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.
