Modal Analysis


This book provides a detailed treatment of the theory of analytical and experimental

modal analysis with applications. It is intended for several uses. The materials can be

selectively used for undergraduate and postgraduate courses. The book can be a

reference text for practising engineers whose work involves modal analysis, and for

researchers in other engineering and science disciplines who use modal analysis as a

tool in their research.





Preface


Though appearing to be specialized, modal analysis has been used in the last two

to three decades in many engineering disciplines and technology fields to solve

increasingly demanding structural dynamic problems. The path of modal analysis

being incorporated into university teaching is paralleled with that taken by finite

element analysis. Currently, the published literature in modal analysis is sparse without

taking on board conference and journal papers. This is not conducive to users of this

technology.

Chapter 1 of this book begins with a brief introduction to the current status of

modal analysis in engineering fields and the practical background which gave rise to

modal analysis as an effective and an advancing technology. This is followed by a

concise clarification of modal analysis and modal testing, and the theoretical framework

for modal analysis. It is succeeded by an outline of applications of modal analysis in

dealing with different types of engineering problems and practical challenges. This

chapter closes on a summary note on the historical development of modal analysis.

Chapter 2 reviews the mathematics tools used in the theory of modal analysis. In

matrix theory, these include matrix inversion, linear simultaneous equations, eigenvalue

problems, different decomposition of a real symmetrical matrix, matrix perturbation

and the derivative of matrices. In addition, this chapter introduces poles and zeros of

a polynomial function, Fourier series and transform, and the variable separation

method for partial differential equations. These mathematics tools will be used in the

following chapters of the book.

Chapter 3 reviews the basic vibration theory which forms the basis of modal

analysis theory. This chapter is an epitome of a textbook for mechanical vibrations or

dynamics of machines. It intends to review relevant materials rather than to offer a

comprehensive coverage of vibration theory. This is to facilitate a more thorough and

smooth excursion in modal analysis theory.

Chapters 4, 5 and 6 constitute the theoretical basis of modal analysis. In Chapter

4, modal analysis theory for an SDoF system is presented. It begins with the frequency

response function (FRF) of an SDoF system, its concept and its different forms and

various formats on which the FRF can be studied. This is followed by an in-depth



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