Vibrations

This book aims at a monographic presentation of mechanical vibrations and the methods of their description and calculation. A comprehensive and fairly complete presentation of linear vibrations in discrete systems is followed by qualitative and quantitative investigations of non-linear vibrations of systems with one and several degrees of freedom. An extensive description of vibrations of continuous engineering systems, i.e., shells, plates, membranes, beams, bars, is presented in Part III. Vibrations of torsional-flexural systems and rotating shafts are also discussed. The presentation of self-excited, parametrically excited, non-autonomous vibrations and vibrations in inhomogeneous systems is unique. The approximate methods applied in continuum systems explain the origin of the equations considered in Parts I and II. The method of finite element makes it possible to calculate vibrations of very complicated systems, for example of aircraft. In the book the concept of natural (principal) vibrations consistently integrates the methods of solving discrete and continuous systems. Part IV presents the physical theories explaining the substantiation of continuum models. The special phenomena which cannot be explained by the continuum theories are discussed by making use of the simple models of the theory of crystals. The last part of the book is devoted to a probabilistic description of vibrations. The reader will also find in it a comprehensive introduction to the probability and random phenomena. The book provides the reader with knowledge useful in studying wave phenomena which have been described in "Waves" (Elsevier, 1992). Owing to the authors' considerable teaching experience the most important patterns are explained in a particularly lucid way. The book will be of interest to scientists, to civil and mechanical engineers, and even to graduate students interested in vibrations.