The theory of random processes is an integral part of the analysis and synthesis of complex engineering systems. This textbook systematically presents the fundamentals of statistical dynamics and reliability theory. The theory of Markovian processes used during the analysis of random dynamic processes in mechanical systems is described in detail. Examples are machines, instruments and structures loaded with perturbations. The reliability and lifetime of those objects depend on how properly these perturbations are taken into account. Random vibrations with finite and infinite numbers of degrees of freedom are analyzed as well as the theory and numerical methods of non-stationary processes under the conditions of statistical indeterminacy. This textbook is addressed to students and post-graduates of technical universities. It can also be useful to lecturers and mechanical engineers, including designers in different industries.

The volume is devoted to the dynamics of rods, which is a branch of mech- ics of deformable bodies. The main goal of the book is to present systema- cally theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Linear and nonlinear equations governing a rod's oscillations are p- sented. Methods of determining eigenvalues and eigenfunctions in conser- tive and non-conservative problems along with numerical methods dealing with forced, parametric, and random oscillations of rods are given. Some - sues of interaction of rods with air (liquid) flows and the dynamics of spa- curved rods containing flows of liquid are considered. The book consists of nine chapters and appendices and may be conv- tionally divided into two parts. That is, Chapters 1 to 6 contain, in the main, theoretical material, whereas Chapters 7 to 9 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 3, 5, and 7. The solutions to most of the problems are given in Appendix B. The monograph is addressed to undergraduate and postgraduate students and teaching staff of technical universities. It may also be useful for scientists and mechanical engineers working in a wide range of industries. I wish to express my deep appreciation to my colleagues, Dr. S.A. Voronov and C.B. Danilenko, for their help in preparing the manuscript.

Constantly increasing attention is paid in the course 'Vibration 'Theory' to vibration of mechanical systems with distributed parameters, since the real elements of machines, devices, and constructions are made of materials that are not perfectly rigid. 'Therefore, vibrations of the objects including, for ex ample, rod elastic elements excite the vibrations of these elements, which can produce a substantial effect on dynamic characteristics of moving objects and on readings of instruments. For a mechanical engineer working in the field of design of new technolo gies the principal thing is his know-how in developing the sophisticated math ematical models in which all specific features of operation of the objects under design in real conditions are meticulously taken into account. So, the main emphasis in this book is made on the methods of derivation of equations and on the algorithms of solving them (exactly or approximately) taking into con sideration all features of actual behavior of the forces acting upon elastic rod elements. 'The eigen value and eigen vector problems are considered at vibrations of curvilinear rods (including the rods with concentrated masses). Also consid ered are the problems with forced vibrations. When investigating into these problems an approximate method of numerical solution of the systems of lin ear differential equations in partial derivatives is described, which uses the principle of virtual displacements. Some problems are more complicated than others and can be used for practical works of students and their graduation theses."

Theory of vibrations belongs to principal subjects needed for training mechani cal engineers in technological universities. Therefore, the basic goal of the mono graph "Advanced Theory of Vibrations 1" is to help students studying vibration theory for gaining experience in application of this theory for solving particular problems. Thus, while choosing the problems and methods to solve them, the close attention was paid to the applied content of vibration theory. The monograph is devoted to systems with a single degree of freedom and sys tems with a finite number of degrees of freedom. In particular, problems are for mulated associated with determination of frequencies and forms of vibrations, study of forced vibrations, analysis of both stable and unstable vibrations (includ ing those caused by periodic but anharmonic forces). The problems of nonlinear vibrations and of vibration stability, and those related to seeking probabilistic characteristics for solutions to these problems in the case of random forces are also considered. Problems related to parametric vibrations and statistical dynamics of mechanical systems, as well as to determination of critical parameters and of dy namic stability are also analyzed. As a rule, problems presented in the monograph are associated with particular mechanical systems and can be applied for current studies in vibration theory. Al lowing for interests of students independently studying theory of vibrations, the majority of problems are supplied with either detailed solutions or algorithms of the solutions."

The monograph text is based on lectures delivered by author during many years for students of Applied Iechanics Department of Bauman Ioscow State Technical University. The monograph includes also analitical results of scientific research obtained in collaboration with industry. Progress in developing new equipment has called for a better understand ing of the physical peculiarities pertaining to the action of designed structures in real conditions. This is necessary for increasing the accuracy of the analysis and making these structures more reliable. It has been found that classical determined perturbations are not principal and that determinism-based methods of classical mechanics prove insufficient for understanding and explaining physical effects that arise at the operation of instruments located on moving objects, the vibration of rocket engines, the motion of a vehicle, and the action of wind and seismic loads. Therefore the necessity arose for devising a new physical model to analyze these dynamic processes and, in particular, for creating a new mathematical apparatus that would allow us to take into account non-deterministic external excitations. The theory of random processes that had been developed well enough as applied to problems of radio engineering and automatic control, where the effect produced by random excitations appeared to be commensurable with that of deterministic excitations and where the ignoring of the random ex citations would bring about incorrect results, became such an apparatus."

This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.

Constantly increasing attention is paid in the course 'Vibration 'Theory' to vibration of mechanical systems with distributed parameters, since the real elements of machines, devices, and constructions are made of materials that are not perfectly rigid. 'Therefore, vibrations of the objects including, for ex ample, rod elastic elements excite the vibrations of these elements, which can produce a substantial effect on dynamic characteristics of moving objects and on readings of instruments. For a mechanical engineer working in the field of design of new technolo gies the principal thing is his know-how in developing the sophisticated math ematical models in which all specific features of operation of the objects under design in real conditions are meticulously taken into account. So, the main emphasis in this book is made on the methods of derivation of equations and on the algorithms of solving them (exactly or approximately) taking into con sideration all features of actual behavior of the forces acting upon elastic rod elements. 'The eigen value and eigen vector problems are considered at vibrations of curvilinear rods (including the rods with concentrated masses). Also consid ered are the problems with forced vibrations. When investigating into these problems an approximate method of numerical solution of the systems of lin ear differential equations in partial derivatives is described, which uses the principle of virtual displacements. Some problems are more complicated than others and can be used for practical works of students and their graduation theses."

Theory of vibrations belongs to principal subjects needed for training mechani cal engineers in technological universities. Therefore, the basic goal of the mono graph "Advanced Theory of Vibrations 1" is to help students studying vibration theory for gaining experience in application of this theory for solving particular problems. Thus, while choosing the problems and methods to solve them, the close attention was paid to the applied content of vibration theory. The monograph is devoted to systems with a single degree of freedom and sys tems with a finite number of degrees of freedom. In particular, problems are for mulated associated with determination of frequencies and forms of vibrations, study of forced vibrations, analysis of both stable and unstable vibrations (includ ing those caused by periodic but anharmonic forces). The problems of nonlinear vibrations and of vibration stability, and those related to seeking probabilistic characteristics for solutions to these problems in the case of random forces are also considered. Problems related to parametric vibrations and statistical dynamics of mechanical systems, as well as to determination of critical parameters and of dy namic stability are also analyzed. As a rule, problems presented in the monograph are associated with particular mechanical systems and can be applied for current studies in vibration theory. Al lowing for interests of students independently studying theory of vibrations, the majority of problems are supplied with either detailed solutions or algorithms of the solutions."