Matrix computer analysis of structures

Book Reviews chapter on crossed-field backward-wave oscillators, which does show good agreement between the experiments of Anderson and the theory of Sedin. After many years of theory and experiments on traveling wave tubes, the nonlinear theory has become more and more sophisticated with time, but in this book the only direct comparison between theory and experiment that is given is the early work of Cutler, which is not at all encouraging. One reason for the lack of comparison with experiment appears to be that the analyses are always highly idealized. They do not deal with real traveling wave tubes in which there are tapers, severs, usually loss applied non-uniformly to the circuit, and several harmonics propagating at once along it. All these effects could, however, be taken into account relatively easily in the theory. Instead, much of the work described is a treatment of some very difficult cases without showing even for the simpler ones whether the theory is well justified. To the reviewer's knowledge, unpublished work has been done at Varian and at Hughes, among other places, which would indicate that, in fact, these nonlinear theories can give extremely good predictions of experimental results on real traveling wave tubes. In more difficult cases the agreement can be very poor. For instance, the author quotes the experimental work of Ruetz who tapered the last few cavities of a high power cloverleaf circuit traveling wave amplifier and obtained a considerable enhancement in the efficiency. Rowe states that if the taper had been more near the optimum, still greater efficiency could have been obtained. However, in this particular case, small signal theory does not even apply well to the cloverleaf traveling wave tube because of the high C involved. One can hardly expect that the large signal theory described in this book would do any better. The author then goes on to describe his own work on the enhancement of efficiency by the use of a taper; once more, however, this work would be far more interesting if the theoretical predictions had been plotted with the experimental results. This is an extremely useful reference work on the existing nonlinear analyses of microwave tube operation; however, the work should be read with some care because it is

202

not always apparent when the theory is useful, and it is not pointed out where the theory is liable to break down. GORDON S. KINO

Department of Electrical Engineering Stanford University Stanford, California MATRIX COMPUTER ANALYSIS OF STRUCTURES, by Moshe F. Rubinstein. 402 pages, diagrams, 6 X 9 in. Englewood Chffs, N.J., Prentice-Hall, 1966. Price, $17.25. A large number of books have been published on the subject of structural matrix analysis (finite element techniques) in recent years. Unfortunately, too many of them are alike and present little that may be termed original. Rubinstein's book is well written but falls into this category. The force approach (flexibility method) described by Rubinstein is out of date and is an impractical tool in this form. More practical force methods, such as the rank force method and the redundant force method, contain automatic selection of redundancy techniques--the rank technique and the structure cutter technique, respectively. Such techniques remove the need to select redundancies manually which is by no means an easy task, particularly for complex structural configurations. The transformation matrices (b* and b°) which give the basic and redundant load systems are automatically generated, either directly or indirectly, when adopting an automatic selection of redundancy techniques. Analysis by substructures is an important phase of practical structural analysis and, in fact, is used continually in aircraft design. This chapter should prove very useful to practicing engineers. The author references a paper by Archer and Samson on structural idealization but neglects this important phase. The book covers the usual items, such as matrices and determinants, linear equations, basic structural theorems, element flexibility and stiffness matrices, semiautomated force approach and the displacement approach. These are clearly presented. JOHN ROBINSON

Institute of Sound and Vibration Research Southampton University of Southampton, England

Journal of The Franklin Institute