Svetlitsky V.A., Lidvansky A.S., Mukhamedshin R.A. Engineering Vibration Analysis: Worked Problems 1

Translated by G.I. Merzon and V.A. Chechin. — Springer-Verlag Berlin Heidelberg, 2004. X, 319 p. — ISBN: 978-3-642-05842-4, ISBN: 978-3-540-40970-0 (eBook).Theory of vibrations belongs to principal subjects needed for training mechanical engineers in technological universities. Therefore, the basic goal of the monograph "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 systems with a finite number of degrees of freedom. In particular, problems are formulated associated with determination of frequencies and forms of vibrations, study of forced vibrations, analysis of both stable and unstable vibrations (including 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 dynamic 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. Allowing for interests of students independently studying theory of vibrations, the majority of problems are supplied with either detailed solutions or algorithms of the solutions.Problems and Examples
Answers and solutions
Statics of rods: basic equations
Basic equations of rod kinematics
Basic equations of rod dynamics
Exact numerical method of determining the frequencies and modes of rod vibrations
Approximate numerical determination of frequencies at small vibrations of rods
Approximate solution of equation of rod forced vibrations.