The Helmholtz Equation Least Squares Method

This book represents the HELS (Helmholtz equation least squares) theory and its applications for visualizing acoustic radiation from an arbitrarily shaped vibrating structure in free or confined space. It culminates the most updated research work of the author and his graduate students since 1997. The book contains six chapters. The first serves as a review of the fundamentals in acoustics and the rest cover five specific topics on the HELS theory.

This book is written for those who want to learn the state-of-the-art technology on visualizing acoustic radiation from vibrating objects, to understand difficulties involved in these inverse acoustic problems, and to acquire the information necessary to conduct successful vibro-acoustic diagnostics on their own. Attention is focused on the new development on nearfield acoustical holography (NAH) beyond the traditional Fourier acoustics that are suitable for separable geometries only.

Specifically, it presents Helmholtz equation least squares (HELS) method, inverse Helmholtz integral equations implemented via boundary element method, hybrid NAH and transient NAH that can be employed to tackle various reconstruction of vibro-acoustic fields generated by arbitrary objects subject to arbitrarily time dependent excitations in free or confined space.

This book can serve both as a textbook for graduate students and as a reference book for acousticians, researchers and noise control engineers with basic knowledge of acoustics. Homework problems are included at the end of each chapter. In addition, examples of computer programs written in Matlab are provided for the readers' convenience.

Covers practical aspects of noise and vibration analysis and control HELS method simplifies the process of reconstructing acoustic fields Explains the differences and interrelationships between the Rayleigh series and the HELS method Includes supplementary material: sn.pub/extras

Auteur

Sean F. Wu received his Ph.D. from Georgia Institute of Technology, U.S.A. in 1987. He joined the Mechanical Engineering Department at Wayne State University as an Assistant Professor in 1988, was promoted to Associate Professor in 1995 and Professor in 1999, was selected in an unanimous vote as the Charles DeVlieg Professor in 2002 and appointed by the Board of Governors to the rank of University Distinguished Professor in 2005.

Dr. Wu holds the rank of Fellow in the American Society of Mechanical Engineers and the Acoustical Society of America, and serves as an Associate Editor and Express Letter Editor for the Journal of the Acoustical Society of America and Co-Editor-In-Chief for Journal of Computational Acoustics.

Texte du rabat

This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.

Contenu
Chapter 1. Introduction.- Chapter 2. The Spherical Wave Functions.- Chapter 3. The Helmholtz Equation Least Squares (HELS) Method.- Chapter 4. Validity of the HELS Method.- Chapter 5. Implementation of the HELS Method.- Chapter 6. Combined Helmholtz Equation Least Squares (CHELS) Method.- Chapter 7. Hybrid HELS.- Chapter 8. Equivalent Sources Using HELS.- Chapter 9. Transient HELS.- Chapter 10. Panel Acoustic Contribution Analysis Using HELS.- References.- Index.