| Description |
1 online resource (xiii, 257 pages) : illustrations (some color) |
| Series |
Foundations of engineering mechanics |
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Foundations of engineering mechanics.
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| Contents |
Preface; References#x82;1.#x80; Cauchy, A. (1847). Methode generale pour la resolution des systemes d'equations simultanees. Comptes rendus de l'Académie des sciences. Tome 25 (p. 536-538).#x82;2. Fletcher, C.A.J. (1984). Computational Galerkin methods (p. 310). Berlin: Springer.#x82;3. Galerkin, B.G. (1915). Rods and plates (Vol. 1, No. 19, pp. 897-908 (in Russian)). Series in some issues of the elastic equilibrium of rods and plates, Herald of engineers.#x82;4. Kantorovich, L.V. (1948). Functional analysis and applie; Contents; Summary; Equations and Methods |
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1 Oscillation Equations of a Rod with Rectilinear Axis1.1 Differential Equations of Longitudinal Vibrations of a Rod; 1.2 Differential Equations of Longitudinal Vibrations of a Rod in the Operator Form; 1.3 Differential Equations of Torsional Vibrations; 1.4 Differential Equations of Transverse Vibrations of a Rectilinear Rod; 1.5 Differential Equations of Transverse Vibrations of a Rod in the Operator Form; 1.6 Joint Longitudinal, Torsional and Transverse Vibrations of a Rod; 1.7 Differential Equations in Displacements and Forces |
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1.8 Integral Equations of Longitudinal and Torsional Vibrations1.9 Integral Equations of Transverse Vibrations of a Rod; 1.10 Equations in Displacements with Integral Operators; 1.11 Converting the Equations with Differential and Integral Operators to the Classical Form; 1.12 Integral Equations of Harmonic Oscillations for an Unattached Elastic Body; References; 2 Vibrations of a Three-Dimensional Body, Plate and Ring; 2.1 Equations of Three-Dimensional Body Vibrations; 2.2 Equations of Plate Vibrations; 2.3 Equations of Ring Vibrations; References; 3 Spectral Theory |
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3.1 Forms and Frequencies of Free Oscillations3.2 Representation of the Amplitude of Forced Harmonic Vibrations as a Series in the Forms of Free Oscillations; 3.3 Bringing Equations to the Classical Form; 3.4 Stationary (Periodic) and Nonstationary Elastic Vibrations; 3.5 Oscillations with the Initial Conditions Given; 3.6 Periodic Oscillations; 3.7 Oscillations of a Rod Under the Action of Concentrated Force; 3.8 Iterative Method for Determination of the First Form and Frequency of Free Elastic Oscillations; 3.9 Determination of Higher Forms and Frequencies of Free Oscillations; References |
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4 Variational and Projection Methods for Solving Vibration Theory Equations4.1 Variational Principle in the Problem of Forced Harmonic Vibrations for the Displacement Equation; 4.2 Variational Principle in the Problem of Free Harmonic Vibrations for the Equation on Displacements Using a Differential Operator; 4.3 Extreme Variational Principle in the Problem of Forced Harmonic Oscillations; 4.4 Mixed Variational Principle in the Problem of Forced Harmonic Oscillations (Principle of Reissner) |
| Summary |
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. |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed July 27, 2017) |
| Subject |
Oscillations -- Mathematics
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Elasticity -- Mathematics
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Mechanics -- Solids.
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Elasticity -- Mathematics
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Oscillations -- Mathematics
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| Form |
Electronic book
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| Author |
Sviyazheninov, Eugene, translator
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| ISBN |
9789811047862 |
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9811047863 |
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