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Share Embed Donate. All Rights Reserved This book or any part thereof may not be reproduced in any form without written permission from the publisher,, First Published. The book deals with mechanics of materials, which tells us about how objects withstand strain and stress and rely upon geometrical and physical considerations of deformations. The study of the strength of materials sometimes refers to different methods used to calculate stresses in structures like a column, shaft or a beam.
A newer set of examples and problems have replaced the older ones, along with answers to all the problems. The reason is the electronic devices divert your attention and also cause strains while reading eBooks. Tension, Compression, and Shear: I 2.
Tension, Compression, and Shear: II 3. In this paper, a boundary element method is developed for the general flexural—torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation.
The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae.
All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. A number of examples and problems with solutions or with answers were included, and in many places new material was added.
The principal additions are as follows In the first chapter a discussion of forced vibration with damping not proportional to velocity is included, and an article on self-excited vibration.
In the chapter on non-linear sys tems an article on the method of successive approximations is added and it is shown how the method can be used in discussing free and forced vibrations of systems with non-linear characteristics. The third chapter is made more complete by including in it a general discussion of the equation of vibratory motion of systems with variable spring characteristics.
The fourth chapter, dealing with systems having several degrees of freedom, is also Considerably enlarged by adding a general discussion of systems with viscous damping an article on stability of motion with an application in studying vibration of a governor of a steam engine an article on whirling of a rotating shaft due to hysteresis and an article on the theory of damp ing vibration absorbers.
There are also several additions in the chapter on torsional and lateral vibrations of shafts. The author takes this opportunity to thank his friends who assisted in various ways in the preparation of the manuscript and particularly Professor L. Jacobsen, who read over the complete manuscript and made many valuable suggestions, and Dr. The principal additions are as follows : In the first chapter a discussion of forced vibration with damping not proportional to velocity is included, and an article on self-excited vibration.
In the chapter on non-linear sys- tems an article on the method of successive approximations is added and it is shown how the method can be used in discussing free and forced vibra- tions of systems with non-linear characteristics. The third chapter is made more complete by including in it a general discussion of the equation of vibratory motion of systems with variable spring characteristics.
The fourth chapter, dealing with systems having several degrees of freedom, is also Considerably enlarged by adding a general discussion of systems with viscous damping; an article on stability of motion with an application in studying vibration of a governor of a steam engine; an article on whirling of a rotating shaft due to hysteresis; and an article on the theory of damp- ing vibration absorbers.
There are also several additions in the chapter on torsional and lateral vibrations of shafts. Jacobsen, who read over the complete manuscript and made many valuable suggestions, and Dr. Wojtaszak, who checked prob- lems of the first chapter. It is well known that problems of great practical significance, such as the balancing of machines, the torsional vibration of shafts and of geared systems, the vibrations of turbine blades and turbine discs, the whirling of rotating shafts, the vibrations of railway track and bridges under the action of rolling loads, the vibration of foundations, can be thoroughly understood only on the basis of the theory of vibration.
Only by using this theory can the most favorable design proportions be found which will remove the working conditions of the machine as far as possible from the critical conditions at which heavy vibrations may occur. In the present book, the fundamentals of the theory of vibration are developed, and their application to the solution of technical problems is illustrated by various examples, taken, in many cases, from actual experience with vibration of machines and structures in service.
In developing this book, the author has followed the lectures on vibration given by him to the mechanical engineers of the Westinghouse Electric and Manufacturing Company during the year , and also certain chapters of his previously published book on the theory of elasticity. The general theory of free and forced vibration is discussed, and the application of this theory to balancing machines and vibration-recording instruments is shown.
The Rayleigh approximate method of investigating vibrations of more com- plicated systems is also discussed, and is applied to the calculation of the whirling speeds of rotating shafts of variable cross-section. Chapter two contains the theory of the non-harmonic vibration of sys- tems with one degree of freedom.
The approximate methods for investi- gating the free and forced vibrations of such systems are discussed. A particular case in which the flexibility of the system varies with the time is considered in detail, and the results of this theory are applied to the inves- tigation of vibrations in electric locomotives with side-rod drive.
II St. Petersburg, Russia. The general theory of vibration of such systems is developed, and also its application in the solution of such engineering problems as: the vibration of vehicles, the torsional vibration of shafts, whirling speeds of shafts on several supports, and vibration absorbers.
Chapter four contains the theory of vibration of elastic bodies. The problems considered are : the longitudinal, torsional, and lateral vibrations of prismatical bars; the vibration of bars of variable cross-section; the vibrations of bridges, turbine blades, and ship hulls; the theory of vibra- tion of circular rings, membranes, plates, and turbine discs. Brief descriptions of the most important vibration-recording instru- ments which are of use in the experimental investigation of vibration are given in the appendix.
The author owes a very large debt of gratitude to the management of the Westinghouse Electric and Manufacturing Company, which company made it possible for him to spend a considerable amount of time in the preparation of the manuscript and to use as examples various actual cases of vibration in machines which were investigated by the company's engineers. He takes this opportunity to thank, also, the numerous friends who have assisted him in various ways in the preparation of the manuscript, particularly Messr.
Lessells, J. Ormondroyd, and J. Den Hartog, who have read over the complete manuscript and have made many valuable suggestions. He is indebted, also, to Mr. Wilharm for the preparation of draw- ings, and to the Van Nostrand Company for their care in the publication oi the book.
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