Theory of Elastic Oscillations
Equations and Methods
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Beschreibung
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.
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 stat
ionary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications.Offers an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems Includes the variational, projection, and iterative gradient methods Provides examples of solutions for selected applications Includes supplementary material: sn.pub/extras
Autor*in
Vladimir Fridman
Themen in »Theory of Elastic Oscillations«
Elastic Distributed Parameter Systems Longitudinal Vibrations of a Rod Torsional Vibrations Mixed Boundary Conditions Newton-Kantorovich Method Bending Vibrations Lubrication