Robust non-dimensional dynamic influence function method using rank-aware determinant evaluation for eigenmode...

Area of Science:

• Acoustics
• Computational Mechanics
• Numerical Analysis

Background:

• The non-dimensional dynamic influence function (NDIF) method is used for eigenvalue and eigenmode analysis of acoustic cavities.
• Conventional NDIF methods can miss low-frequency eigenvalues due to system matrix ill-conditioning and rank deficiency.

Purpose of the Study:

• To develop an improved determinant evaluation scheme for accurate eigenvalue and eigenmode analysis of arbitrarily shaped 2D acoustic cavities.
• To address the limitations of the conventional NDIF method in identifying lower-order eigenvalues.

Main Methods:

• A rank-aware determinant evaluation scheme is proposed, incorporating rank information from both acoustic and membrane system matrices.
• A discontinuity-removal procedure is introduced to handle rank variations and ensure robust eigenvalue identification.

Main Results:

• The proposed method successfully overcomes the limitations of the conventional NDIF method.
• Eigenvalues and mode shapes extracted for a circular cavity show exact agreement with analytical solutions.
• Analysis of arbitrarily shaped cavities demonstrates close agreement with finite-element method results.

Conclusions:

• The rank-aware determinant evaluation scheme provides a robust and accurate method for eigenvalue and eigenmode analysis of acoustic cavities.
• This improved method is effective for both simple and complex arbitrarily shaped cavity geometries.