PREFACE

This book is based on a series of technical papers and lecture notes written by us and our graduate students and research associates over the last decade. During this period, the subject of the book, The Design of Quiet Structures, has been our principal focus which we feel is central to the emerging technology that allows noise control to be included as one of the primary variables in the design stage of quiet structures. The disciplines supporting this technology include dynamics of structures, acoustics and optimization. As the technology develops, disciplines related to modeling composite materials will play an ever increasing role in the noise-control-by-design process.

Accordingly, we have written this book for engineers and scientists who wish to learn how to incorporate sound power output as a parameter at a conceptual design stage. We assume that the reader has enough fundamental understanding of acoustics and the vibration of structures to follow the integrated design methodology as it unfolds in the text. We have included ample references that supplement the material presented. Several practical applications of the methodology are given to demonstrate its usefulness. We should emphasize that the book is not a complete set of design tools for the noise control engineer and scientist. While several new tools are presented, the focus is on how available computational tools are integrated into a unified design methodology. Many design tools referenced in the text, e.g., structural finite element methods or optimization routines are available commercially and are constantly being updated with, hopefully, features that make them more and more user friendly.

Strategies for designing quiet structures require extensive analytical and experimental tools and thus, much of our research effort has been directed to developing such tools. These are introduced in the first few chapters of the book. Design strategies require simple quantities on which to optimize. Throughout the book, this quantity is sound power, a simple scalar that by far best characterizes the sound radiation from a structure. Towards this end, we have expended considerable effort to develop numerical algorithms for computing sound power radiated from complex structures. As those researchers in the numerical acoustics community appreciate, this is no easy task. However, we think that the lumped parameter approach outlined in the second and third chapter of the book exemplifies the art of simplification, the essence of all good engineering design. Lumped parameter analysis provides a straightforward and highly efficient way of linking models of structures with their acoustic fields within acceptable, engineering limits of accuracy.

Throughout the book, the sound power is often formulated in terms of the volume velocity of the radiating structure and its surface acoustic resistance. Much attention is given to methods for determining the latter quantity, both numerically and experimentally. We shall see that the acoustic surface resistance (a matrix) provides the designer with a means of optimizing the velocity distributions on the surface of a structure to minimize its radiated sound power. If this is done by changing the characteristics of the structure passively, we call this “material tailoring”. If the velocity distributions of the structure are altered with externally applied forces, the term “active noise control” is used. Several examples of both methods are presented.

Chapter 1, an introductory chapter, provides a brief review of the fundamental equations that are used to derive the Helmholtz equation for harmonic vibrations and boundary conditions that lead to expressions for sound power. The free field Green’s function is then used to build the Kirchhoff-Helmholtz equation which forms the basis for most of the boundary element programs used in numerical acoustics.

In Chapter 2, we set the stage for introducing the lumped parameter model of the acoustic radiation problem. We choose a Green’s function that requires only surface velocity terms within the Kirchhoff-Helmholtz integral. By dividing the surface integral into surface elements, the boundary condition for the normal component of the surface velocity can be converted to an average form in terms of elemental volume velocities. The acoustic power output for a structural radiator is then written as a lumped parameter model in terms of the volume velocities. The chapter concludes with a series of examples that illustrate the conditions that must be met for a valid application of the lumped parameter model.

Chapter 3, the longest chapter in the book, enters the realm of numerical methods in acoustics and describes the logic behind POWER, a FORTRAN computer program written by John B. Fahnline to compute the power radiated from a vibrating structure. POWER builds on the lumped parameter model and thus uses volume velocity matching as a means of satisfying the boundary conditions on a structural radiator. Combinations of simple dipole and tripole sources are used to generate the required equivalent volume velocity fields and thus POWER is an equivalent source or superposition method. Interestingly, using combined sources eliminates a host of mathematical difficulties (e.g., non-uniqueness) which are ever present in most commercially available acoustic boundary element routines currently. This chapter also contains a very useful comparison between three competing methods used to satisfy the boundary condition problem, i.e., the collocation method, the method of least squares, and the volume velocity matching method (which is shown to be superior in both efficiency and accuracy). The examples that follow show how the volume velocity matching scheme is implemented practically. The chapter concludes with computations of sound power from real three-dimensional structures including a finite, cylindrical horn, and a “muffler-like” geometry.

In Chapter 4, we demonstrate how the lumped parameter model provides a direct means for measuring a structure’s acoustic surface resistance experimentally. This approach is necessary in cases where the geometry of the structural radiator is too complicated to model analytically. The experimental method outlined provides a direct measure of the structure’s acoustic resistance matrix, the quantity that when combined with the structure’s surface vibration data gives sound power. For this measurement, a resistance probe was developed especially and since this is a new device, a fairly detailed account of its design, calibration and operating range criteria is presented. The chapter concludes with an example outlining the procedure for measuring the surface resistance on an actual structure, e.g. a simple expansion chamber. Sample data of the direct and cross resistance terms measured over radiating surfaces are presented along with a layout of the instrumentation required for the probe’s operation.

We have written Chapter 5 to illustrate the basic characteristics of the resistance matrix as a function of frequency as well as how structural modes radiate sound. In the first part of the chapter, we show how the resistance matrix can be combined with a structure’s volume velocity distribution to predict its radiated sound power. After the resistance matrix has been computed, any structural changes that affect its volume velocity and hence its radiated sound power are immediately quantifiable. We shall see that this procedure requires only a matrix multiplication operation and thus reduces computation time considerably. Examples of sound power computations for a variety of structural radiators are presented, beginning with idealized cases and proceeding to more realistic problems.

We think of Chapter 6 as a primer for engineers wishing to use the lumped parameter model to design quiet structures via material tailoring. While material tailoring is employed extensively for designing structures for minimum vibration response, few examples are available in the literature where the acoustic response of a structure is minimized. Chapter 6 lays out a strategy for doing so defining the objective function, i.e., the design variable to be minimized, as the radiated sound power. Search routines for optimal searches require sensitivity analyses. We present this in outline form to show the various steps required for its computation. Initially, the quasi-analytical examples we have chosen to illustrate the fundamentals of the design strategy appear (deceptively) quite simple. However, it soon becomes evident that, even for these single variable problems a degree of complexity exists that challenges the level of an introductory text. Chapter 6 thus can be considered as a first step in demonstrating the efficacy of the material tailoring method. A comprehensive treatment of the sound-power-based, material-tailoring design method has yet to be developed. It will rely heavily on the availability of efficient numerical programs that combine advanced structural and acoustic models in a manner compatible with search routines found in advanced optimization programs.

In Chapter 7 we show how the design method is extended to include active control strategies for reducing the sound power radiated from structures into open spaces. The strategy is quite straightforward and lends itself nicely to an instructive physical interpretation. Given a computed or measured form of the resistance matrix, the sound power is minimized by treating portions of the surface of a structure as control surfaces. These are...