Selected topics in vibrational mechanics [electronic resource] / edited by Ilya Blekhman ; contributing authors, I.I. Blekhman [and others].

Cover image for Selected topics in vibrational mechanics [electronic resource] / edited by Ilya Blekhman ; contributing authors, I.I. Blekhman [and others].

ISBN:

9789812794529

Title:

Selected topics in vibrational mechanics [electronic resource] / edited by Ilya Blekhman ; contributing authors, I.I. Blekhman [and others].

Author:

Blekhman, I. I. (Ilʹi͡a Izrailevich)

Publication Information:

Physical Description:

1 online resource (xxi, 409 pages) : illustrations.

Series:

Series on stability, vibration, and control of systems. Series A ; v. 11

Contents:

Foreword; Preface; Contents; Part I. The Basis of Vibrational Mechanics; Chapter 1. On Some Nonlinear Oscillatory Effects. The Main Idea of Vibrational Mechanics; 1.1 On the Effects Caused by the Action of Vibration in Nonlinear Oscillatory Systems; 1.2 The Main Idea of Vibrational Mechanics. Observer O and Observer V; Chapter 2. The Main Mathematical Apparatus of Vibrational Mechanics and of the Method of Direct Separation of Motions; 2.1 Preliminary Remarks; 2.2 The Initial Equation and Its Reduction to a System of Integro-differential Equations.

2.3 The Case When a Separate Equation for the Slow Component is Obtained2.4 The Main Assumption of Vibrational Mechanics Its Formalization and Conditions of its Fulfillment; 2.5 The Main Equation of Vibrational Mechanics. Vibrational Forces Observers O and V; 2.6 Method of an Approximate Derivation of the Expression of Vibrational Forces and of Composing the Main Equation of Vibrational Mechanics; 2.10 Additional Remarks Certain Generalizations; 2.7 Important Special Case; 2.8 On the Case of a Mechanical Systems with Constraints.

2.9 On the Simplifications of Solving Equations for the Fast Component of Motion. Purely Inertial Approximation2.11 Summary: On the Procedure of the Practical Use of the Method; Chapter 3. On Other Methods of Obtaining Expressions for the Vibrational Forces and the Main Equations of Vibrational Mechanics; 3.1 Well Known Methods; 3.2 Two Other Methods; Chapter 4. A Simplest Example: Solving the Problem about a Pendulum with a Vibrating Axis of Suspension by Different Methods of the Theory of Nonlinear Oscillations; 4.1 Preliminary Remarks; 4.2 Equation of Motion.

4.3 The Poincare-Lyapunov Method of Small Parameter4.4 The Use of Floquet-Lyapunov's Theory and of Ince-Strutt's Diagram; 4.5 Asymptotic Method; 4.6 Method of Multiple Scales; 4.7 Methods of Harmonic Balance and of Bubnov-Galerkin; 4.8 Method of Direct Separation of Motions; 4.9 Discussion; Chapter 5. Conclusion: On the Main Peculiarities and Advantages of the Approaches of Vibrational Mechanics and of the Method of Direct Separation of Motions as Compared to Other Methods of Nonlinear Mechanics; 5.1 Peculiarities and Limitations; 5.2 Advantages; 5.3 Final Remarks; References to Part 1.

Part II. Pendulum and Pendulum Systems under High-Frequency Excitation -- Non-Trivial EffectsChapter 6. Quasi-equilibrium Positions and Stationary Rotations of the Pendulums with a Periodically Vibrating Axis; 6.1 Preliminary Remarks Equation of Motion; 6.2 Regimes of Quasi-Equilibrium; 6.3 Regimes of Rotation; References; Chapter 7. Non-Trivial Effects of High-Frequency Excitation for Pendulum Systems; 7.1 Preliminary Remarks; 7.2 Chelomei's Pendulum -- Resolving a Paradox; 7.3 Nonlinear Dynamics of the Follower-Loaded Double Pendulum with Added Support-Excitation.

Local Note:

eBooks on EBSCOhost

Subject Term:

Vibration.

Mechanics, Analytic.

Added Author:

Blekhman, I. I. (Ilʹi͡a Izrailevich)

Format:

Electronic Resources

Electronic Access:

Click here to view

Publication Date:

2004

Publication Information:

Available:*

Shelf Number	Material Type	Copy	Shelf Location	Status
620.3 22	1:E-BOOK	1	1:ONLINE	Searching... Unknown

Bound With These Titles

On Order

Summary

Vibrational mechanics is a new, intensively developing section of nonlinear dynamics and of the theory of nonlinear oscillations. It presents a general approach to the study of the effects of vibration on nonlinear systems. This approach is characterized by simplicity of application and by physical clearness.In recent years a number of new, essential results have been obtained both on the development of the mathematical apparatus of vibrational mechanics and on the solution of certain applied problems. This book reflects those results through the ingenious presentation of the authors -- well-known scientists from Germany, Denmark and Russia. For the convenience of readers, the main content is preceded by a brief description of the main theses of vibrational mechanics.