center-mass-loaded membrane, indicating a fundamental design similarity.
• The combined structure of the modified expansion chamber and membrane array achieves double negative behavior, with simultaneous negative effective modulus and density.
• Finite element modeling confirms the existence of a frequency band where both bulk modulus and density are negative, enabling unique wave manipulation.
• The double negative behavior is most prominent in the low-frequency range, suitable for noise control and subwavelength acoustic focusing applications.