Ebook: The Helmholtz Equation Least Squares Method: For Reconstructing and Predicting Acoustic Radiation

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 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.