Theory of Elastic Oscillations : Equations and Methods

Description

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 stationary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications. . Read more... Abstract: 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 stationary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications Front Matter....Pages i-xiii Front Matter....Pages 1-1 Oscillation Equations of a Rod with Rectilinear Axis....Pages 3-39 Vibrations of a Three-Dimensional Body, Plate and Ring....Pages 41-52 Spectral Theory....Pages 53-77 Variational and Projection Methods for Solving Vibration Theory Equations....Pages 79-108 Harmonic Analysis....Pages 109-122 Discontinuous Functions. Complicated Boundary Conditions....Pages 123-139 Exact Solutions of Equations of Oscillation Theory....Pages 141-178 Nonlinear Periodic Oscillations....Pages 179-189 Front Matter....Pages 191-191 Determination of Elastic Damping Characteristics of Slide Bearings....Pages 193-208 Vibrations of Shafts, Blades and Disks....Pages 209-228 Stability of the Equilibrium Position of a Rotating Shaft Axis....Pages 229-237 Vibrations of an Internal Combustion Engine....Pages 239-247 Back Matter....Pages 249-257