Theory of Elastic Oscillations Equations and Methods - Fridman, Vladimir; SpringerLink (Online service) (Singapore : Springer Nature Singapore : Imprint: Springer, 2018)
This book presents in detail an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems. It includes the so-called variational, projection and iterative gradient methods, which, when applied to nonlinear problems, use the procedure of linearization of the original non-linear equations. These methods are not universal and require a different solution for each problem or class of problems.However, in many cases the combination of the methods shown in this book leads to more efficient algorithms for solving important applied problems.To record these algorithms in a unified form, the first part of the book and its appendix devote considerable attention to compiling the general operator equations, which include (as particular cases) equations for vibrations in rods, plates, shells and three-dimensional bodies. They are mainly considered to be periodic or nearly periodic oscillations, which correspond to stationaryor nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications. .
Part 1. Equations and Methods: Oscillation Equations of a Rod with Rectilinear Axis -- Vibrations of Three-Dimensional Body, Plate and Ring -- Spectral Theory -- Variational and Projection Methods for  Solving the Vibration Theory Equations -- Harmonic Analysis -- Discontinuous Functions. Complicated Boundary Conditions -- Exact Solutions of Equations of Oscillation Theory -- Nonlinear Periodic Oscillations.- Part 2. Some Applied Problems: Determination of Elastic-Damping Characteristics of Slide Bearings -- Vibrations of Shafts, Blades and Disks -- Stability of The Equilibrium Position of Rotating Shaft Axis -- Vibrations of Internal Combustion Engine.
Keywords: Multibody systems; Vibration; Mechanics, Applied; Mathematics -- Data processing; Solids; Multibody Systems and Mechanical Vibrations; Computational Science and Engineering; Solid Mechanics