Application of Nondimensional Dynamic Influence Function Method for Eigenmode Analysis of Two-Dimensional Acoustic Cavities

S W Kang,S N Atluri

doi:10.1155/2014/363570

Abstract

This paper establishes an improved NDIF method for the eigenvalue extraction of two-dimensional acoustic cavities with arbitrary shapes. The NDIF method, which was introduced by the authors in 1999, gives highly accurate eigenvalues despite employing a small number of nodes. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. The paper proposes a practical approach for overcoming the inefficient procedure by making the final system matrix equation of the NDIF method into a form of algebraic eigenvalue problem. The solution quality of the proposed method is investigated by obtaining the eigenvalues and mode shapes of a circular, a rectangular, and an arbitrarily shaped cavity.

Highlights

The authors developed the nondimensional dynamic influence function method (NDIF method) for extracting highly accurate eigenvalues and eigenmodes of arbitrarily shaped membranes and acoustic cavities [1, 2]
In the NDIF method, as in the boundary element method (BEM) [8], a field problem is solved on its boundary along which nodes are distributed
The distinct feature of the NDIF method is related to the fact that no interpolation functions between the nodes are required, so that the basic collocation method is employed to satisfy a given boundary condition

Summary

Introduction

The authors developed the nondimensional dynamic influence function method (NDIF method) for extracting highly accurate eigenvalues and eigenmodes of arbitrarily shaped membranes and acoustic cavities [1, 2]. The final system matrix equation of FEM has a form of algebraic eigenvalue problem [10] and as the result its system matrices are independent of the frequency parameter To overcome this weak point for the NDIF method, the authors employed a modified approach of expanding the nondimensional dynamic influence function in a Taylor series for free vibration analysis of membranes with arbitrary shapes [11]. A simple and practical approach, which is applicable to arbitrary shapes and offers a highly accurate solution, is proposed by extending the authors’ previous research [11]

Theoretical Formulation

Verification Examples

Findings

Conclusion