The Boundary Element Method: Applications in Sound and Vibration

ISBN-13: 9780367446550 / Angielski / Miękka / 2020 / 200 str.

A. Ali; C. Rajakumar

Opis

Reviews all Boundary Element eigenvalue methods proposed to date, from the basics of the BEM, through an outline of the non-algebraic BE eigenvalue analysis technique, to in-depth consideration of the more elegant algebraic eigenvalue formulations.

Spis treści

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

method

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

O autorze

Ali\, A.; Rajakumar\, C.