Although the prediction of the analysis of the response of rotating machines is of vital importance to many industries, there are few books on the subject. This book is the second edition; the first edition was published in 1990 and reviewed by A. G. Parkinson in 1991 (*Journal of Sound and Vibration*, **147**, 547-548). The second edition is a minor revision to the first. A chapter on simple models of multirotors has been added, different industrial case studies have been considered and a more detailed description of the computer program included. The authors’ target audience for the book are engineers and undergraduate and graduate students, and the authors’ indicate that background knowledge in rigid body mechanics, strength of materials, matrix calculations, differential equations and mechanical vibrations is required. In reality the reader requires a sound knowledge of multi degree of freedom vibration analysis, energy methods and finite element analysis. If the reader has this knowledge then the extra modelling and analysis required for rotating machines is presented in a concise style. However, this style is not one that every reader will find attractive.

Chapter 1 considers the basic elements of rotating systems, namely disks, shafts, bearings, seals and mass unbalance. Throughout the book the equations of motion are derived by an energy approach via Lagrange’s equations. This chapter expresses the strain and kinetic energies for the components very generally, and should really be thought of as a review of requisite knowledge that is required for the subsequent chapters. This is reinforced by Lagrange’s equations appearing on the first page.

Chapter 2 introduces many of the basic phenomena encountered in rotordynamics using a simple two degree of freedom model of a monorotor derived via a Rayleigh-Ritz analysis. Using such a model allows many of the equations to be solved by hand, and gives great insight to many of the important phenomena. Numerical examples are given throughout the chapter to illustrate the phenomena. The Campbell diagram, the unbalance response, the response to asynchronous forcing, and the response to a stationary harmonic force are described. The concepts of forward and backward whirl, critical speeds and rotor instability are introduced and the effect of damping and bearing support asymmetry are highlighted. Chapter 3 then goes through a similar analysis for coaxial multirotors.

The element matrices of a finite element model of a rotating machine are derived in chapter 4. This chapter should be considered as a summary of the elements useful in rotordynamic modelling, as the reader really has to have a background in finite element analysis. This is confirmed by the lack of any description of how the element matrices may be assembled into global matrices. The calculation of natural frequencies, instabilities and rotor response from the matrix equations are then described. A modal reduction method, based on the undamped modes using a symmetrical stiffness matrix is developed. These methods are coded into a computer program that is described in chapter 5. The program is available over the internet, as described in Appendix B, and downloading the software is relatively straightforward. The software is DOS based, which made installation in a Windows 95 environment difficult compared to standard Windows software. The model is entered as an ASCII data file that is then processed to give the natural frequencies (including the Campbell diagram), mode shapes and the response to mass unbalance, asynchronous forces and stationary harmonic forces. Although the software works efficiently, it is a little disappointing that the user interface is not Windows based.

Chapter 6 considers the accuracy issues in the analysis and modelling of rotating machines. There is a good illustration of how the number of modes retained in the model reduction affects the accuracy of the results. The choice of the number of shaft elements, how the disk/shaft interface can change the rotor stiffness and the calculation of the force transmitted through the bearings are addressed. The effect on the natural frequencies of changes in the bearing stiffness are considered, although the derivation of bearing characteristics is only briefly mentioned.

Seven industrial case studies are described in chapter 8. The studies cover a wide range of different machines and the range of analysis described earlier in the book. The inclusion of real studies is to be applauded, however little detail of the modelling process is described. Generally a picture of the rotor is given together with a diagram of the associated finite element mesh. No mention is made of how the detail of the actual system is transferred to the model, and the basis of any approximations are never described. Only limited remarks on the results are given.

Chapter 8 covers transient motion, particularly the run up and run down of a machine. Both the simple two degree of freedom model and more complex examples are given. The effect of the speed of the run up is described. Chapter 9 considers torsional vibration using finite element models, and includes a simple example and an industrial case study. The final chapter introduces miscellaneous topics such as asymmetrical shafts and the influence of axial torque on bending vibration. Equations with periodic coefficients are briefly considered, although few readers will obtain much enlightenment from the very brief introduction to Floquet theory.

This book is a relatively minor revision of the first edition, although some improvements in notation have been made. For example, $\dot{\phi}$ is now used for the time derivative rather than $\phi ^{0}$. However there are still inconsistencies in notation, with vectors emboldened in chapter 2 and with an arrow notation in chapter 3, for example. The material gives a concise description of the analysis of rotating machines, providing the reader has sufficient prerequisite knowledge. Although the industrial case studies are impressive, an opportunity to help the reader through the modelling process has been lost. Despite this, the limited number of books describing the modelling of rotating machines means the book is essential for engineers and graduate students interested in this area.

M. I. FRISWELL