1st Edition

The Boundary Element Method Applications in Sound and Vibration

By A. Ali, C. Rajakumar Copyright 2004
    200 Pages
    by CRC Press

    200 Pages
    by CRC Press

    The Boundary Element Method, or BEM, is a powerful numerical analysis tool with particular advantages over other analytical methods. With research in this area increasing rapidly and more uses for the method appearing, this timely book provides a full chronological review of all techniques that have been proposed so far, covering not only the fundamentals of the BEM but also a wealth of information on related computational analysis techniques and formulations, and their applications in engineering, physics and mathematics. An indispensable handbook and source of inspiration for researchers and professionals in these fields, this book is also an ideal textbook for graduate engineering students.

    1 Introduction

    1.1 Why the boundary element method?

    1.2 Typical applications of the boundary element method

    1.3 Emergence of the boundary element method

    1.4 History of boundary element eigenformulations

    1.5 Organization of the book

    2 Boundary Element Method Fundamentals

    2.1 Introduction

    2.2 Direct method: weighted residuals

    2.3 Examples

    2.4 Direct method: Green’s integral theorem

    2.5 Indirect method

    2.6 Body forces

    3 Isoparametric Boundary Elements

    3.1 Introduction

    3.2 Two-dimensional linear boundary elements

    3.3 Higher-order elements in 2-D

    3.4 Boundary elements in 3-D

    3.5 Examples

    4 Anisotropy, Axisymmetry and Zoning

    4.1 Introduction

    4.2 Anisotropic materials

    4.3 Axisymmetric problems

    4.4 Inhomogeneous regions and zoning

    5 Time-Harmonic Analysis in Acoustics and Elasticity

    5.1 Introduction

    5.2 Acoustics

    5.3 Elasticity

    6 Dynamic Analysis: Acoustics and Elasticity

    6.1 Introduction

    6.2 Eigenvalue problem in acoustics

    6.3 Eigenvalue problem in elasticity

    6.4 Characteristic equation for eigenvalues

    7 Basics of Algebraic Eigenvalue Problem Formulation

    7.1 Introduction

    7.2 Development of BE algebraic eigenvalue problem

    7.3 Formulation of Internal Cell Method

    7.4 Example of internal cell method: rectangular plate vibration

    8 Algebraic Eigenvalue Problem in Boundary Elements

    8.1 Introduction

    8.2 Eigenproblem using dual reciprocity method in acoustics

    8.3 Eigenproblem using particular integral method in elasticity

    9 Advanced Concepts in Boundary Element Algebraic Eigenproblem

    9.1 Introduction

    9.2 Algebraic eigenvalue formulation using fictitious function


    9.3 Example problems using fictitious function method

    9.4 Effect of internal collocation points on eigensolutions

    9.5 Polynomial-based particular integral method

    9.6 Multiple reciprocity method (MRM)

    9.7 Series expansion methods (SEM) with matrix augmentation

    10 Acoustic Fluid–Structure Interaction Problems

    10.1 Introduction

    10.2 Boundary element–finite element coupled eigenanalysis of

    fluid–structure system

    10.3 Acoustic eigenproblem for enclosures with dissipative boundaries

    10.4 Examples of acoustic eigenproblem with sound absorption

    11 Solution Methods of Eigenvalue Problems

    11.1 Introduction

    11.2 Lanczos-based subspace approach

    11.3 Lanczos recursion method

    11.4 Example problems

    11.5 Summary statements on the non-symmetric Lanczos eigensolver

    11.6 Damped system eigenvalue problem solution

    11.7 Lanczos two-sided recursion for the quadratic eigenvalue problem

    11.8 Summary statements on eigenvalue computation algorithms

    12 Discussion and Future Research

    12.1 Discussion on boundary element eigenvalue methodologies

    12.2 Comparison of eigenanalysis using BEM and FEM

    12.3 Topics not covered in the book

    12.4 Future research on BEM eigenanalysis


    Ali\, A.; Rajakumar\, C.