7R8. Mechanical and Structural Vibration: Theory and Applications. - JH Ginsberg (Georgia Inst of Tech, Atlanta GA 30332). Wiley, New York. 2001. 692 pp. ISBN 0-471-12808-2.

Reviewed by WE Seemann (Dept of Mech and Process Eng., Univ of Kaiserslautern, PO 3049, Kaiserslautern, 67653, Germany).

Congratulations to the author for writing this textbook for undergraduate and graduate students. This book may serve as an excellent basis for courses on linear vibration of one-dof systems, discrete systems, and one-dimensional continua. Especially, the introduction to vibrations of beams and continua is different from the approach normally found in textbooks. Therefore, undergraduate students may get an idea of vibrations of beams without having the necessity of solving partial differential equations.

The first chapter gives an introduction into the derivation of the equations of motion for discrete systems. The equations for planar systems are derived by Newton-Euler’s equations. As a second possibility, the Power Balance Method is presented for time-invariant systems. In addition, Lagrange’s Equations are shown in the appendix. The second chapter deals with harmonic functions, free vibration, and with forced vibration to basic excitations like step function or impulse. Chapter 3 treats steady-state response to harmonic excitation. In this chapter, expressions like complex notation, resonance, frequency response, quality factor, structural damping, force transmission, and complex Fourier series for periodic excitations are explained. This leads to the discrete Fourier transform (DFT), the inverse discrete Fourier transform (IDFT), and to the Fast Fourier Transform (FFT). For the solution of transient excitations, the convolution integral and FFT are used. Difficulties arising with FFT like sampling, aliasing, as well as windowing are addressed. The fourth chapter introduces modal analysis and leads to expressions like eigenfrequencies, modes, orthogonality and normalization, modal transformations and modal damping. Both zero eigenvalues and rigid body modes as well as multiple eigenvalues are discussed. Chapter 5 is a short introduction to harmonic excitation of multi-degree-of-freedom systems with an application in vibration absorbers. The next chapter deals with vibrations of bars based on discretization methods so that they can be solved by the methods developed in the previous sections. The Rayleigh ratio is introduced which serves as a basis for several approximation methods. Something normally not found in standard textbooks is a method which allows one to solve problems with time dependent boundary conditions. Chapter 7 is dedicated to the field description for vibrating bars leading to eigenvalue problems with a characteristic equation involving transcendental functions. Also the wave character of the motion is derived. Orthogonality of the modes yields modal analysis and thus steady and transient responses of such systems. The difference between Bernoulli-Euler and Timoshenko beam theory is shown. The following chapter introduces the finite element method. Chapters 9 and 10 show substructuring and the state space formulation. Chapter 11 presents the modal analysis for gyroscopic and circulatory systems in which the matrices are unsymmetric. Therefore, right and left eigenvectors are used for decomposition and questions of dynamic stability are discussed. The last chapter gives an introduction to rotor dynamics covering topics like internal and external damping as well as orthotropic bearings, orthotropic shafts, and gyroscopic effects.

Being aware of many other textbooks dealing with vibration, it was a pleasure to read Mechanical and Structural Vibration, and this reviewer highly recommends the book for instructors and students. The large number of examples and exercises which are given within the text or at the end of each chapter allow the student to check if the theory is understood well. The way modern software like MATLAB and MATHCAD are frequently used to solve the examples makes the book valuable for lecturers and students and is an advantage compared to standard textbooks. Though this reviewer knew all the methods presented in this book, he profited from the didactically excellent way the methods are presented. As it is a book for use in classes, it is not a drawback that topics like nonlinear vibration or vibration of plates and other complicated structures are not treated in this monograph, because otherwise the volume of material covered in the book would be too large and the reader would be lost. On the contrary, someone who wants to find a special topic covered by the book will find it very quickly. In this reviewer’s opinion, only the first chapter could be enhanced in which the equations of motion are derived. For example having Lagrange’s equations in this chapter instead of showing them in an appendix would be better. In addition, the title of Chapter 11 is misleading as not only gyroscopic systems are covered, but also circulatory systems and moving continuous systems. A guideline for a first-level semester course and a senior-level semester course is given on the front inside cover.