Page 73 - 2018Fall
P. 73

Chapter 2, Basic Equations of Structural Acoustics and Vi- bration, describes the fundamental equations governing the three classical problems in mechanics: linear acoustics, lin- ear elastodynamics and linear poro-elasticity.
Chapter 3, Integral Formulation of the Problem of Struc- tural Acoustics and Vibration, introduces classical methods for obtaining the variational integral formulation associated with some common problems in continuum mechanics. This chapter also discusses important topics like principles of stationarity, virtual work and minimum potential energy with many good examples.
Chapter 4, The Finite Element Method: An Introduction, discusses fundamental concepts of the finite element meth- od through the study of the solution of the one-dimensional wave equation. The chapter concludes with several examples for different boundary conditions and use of various finite element basis functions.
Chapter 5, Solving Uncoupled Structural Acoustics and Vi- bration Problems Using the Finite Element Method, revisits the step by step finite element methodology introduced in Chapter 4 with several examples, applied to the uncoupled 3D acoustic and structure problems. The appendices de- scribe various shape functions in two and three dimensions and present formulas for their numerical integration over various elements, accompanied by useful Fortran codes.
Chapter 6, Interior Structural Acoustic Coupling, discusses the coupled interior acoustic problem. It introduces various formulations with emphasis on the classical pressure-dis- placement formulation. The implementation of this method using the uncoupled modes of the structure is discussed in detail.
Chapter 7, Solving Structural Acoustics and Vibration Problems Using the Boundary Element Method, provides a detailed description of the acoustic application of the BE method. Its various formulations (direct, indirect and
variational) are presented with an emphasis on numerical implementation and techniques to reduce the difficulties as- sociated with the calculation of singular integrals. The non- uniqueness problems associated with the BE method is dis- cussed and both the CHIEF and the Burton-Miller methods are described in detail.
Chapter 8, Problem of Exterior Coupling, discusses the flu- id-structure interaction for the exterior problem. This chap- ter presents various formulations combining the FE method for the structure and the BE for the unbounded fluid medi- um and discusses their advantages and disadvantages. Like some other chapters, this chapter uses examples to illustrate the accuracy of the methods by comparing the resulting solutions with those obtained from analytical or other FE- based solutions.
The book contains a rich collection of references and in- cludes MATLAB codes that can readily be used and expand- ed. I find the latter particularly useful in understanding the concepts. I have a few comments about the writing of the book. I think there is some loss in translation. For example, the use of the word ‘resolution’ apparently as a substitute for ‘solution’ or ‘...vibrations’ instead of ‘...vibration’ in the title of Chapter 3 or the omission of the article ‘The’ in the title of Chapter 8. There are probably other cases that I haven’t caught, but some might just be typos. Despite these minor issues, I find the book very useful and highly recommend it to students and researchers in science and engineering.
Review by:
Chief Scientist
HLS Research
San Diego, CA 92130
[Published online June 9, 2017, The Journal of the Acoustical Society of America 141(6)]
Fall 2017 | Acoustics Today | 71

   71   72   73   74   75